project.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Vorwort\n",
    "Musik ist ein wichtiger Bestandteil unserer Identiät und der Persönlichkeit eines jeden Menschens. In der heutigen Zeit sind wir häufig von Musik umgeben und sie spielt auch in unserer Kulter eine zentrale Rolle. Viele Gründe führen dazu, dass sie zentraler Bestandteil der Gesellschaft ist. Unter anderem fördert sie oder erzeugt sie ein Gemeinschaftsgefühl, das sich durch gemeinsames Tanzen und musikalischen Ritualen verstärkt. Gleichzeitig zeigt sie Zusammenhalt: In Chören wird gemeinschaftlich gesungen, ganz gleich, ob in einem Konzertsaal oder im Fußballstadion. Diese Eigenschaften wurden auch zum Beispiel in Ausnahme- und Krisensituationen wie Unterdrückung oder Kriegen genutzt, um ein Identitätsbewusstsein zu förden. Die Musikrichtung Blues entstandt in der aufstrebenden Bewegung gegen die Unterdrückung der afroamerikanischen Bevölkerung in den 1950ern (vgl. Grünewald-Schukalla 2022, S. 20ff.). Schließlich wird mit der Musik auch die persönliche Gefühlslage ausgedrückt, ganz egal, ob sie in einer fröhlichen oder auch traurigen Situation stattfindet.\n",
    "\n",
    "Streamingdienstleister wie Spotify haben die Musikindustrie nachhaltig verändert. Um 2010 polarisierten hauptsächlich illegale Streamingdienste oder illegale Youtube-Downloader im Internet. Währenddessen hatte die Musikindustrie massive Probleme damit, illegales Streaming zu unterbinden. Seit 2011 steht Spotify als legaler Streamingdienst zur Verfügung, der auch kostenlos nutzbar ist und dabei trotzdem den Künstlerinnen und Künstlern Provisionen zukommen lässt. Im Jahr 2017 haben die Musiklabels zum ersten Mal mehr Geld mit Streaming als mit dem Verkauf von CDs verdient. Heutzutage hat Spotify unter den Anbietern von Musikstreamingdiensten einen Marktanteil von $38\\%$ (vgl. Nusca et al. 2019, S. 84ff.). Damit bilden die Spotify-Charts die aktuelle Beliebtheit der Musik gut ab."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1 Importierung benötigter Bibliotheken und des Datensatzes\n",
    "In diesem Kapitel werden zuerst die benötigten Bibliotheken importiert. Anschließend wird der zur Verfügung gestellte Basisdatensatz eingelesen, um mit der Bearbeitung zu beginnen.\n",
    "\n",
    "### 1.1 Laden der Bibliotheken\n",
    "Innerhalb des Datenexplorationsprojektes werden unter anderem die Bibliotheken ```pandas```, ```numpy```, ```seaborn```, ```spotipy```, ```tensorflow```, ```matplotlib``` und ```sklearn``` benötigt. Die verwendeten Bibliotheken und Pakete werden in der folgenden Zelle alle importiert."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import time\n",
    "import random\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "\n",
    "import spotipy\n",
    "from spotipy.oauth2 import SpotifyClientCredentials\n",
    "\n",
    "import tensorflow as tf\n",
    "from tensorflow import keras\n",
    "\n",
    "from sklearn.linear_model import LinearRegression, LogisticRegression, Lasso, LassoCV\n",
    "from sklearn.ensemble import RandomForestRegressor, RandomForestClassifier, GradientBoostingRegressor\n",
    "from sklearn.preprocessing import StandardScaler, RobustScaler\n",
    "from sklearn.model_selection import train_test_split, RandomizedSearchCV\n",
    "from sklearn.metrics import accuracy_score, confusion_matrix, classification_report, mean_squared_error, r2_score, roc_auc_score, roc_curve\n",
    "from sklearn.compose import ColumnTransformer\n",
    "from sklearn.svm import SVR\n",
    "from sklearn.utils import resample\n",
    "\n",
    "from matplotlib import pyplot as plt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.2 Laden des Basis-Datensatzes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 18835 entries, 0 to 18834\n",
      "Data columns (total 15 columns):\n",
      " #   Column            Non-Null Count  Dtype  \n",
      "---  ------            --------------  -----  \n",
      " 0   song_name         18835 non-null  object \n",
      " 1   song_popularity   18835 non-null  int64  \n",
      " 2   song_duration_ms  18835 non-null  int64  \n",
      " 3   acousticness      18835 non-null  float64\n",
      " 4   danceability      18835 non-null  float64\n",
      " 5   energy            18835 non-null  float64\n",
      " 6   instrumentalness  18835 non-null  float64\n",
      " 7   key               18835 non-null  int64  \n",
      " 8   liveness          18835 non-null  float64\n",
      " 9   loudness          18835 non-null  float64\n",
      " 10  audio_mode        18835 non-null  int64  \n",
      " 11  speechiness       18835 non-null  float64\n",
      " 12  tempo             18835 non-null  float64\n",
      " 13  time_signature    18835 non-null  int64  \n",
      " 14  audio_valence     18835 non-null  float64\n",
      "dtypes: float64(9), int64(5), object(1)\n",
      "memory usage: 2.2+ MB\n"
     ]
    }
   ],
   "source": [
    "base_data = pd.read_csv(\"song_data.csv\")\n",
    "base_data.info()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Der Basisdatensatz besteht aus 18.835 Einträgen mit je 15 Attributen. Der Datensatz besitzt keine Lücken bzw. keine Null-Werte, sodass alle Zellen ausgefüllt sind. Von den 15 Attributen liegen neun als float64, fünf als int64 und eins als Object vor. Das \"Object\"-Attribut ist der Bezeichnung entsprechend der Name des Songs, die einzige Textzelle im Datensatz."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th>song_name</th>\n",
       "      <th>song_popularity</th>\n",
       "      <th>song_duration_ms</th>\n",
       "      <th>acousticness</th>\n",
       "      <th>danceability</th>\n",
       "      <th>energy</th>\n",
       "      <th>instrumentalness</th>\n",
       "      <th>key</th>\n",
       "      <th>liveness</th>\n",
       "      <th>loudness</th>\n",
       "      <th>audio_mode</th>\n",
       "      <th>speechiness</th>\n",
       "      <th>tempo</th>\n",
       "      <th>time_signature</th>\n",
       "      <th>audio_valence</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Boulevard of Broken Dreams</td>\n",
       "      <td>73</td>\n",
       "      <td>262333</td>\n",
       "      <td>0.005520</td>\n",
       "      <td>0.496</td>\n",
       "      <td>0.682</td>\n",
       "      <td>0.000029</td>\n",
       "      <td>8</td>\n",
       "      <td>0.0589</td>\n",
       "      <td>-4.095</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0294</td>\n",
       "      <td>167.060</td>\n",
       "      <td>4</td>\n",
       "      <td>0.474</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>In The End</td>\n",
       "      <td>66</td>\n",
       "      <td>216933</td>\n",
       "      <td>0.010300</td>\n",
       "      <td>0.542</td>\n",
       "      <td>0.853</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>3</td>\n",
       "      <td>0.1080</td>\n",
       "      <td>-6.407</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0498</td>\n",
       "      <td>105.256</td>\n",
       "      <td>4</td>\n",
       "      <td>0.370</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Seven Nation Army</td>\n",
       "      <td>76</td>\n",
       "      <td>231733</td>\n",
       "      <td>0.008170</td>\n",
       "      <td>0.737</td>\n",
       "      <td>0.463</td>\n",
       "      <td>0.447000</td>\n",
       "      <td>0</td>\n",
       "      <td>0.2550</td>\n",
       "      <td>-7.828</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0792</td>\n",
       "      <td>123.881</td>\n",
       "      <td>4</td>\n",
       "      <td>0.324</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>By The Way</td>\n",
       "      <td>74</td>\n",
       "      <td>216933</td>\n",
       "      <td>0.026400</td>\n",
       "      <td>0.451</td>\n",
       "      <td>0.970</td>\n",
       "      <td>0.003550</td>\n",
       "      <td>0</td>\n",
       "      <td>0.1020</td>\n",
       "      <td>-4.938</td>\n",
       "      <td>1</td>\n",
       "      <td>0.1070</td>\n",
       "      <td>122.444</td>\n",
       "      <td>4</td>\n",
       "      <td>0.198</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>How You Remind Me</td>\n",
       "      <td>56</td>\n",
       "      <td>223826</td>\n",
       "      <td>0.000954</td>\n",
       "      <td>0.447</td>\n",
       "      <td>0.766</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>10</td>\n",
       "      <td>0.1130</td>\n",
       "      <td>-5.065</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0313</td>\n",
       "      <td>172.011</td>\n",
       "      <td>4</td>\n",
       "      <td>0.574</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      "text/plain": [
       "                    song_name  song_popularity  song_duration_ms  \\\n",
       "0  Boulevard of Broken Dreams               73            262333   \n",
       "1                  In The End               66            216933   \n",
       "2           Seven Nation Army               76            231733   \n",
       "3                  By The Way               74            216933   \n",
       "4           How You Remind Me               56            223826   \n",
       "\n",
       "   acousticness  danceability  energy  instrumentalness  key  liveness  \\\n",
       "0      0.005520         0.496   0.682          0.000029    8    0.0589   \n",
       "1      0.010300         0.542   0.853          0.000000    3    0.1080   \n",
       "2      0.008170         0.737   0.463          0.447000    0    0.2550   \n",
       "3      0.026400         0.451   0.970          0.003550    0    0.1020   \n",
       "4      0.000954         0.447   0.766          0.000000   10    0.1130   \n",
       "\n",
       "   loudness  audio_mode  speechiness    tempo  time_signature  audio_valence  \n",
       "0    -4.095           1       0.0294  167.060               4          0.474  \n",
       "1    -6.407           0       0.0498  105.256               4          0.370  \n",
       "2    -7.828           1       0.0792  123.881               4          0.324  \n",
       "3    -4.938           1       0.1070  122.444               4          0.198  \n",
       "4    -5.065           1       0.0313  172.011               4          0.574  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "base_data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2 Übersicht und Interpretation der Datenwerte\n",
    "In diesem Kapitel geht es darum, die grundlegenden Eigenschaften der Datenwerte und ihre zulässigen Wertebereiche zu ermitteln. Zunächst soll festgestellt werden, welchem Skalenniveau welcher Datenwert zugeordnet werden kann."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "audio_mode              2\n",
       "time_signature          5\n",
       "key                    12\n",
       "song_popularity       101\n",
       "danceability          849\n",
       "energy               1132\n",
       "speechiness          1224\n",
       "audio_valence        1246\n",
       "liveness             1425\n",
       "acousticness         3209\n",
       "instrumentalness     3925\n",
       "loudness             8416\n",
       "song_duration_ms    11771\n",
       "tempo               12112\n",
       "song_name           13070\n",
       "dtype: int64"
      ]
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     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "base_data.nunique().sort_values()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Über die Anzahl einzigartiger Werte eines Feldes ist ersichtlich, dass kategorische Werte ```audio_mode```, ```time_signature``` und ```key```, wobei ```audio_mode``` sogar binär ist, und alle weiteren Werte numerisch sind.\n",
    "\n",
    "Nachfolgend sind die 20 beliebtesten Lieder dargestellt, um einen ersten Eindruck vom Datensatz zu bekommen. Hierbei ist erkennbar, dass innerhalb der 20 obersten Werte nur zwei Lieder vertreten sind, die mehrfach vorliegen. Der Umgang mit den Redundanzen wird genauer in Kapitel 2.1 aufgegriffen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
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       "      <td>0.0</td>\n",
       "      <td>5</td>\n",
       "      <td>0.167</td>\n",
       "      <td>-2.749</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0452</td>\n",
       "      <td>100.015</td>\n",
       "      <td>4</td>\n",
       "      <td>0.671</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17590</th>\n",
       "      <td>Happier</td>\n",
       "      <td>100</td>\n",
       "      <td>214289</td>\n",
       "      <td>0.1910</td>\n",
       "      <td>0.687</td>\n",
       "      <td>0.792</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5</td>\n",
       "      <td>0.167</td>\n",
       "      <td>-2.749</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0452</td>\n",
       "      <td>100.015</td>\n",
       "      <td>4</td>\n",
       "      <td>0.671</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7636</th>\n",
       "      <td>Happier</td>\n",
       "      <td>100</td>\n",
       "      <td>214289</td>\n",
       "      <td>0.1910</td>\n",
       "      <td>0.687</td>\n",
       "      <td>0.792</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5</td>\n",
       "      <td>0.167</td>\n",
       "      <td>-2.749</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0452</td>\n",
       "      <td>100.015</td>\n",
       "      <td>4</td>\n",
       "      <td>0.671</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17638</th>\n",
       "      <td>Happier</td>\n",
       "      <td>100</td>\n",
       "      <td>214289</td>\n",
       "      <td>0.1910</td>\n",
       "      <td>0.687</td>\n",
       "      <td>0.792</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5</td>\n",
       "      <td>0.167</td>\n",
       "      <td>-2.749</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0452</td>\n",
       "      <td>100.015</td>\n",
       "      <td>4</td>\n",
       "      <td>0.671</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1229</th>\n",
       "      <td>I Love It (&amp; Lil Pump)</td>\n",
       "      <td>99</td>\n",
       "      <td>127946</td>\n",
       "      <td>0.0114</td>\n",
       "      <td>0.901</td>\n",
       "      <td>0.522</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2</td>\n",
       "      <td>0.259</td>\n",
       "      <td>-8.304</td>\n",
       "      <td>1</td>\n",
       "      <td>0.3300</td>\n",
       "      <td>104.053</td>\n",
       "      <td>4</td>\n",
       "      <td>0.329</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11777</th>\n",
       "      <td>I Love It (&amp; Lil Pump)</td>\n",
       "      <td>99</td>\n",
       "      <td>127946</td>\n",
       "      <td>0.0114</td>\n",
       "      <td>0.901</td>\n",
       "      <td>0.522</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2</td>\n",
       "      <td>0.259</td>\n",
       "      <td>-8.304</td>\n",
       "      <td>1</td>\n",
       "      <td>0.3300</td>\n",
       "      <td>104.053</td>\n",
       "      <td>4</td>\n",
       "      <td>0.329</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17113</th>\n",
       "      <td>I Love It (&amp; Lil Pump)</td>\n",
       "      <td>99</td>\n",
       "      <td>127946</td>\n",
       "      <td>0.0114</td>\n",
       "      <td>0.901</td>\n",
       "      <td>0.522</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2</td>\n",
       "      <td>0.259</td>\n",
       "      <td>-8.304</td>\n",
       "      <td>1</td>\n",
       "      <td>0.3300</td>\n",
       "      <td>104.053</td>\n",
       "      <td>4</td>\n",
       "      <td>0.329</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17603</th>\n",
       "      <td>I Love It (&amp; Lil Pump)</td>\n",
       "      <td>99</td>\n",
       "      <td>127946</td>\n",
       "      <td>0.0114</td>\n",
       "      <td>0.901</td>\n",
       "      <td>0.522</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2</td>\n",
       "      <td>0.259</td>\n",
       "      <td>-8.304</td>\n",
       "      <td>1</td>\n",
       "      <td>0.3300</td>\n",
       "      <td>104.053</td>\n",
       "      <td>4</td>\n",
       "      <td>0.329</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4301</th>\n",
       "      <td>I Love It (&amp; Lil Pump)</td>\n",
       "      <td>99</td>\n",
       "      <td>127946</td>\n",
       "      <td>0.0114</td>\n",
       "      <td>0.901</td>\n",
       "      <td>0.522</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2</td>\n",
       "      <td>0.259</td>\n",
       "      <td>-8.304</td>\n",
       "      <td>1</td>\n",
       "      <td>0.3300</td>\n",
       "      <td>104.053</td>\n",
       "      <td>4</td>\n",
       "      <td>0.329</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17660</th>\n",
       "      <td>I Love It (&amp; Lil Pump)</td>\n",
       "      <td>99</td>\n",
       "      <td>127946</td>\n",
       "      <td>0.0114</td>\n",
       "      <td>0.901</td>\n",
       "      <td>0.522</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2</td>\n",
       "      <td>0.259</td>\n",
       "      <td>-8.304</td>\n",
       "      <td>1</td>\n",
       "      <td>0.3300</td>\n",
       "      <td>104.053</td>\n",
       "      <td>4</td>\n",
       "      <td>0.329</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14314</th>\n",
       "      <td>I Love It (&amp; Lil Pump)</td>\n",
       "      <td>99</td>\n",
       "      <td>127946</td>\n",
       "      <td>0.0114</td>\n",
       "      <td>0.901</td>\n",
       "      <td>0.522</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2</td>\n",
       "      <td>0.259</td>\n",
       "      <td>-8.304</td>\n",
       "      <td>1</td>\n",
       "      <td>0.3300</td>\n",
       "      <td>104.053</td>\n",
       "      <td>4</td>\n",
       "      <td>0.329</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5608</th>\n",
       "      <td>I Love It (&amp; Lil Pump)</td>\n",
       "      <td>99</td>\n",
       "      <td>127946</td>\n",
       "      <td>0.0114</td>\n",
       "      <td>0.901</td>\n",
       "      <td>0.522</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2</td>\n",
       "      <td>0.259</td>\n",
       "      <td>-8.304</td>\n",
       "      <td>1</td>\n",
       "      <td>0.3300</td>\n",
       "      <td>104.053</td>\n",
       "      <td>4</td>\n",
       "      <td>0.329</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                    song_name  song_popularity  song_duration_ms  \\\n",
       "7568                  Happier              100            214289   \n",
       "15091                 Happier              100            214289   \n",
       "17392                 Happier              100            214289   \n",
       "14176                 Happier              100            214289   \n",
       "11665                 Happier              100            214289   \n",
       "11697                 Happier              100            214289   \n",
       "5593                  Happier              100            214289   \n",
       "4299                  Happier              100            214289   \n",
       "16497                 Happier              100            214289   \n",
       "17590                 Happier              100            214289   \n",
       "7636                  Happier              100            214289   \n",
       "17638                 Happier              100            214289   \n",
       "1229   I Love It (& Lil Pump)               99            127946   \n",
       "11777  I Love It (& Lil Pump)               99            127946   \n",
       "17113  I Love It (& Lil Pump)               99            127946   \n",
       "17603  I Love It (& Lil Pump)               99            127946   \n",
       "4301   I Love It (& Lil Pump)               99            127946   \n",
       "17660  I Love It (& Lil Pump)               99            127946   \n",
       "14314  I Love It (& Lil Pump)               99            127946   \n",
       "5608   I Love It (& Lil Pump)               99            127946   \n",
       "\n",
       "       acousticness  danceability  energy  instrumentalness  key  liveness  \\\n",
       "7568         0.1910         0.687   0.792               0.0    5     0.167   \n",
       "15091        0.1910         0.687   0.792               0.0    5     0.167   \n",
       "17392        0.1910         0.687   0.792               0.0    5     0.167   \n",
       "14176        0.1910         0.687   0.792               0.0    5     0.167   \n",
       "11665        0.1910         0.687   0.792               0.0    5     0.167   \n",
       "11697        0.1910         0.687   0.792               0.0    5     0.167   \n",
       "5593         0.1910         0.687   0.792               0.0    5     0.167   \n",
       "4299         0.1910         0.687   0.792               0.0    5     0.167   \n",
       "16497        0.1910         0.687   0.792               0.0    5     0.167   \n",
       "17590        0.1910         0.687   0.792               0.0    5     0.167   \n",
       "7636         0.1910         0.687   0.792               0.0    5     0.167   \n",
       "17638        0.1910         0.687   0.792               0.0    5     0.167   \n",
       "1229         0.0114         0.901   0.522               0.0    2     0.259   \n",
       "11777        0.0114         0.901   0.522               0.0    2     0.259   \n",
       "17113        0.0114         0.901   0.522               0.0    2     0.259   \n",
       "17603        0.0114         0.901   0.522               0.0    2     0.259   \n",
       "4301         0.0114         0.901   0.522               0.0    2     0.259   \n",
       "17660        0.0114         0.901   0.522               0.0    2     0.259   \n",
       "14314        0.0114         0.901   0.522               0.0    2     0.259   \n",
       "5608         0.0114         0.901   0.522               0.0    2     0.259   \n",
       "\n",
       "       loudness  audio_mode  speechiness    tempo  time_signature  \\\n",
       "7568     -2.749           1       0.0452  100.015               4   \n",
       "15091    -2.749           1       0.0452  100.015               4   \n",
       "17392    -2.749           1       0.0452  100.015               4   \n",
       "14176    -2.749           1       0.0452  100.015               4   \n",
       "11665    -2.749           1       0.0452  100.015               4   \n",
       "11697    -2.749           1       0.0452  100.015               4   \n",
       "5593     -2.749           1       0.0452  100.015               4   \n",
       "4299     -2.749           1       0.0452  100.015               4   \n",
       "16497    -2.749           1       0.0452  100.015               4   \n",
       "17590    -2.749           1       0.0452  100.015               4   \n",
       "7636     -2.749           1       0.0452  100.015               4   \n",
       "17638    -2.749           1       0.0452  100.015               4   \n",
       "1229     -8.304           1       0.3300  104.053               4   \n",
       "11777    -8.304           1       0.3300  104.053               4   \n",
       "17113    -8.304           1       0.3300  104.053               4   \n",
       "17603    -8.304           1       0.3300  104.053               4   \n",
       "4301     -8.304           1       0.3300  104.053               4   \n",
       "17660    -8.304           1       0.3300  104.053               4   \n",
       "14314    -8.304           1       0.3300  104.053               4   \n",
       "5608     -8.304           1       0.3300  104.053               4   \n",
       "\n",
       "       audio_valence  \n",
       "7568           0.671  \n",
       "15091          0.671  \n",
       "17392          0.671  \n",
       "14176          0.671  \n",
       "11665          0.671  \n",
       "11697          0.671  \n",
       "5593           0.671  \n",
       "4299           0.671  \n",
       "16497          0.671  \n",
       "17590          0.671  \n",
       "7636           0.671  \n",
       "17638          0.671  \n",
       "1229           0.329  \n",
       "11777          0.329  \n",
       "17113          0.329  \n",
       "17603          0.329  \n",
       "4301           0.329  \n",
       "17660          0.329  \n",
       "14314          0.329  \n",
       "5608           0.329  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "base_data.sort_values(by=[\"song_popularity\"], ascending=False).head(20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nachffolgend wird die Bedeutung des jeweiligen Feldes in einer Tabelle dargestellt. Dabei wurden manche Angaben durch den Kontext erschlossen und manche Angaben konnten über die Dokumentation der Spotify Web API interpretiert werden (vgl. Spotify Web API 2022)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "| Feldname | Datentyp / Wertebereich | Beschreibung |\n",
    "| --- | --- | --- |\n",
    "| song_name| String | Gibt den Titel des Liedes, Podcasts oder der Rede an |\n",
    "| song_popularity | int $[0;100]$ | Die relative Beliebtheit eines Liedes in Prozent. Die Beliebtheit wird an der Gesamtzahl der Streams eines Liedes gemessen. Das Lied mit dem Wert 100 ist zum aktuellen Zeitpunkt das beliebteste Lied. |\n",
    "| song_duration | int $[0;∞]$ | Gibt die Länge eines Liedes, Podcasts oder einer Rede in Millisekunden an |\n",
    "| acousticness | float $[0;1]$ | Die Akustikt eines Liedes in Prozent. Ein Wert von $1,0$ bedeutet, dass ein Lied sehr akustisch ist und nicht elektronisch verstärkt wurde |\n",
    "| danceability | float $[0;1]$ | Die Tanzbarkeit eines Liedes in Prozent. Ein Wert von $1,0$ bedeutet, dass dieses Lied zum Tanzen anregt. Der Wert wird über die musikalischen Elementen wie unteranderem dem Tempo, der Stabilität der Rhytmik und der Stärke des Bass's ermittelt. |\n",
    "| energy | float $[0;1]$ | Die Intensität und Aktivität des Liedes in Prozent, basierend auf der Schnelligkeit, Lautstärke und Rauschen des Liedes, sowie der generellen Entropie. Ein Wert von $1,0$ bedeutet, dass ein Lied sehr energetisch ist, wie zum Beispiel Death Metal. |\n",
    "| instrumentalness | float $[0;1]$ | Die Instrumentalität gibt an, inwieweit Vocals im Lied vorhanden sind. Je näher der Wert an $1,0$ liegt, desto wahrscheinlicher ist das Lied rein akustisch. Je näher sich der Wert an die $0$ annähert, desto weniger Instrumente sind zu hören. So könnte versucht werden Reden zu erkennen, da diese einen Wert von $0$ haben müssten. |\n",
    "| key | int $[-1;11]$ | Gibt die Tonart des Liedes an. Der Wert nimmt $-1$ an, wenn keine primäre Tonart erkannt wurde. (Siehe https://de.wikipedia.org/wiki/Tonklasse) |\n",
    "| liveness | float $[0;1]$ | Die Wahrscheinlichkeit, dass das Lied eine Liveversion ist. Dies basiert auf Zuschauerinnen/Zuhörern, die im Hintergrund gehört werden. Ab $0,8$ kann von einer Liveversion ausgegangen werden. |\n",
    "| loudness | float $[-38.0;1,5]$ | Die Loudness gibt die durchschnittliche Lautstärke des Liedes in Decibel an. Die Lautstärke ist dabei relativ angegeben. |\n",
    "| audio_mode | int $[0;1]$ | Gibt die Modalität des Liedes wieder. Dabei steht $0$ für Moll und $1$ für Dur. |\n",
    "| speechiness | int $[0;1]$ | Gibt wieder ob exklusiv gesprochen wird, wie zum Beispiel bei Acapella-Liedern oder Reden (Racism And Injustice von Martin L. King). Bei allem $>0.66$, ist es wahrscheinlicher, dass nur gesprochen wird, bei $<0.33$ gibt es nur weniges oder kein gesprochenes Wort. |\n",
    "| tempo | float $[0;∞]$ | Eine Schätzung der Geschwindigkeit des Liedes in Beats per Minute (BPM). |\n",
    "| time_signature | int $[3;7]$ | Gib die primäre Taktangabe des Liedes an. Sie gibt Takte von 3/4 bis 7/4 an. |\n",
    "| audio_valence | float $[0;1]$ | Die positivität des Liedes. Dabei deutet ein hoher Wert auf eine positive (fröhlich, euphorisch), ein niedriger Wert auf eine negative Stimmung hin (aggresiv, melancholisch). |"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.1 Umgang mit fehlenden Werten, Redundanzen und Inkonsistenzen\n",
    "Um zuverlässige Ergebnisse zu erzielen, ist es wichtig, wie mit Redundanzen umgegangen wird, da sie die Performance von späteren Modellen maßgeblich beeinflussen können. Hierbei kann zwischen zwei Optionen entschieden werden: Einerseits könnten die Redundanzen im Datensatz behalten werden, wobei beim Splitten des Datensatzes in einen Trainings- und Testdatensatz es wichtig wäre, alle gleichen Einträge entweder vollständig in den Trainings- bzw. in den Testdatensatz aufzunehmen, sodass diese disjunkt bleiben und keine Memorisierung gefördert wird. Anderseits können die Redundanzen entfernt werden, mit der Folge, dass der Datensatz kleiner wird und nur eine Instanz übrig bleibt. Im Rahmen dieser Ausarbeitung werden doppelte Einträge entfernt, wenn sie den selben Liednamen und die gleiche Länge haben. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 14468 entries, 0 to 14467\n",
      "Data columns (total 15 columns):\n",
      " #   Column            Non-Null Count  Dtype  \n",
      "---  ------            --------------  -----  \n",
      " 0   song_name         14468 non-null  object \n",
      " 1   song_popularity   14468 non-null  int64  \n",
      " 2   song_duration_ms  14468 non-null  int64  \n",
      " 3   acousticness      14468 non-null  float64\n",
      " 4   danceability      14468 non-null  float64\n",
      " 5   energy            14468 non-null  float64\n",
      " 6   instrumentalness  14468 non-null  float64\n",
      " 7   key               14468 non-null  int64  \n",
      " 8   liveness          14468 non-null  float64\n",
      " 9   loudness          14468 non-null  float64\n",
      " 10  audio_mode        14468 non-null  int64  \n",
      " 11  speechiness       14468 non-null  float64\n",
      " 12  tempo             14468 non-null  float64\n",
      " 13  time_signature    14468 non-null  int64  \n",
      " 14  audio_valence     14468 non-null  float64\n",
      "dtypes: float64(9), int64(5), object(1)\n",
      "memory usage: 1.7+ MB\n"
     ]
    }
   ],
   "source": [
    "cleared = base_data.drop_duplicates(subset = [\"song_name\", \"song_duration_ms\"], keep = \"last\").reset_index(drop = True)\n",
    "cleared.info()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Da Redundanzen vorhanden sind werden diese anhand gleichem Songtitel und gleicher Songlänge entfernt. Dadurch landen wir bei 14.468 Songs, was bedeutet dass somit circa 4.400 Redundanzen entfernt wurden."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "\n",
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>song_name</th>\n",
       "      <th>song_popularity</th>\n",
       "      <th>song_duration_ms</th>\n",
       "      <th>acousticness</th>\n",
       "      <th>danceability</th>\n",
       "      <th>energy</th>\n",
       "      <th>instrumentalness</th>\n",
       "      <th>key</th>\n",
       "      <th>liveness</th>\n",
       "      <th>loudness</th>\n",
       "      <th>audio_mode</th>\n",
       "      <th>speechiness</th>\n",
       "      <th>tempo</th>\n",
       "      <th>time_signature</th>\n",
       "      <th>audio_valence</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>13326</th>\n",
       "      <td>Happier</td>\n",
       "      <td>100</td>\n",
       "      <td>214289</td>\n",
       "      <td>0.19100</td>\n",
       "      <td>0.687</td>\n",
       "      <td>0.792</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>5</td>\n",
       "      <td>0.1670</td>\n",
       "      <td>-2.749</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0452</td>\n",
       "      <td>100.015</td>\n",
       "      <td>4</td>\n",
       "      <td>0.671</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13346</th>\n",
       "      <td>I Love It (&amp; Lil Pump)</td>\n",
       "      <td>99</td>\n",
       "      <td>127946</td>\n",
       "      <td>0.01140</td>\n",
       "      <td>0.901</td>\n",
       "      <td>0.522</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>2</td>\n",
       "      <td>0.2590</td>\n",
       "      <td>-8.304</td>\n",
       "      <td>1</td>\n",
       "      <td>0.3300</td>\n",
       "      <td>104.053</td>\n",
       "      <td>4</td>\n",
       "      <td>0.329</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13490</th>\n",
       "      <td>Taki Taki (with Selena Gomez, Ozuna &amp; Cardi B)</td>\n",
       "      <td>98</td>\n",
       "      <td>212500</td>\n",
       "      <td>0.15300</td>\n",
       "      <td>0.841</td>\n",
       "      <td>0.798</td>\n",
       "      <td>0.000003</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0618</td>\n",
       "      <td>-4.206</td>\n",
       "      <td>0</td>\n",
       "      <td>0.2290</td>\n",
       "      <td>95.948</td>\n",
       "      <td>4</td>\n",
       "      <td>0.591</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13592</th>\n",
       "      <td>Promises (with Sam Smith)</td>\n",
       "      <td>98</td>\n",
       "      <td>213309</td>\n",
       "      <td>0.01190</td>\n",
       "      <td>0.781</td>\n",
       "      <td>0.768</td>\n",
       "      <td>0.000005</td>\n",
       "      <td>11</td>\n",
       "      <td>0.3250</td>\n",
       "      <td>-5.991</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0394</td>\n",
       "      <td>123.070</td>\n",
       "      <td>4</td>\n",
       "      <td>0.486</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13308</th>\n",
       "      <td>In My Feelings</td>\n",
       "      <td>98</td>\n",
       "      <td>217925</td>\n",
       "      <td>0.05890</td>\n",
       "      <td>0.835</td>\n",
       "      <td>0.626</td>\n",
       "      <td>0.000060</td>\n",
       "      <td>1</td>\n",
       "      <td>0.3960</td>\n",
       "      <td>-5.833</td>\n",
       "      <td>1</td>\n",
       "      <td>0.1250</td>\n",
       "      <td>91.030</td>\n",
       "      <td>4</td>\n",
       "      <td>0.350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13472</th>\n",
       "      <td>Eastside (with Halsey &amp; Khalid)</td>\n",
       "      <td>98</td>\n",
       "      <td>173799</td>\n",
       "      <td>0.55500</td>\n",
       "      <td>0.560</td>\n",
       "      <td>0.680</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>6</td>\n",
       "      <td>0.1160</td>\n",
       "      <td>-7.648</td>\n",
       "      <td>0</td>\n",
       "      <td>0.3210</td>\n",
       "      <td>89.391</td>\n",
       "      <td>4</td>\n",
       "      <td>0.319</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13290</th>\n",
       "      <td>Lucid Dreams</td>\n",
       "      <td>97</td>\n",
       "      <td>239835</td>\n",
       "      <td>0.34900</td>\n",
       "      <td>0.511</td>\n",
       "      <td>0.566</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>6</td>\n",
       "      <td>0.3400</td>\n",
       "      <td>-7.230</td>\n",
       "      <td>0</td>\n",
       "      <td>0.2000</td>\n",
       "      <td>83.903</td>\n",
       "      <td>4</td>\n",
       "      <td>0.218</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11606</th>\n",
       "      <td>In My Mind</td>\n",
       "      <td>97</td>\n",
       "      <td>184560</td>\n",
       "      <td>0.17600</td>\n",
       "      <td>0.694</td>\n",
       "      <td>0.770</td>\n",
       "      <td>0.000011</td>\n",
       "      <td>6</td>\n",
       "      <td>0.1180</td>\n",
       "      <td>-5.335</td>\n",
       "      <td>1</td>\n",
       "      <td>0.1490</td>\n",
       "      <td>125.905</td>\n",
       "      <td>4</td>\n",
       "      <td>0.163</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13319</th>\n",
       "      <td>Falling Down</td>\n",
       "      <td>97</td>\n",
       "      <td>196400</td>\n",
       "      <td>0.01750</td>\n",
       "      <td>0.669</td>\n",
       "      <td>0.574</td>\n",
       "      <td>0.002940</td>\n",
       "      <td>4</td>\n",
       "      <td>0.1460</td>\n",
       "      <td>-6.442</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0286</td>\n",
       "      <td>120.013</td>\n",
       "      <td>4</td>\n",
       "      <td>0.273</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13469</th>\n",
       "      <td>SICKO MODE</td>\n",
       "      <td>97</td>\n",
       "      <td>312820</td>\n",
       "      <td>0.00513</td>\n",
       "      <td>0.834</td>\n",
       "      <td>0.730</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>8</td>\n",
       "      <td>0.1240</td>\n",
       "      <td>-3.714</td>\n",
       "      <td>1</td>\n",
       "      <td>0.2220</td>\n",
       "      <td>155.008</td>\n",
       "      <td>4</td>\n",
       "      <td>0.446</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13476</th>\n",
       "      <td>Be Alright</td>\n",
       "      <td>96</td>\n",
       "      <td>196373</td>\n",
       "      <td>0.69700</td>\n",
       "      <td>0.553</td>\n",
       "      <td>0.586</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>11</td>\n",
       "      <td>0.0813</td>\n",
       "      <td>-6.319</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0362</td>\n",
       "      <td>126.684</td>\n",
       "      <td>4</td>\n",
       "      <td>0.443</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13296</th>\n",
       "      <td>SAD!</td>\n",
       "      <td>96</td>\n",
       "      <td>166605</td>\n",
       "      <td>0.25800</td>\n",
       "      <td>0.740</td>\n",
       "      <td>0.613</td>\n",
       "      <td>0.003720</td>\n",
       "      <td>8</td>\n",
       "      <td>0.1230</td>\n",
       "      <td>-4.880</td>\n",
       "      <td>1</td>\n",
       "      <td>0.1450</td>\n",
       "      <td>75.023</td>\n",
       "      <td>4</td>\n",
       "      <td>0.473</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13294</th>\n",
       "      <td>Moonlight</td>\n",
       "      <td>96</td>\n",
       "      <td>135090</td>\n",
       "      <td>0.55600</td>\n",
       "      <td>0.921</td>\n",
       "      <td>0.537</td>\n",
       "      <td>0.004040</td>\n",
       "      <td>9</td>\n",
       "      <td>0.1020</td>\n",
       "      <td>-5.723</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0804</td>\n",
       "      <td>128.009</td>\n",
       "      <td>4</td>\n",
       "      <td>0.711</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13480</th>\n",
       "      <td>FEFE (feat. Nicki Minaj &amp; Murda Beatz)</td>\n",
       "      <td>96</td>\n",
       "      <td>179404</td>\n",
       "      <td>0.08800</td>\n",
       "      <td>0.931</td>\n",
       "      <td>0.387</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1</td>\n",
       "      <td>0.1360</td>\n",
       "      <td>-9.127</td>\n",
       "      <td>1</td>\n",
       "      <td>0.4120</td>\n",
       "      <td>125.978</td>\n",
       "      <td>4</td>\n",
       "      <td>0.376</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10609</th>\n",
       "      <td>Lucky You (feat. Joyner Lucas)</td>\n",
       "      <td>96</td>\n",
       "      <td>244679</td>\n",
       "      <td>0.06270</td>\n",
       "      <td>0.876</td>\n",
       "      <td>0.786</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>10</td>\n",
       "      <td>0.1270</td>\n",
       "      <td>-4.884</td>\n",
       "      <td>0</td>\n",
       "      <td>0.3060</td>\n",
       "      <td>153.068</td>\n",
       "      <td>4</td>\n",
       "      <td>0.575</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13500</th>\n",
       "      <td>BEBE</td>\n",
       "      <td>95</td>\n",
       "      <td>217822</td>\n",
       "      <td>0.17200</td>\n",
       "      <td>0.635</td>\n",
       "      <td>0.902</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0</td>\n",
       "      <td>0.1250</td>\n",
       "      <td>-3.559</td>\n",
       "      <td>1</td>\n",
       "      <td>0.1090</td>\n",
       "      <td>102.063</td>\n",
       "      <td>4</td>\n",
       "      <td>0.286</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13144</th>\n",
       "      <td>Natural</td>\n",
       "      <td>95</td>\n",
       "      <td>189466</td>\n",
       "      <td>0.21600</td>\n",
       "      <td>0.448</td>\n",
       "      <td>0.612</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>2</td>\n",
       "      <td>0.0800</td>\n",
       "      <td>-6.106</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0708</td>\n",
       "      <td>97.773</td>\n",
       "      <td>4</td>\n",
       "      <td>0.213</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14123</th>\n",
       "      <td>Taste (feat. Offset)</td>\n",
       "      <td>95</td>\n",
       "      <td>232959</td>\n",
       "      <td>0.02360</td>\n",
       "      <td>0.884</td>\n",
       "      <td>0.559</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0</td>\n",
       "      <td>0.1010</td>\n",
       "      <td>-7.442</td>\n",
       "      <td>1</td>\n",
       "      <td>0.1200</td>\n",
       "      <td>97.994</td>\n",
       "      <td>4</td>\n",
       "      <td>0.342</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13298</th>\n",
       "      <td>Better Now</td>\n",
       "      <td>95</td>\n",
       "      <td>231266</td>\n",
       "      <td>0.35400</td>\n",
       "      <td>0.680</td>\n",
       "      <td>0.563</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>10</td>\n",
       "      <td>0.1360</td>\n",
       "      <td>-5.843</td>\n",
       "      <td>1</td>\n",
       "      <td>0.0454</td>\n",
       "      <td>145.028</td>\n",
       "      <td>4</td>\n",
       "      <td>0.374</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13517</th>\n",
       "      <td>I Like It</td>\n",
       "      <td>95</td>\n",
       "      <td>253390</td>\n",
       "      <td>0.09900</td>\n",
       "      <td>0.816</td>\n",
       "      <td>0.726</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>5</td>\n",
       "      <td>0.3720</td>\n",
       "      <td>-3.998</td>\n",
       "      <td>0</td>\n",
       "      <td>0.1290</td>\n",
       "      <td>136.048</td>\n",
       "      <td>4</td>\n",
       "      <td>0.650</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                            song_name  song_popularity  \\\n",
       "13326                                         Happier              100   \n",
       "13346                          I Love It (& Lil Pump)               99   \n",
       "13490  Taki Taki (with Selena Gomez, Ozuna & Cardi B)               98   \n",
       "13592                       Promises (with Sam Smith)               98   \n",
       "13308                                  In My Feelings               98   \n",
       "13472                 Eastside (with Halsey & Khalid)               98   \n",
       "13290                                    Lucid Dreams               97   \n",
       "11606                                      In My Mind               97   \n",
       "13319                                    Falling Down               97   \n",
       "13469                                      SICKO MODE               97   \n",
       "13476                                      Be Alright               96   \n",
       "13296                                            SAD!               96   \n",
       "13294                                       Moonlight               96   \n",
       "13480          FEFE (feat. Nicki Minaj & Murda Beatz)               96   \n",
       "10609                  Lucky You (feat. Joyner Lucas)               96   \n",
       "13500                                            BEBE               95   \n",
       "13144                                         Natural               95   \n",
       "14123                            Taste (feat. Offset)               95   \n",
       "13298                                      Better Now               95   \n",
       "13517                                       I Like It               95   \n",
       "\n",
       "       song_duration_ms  acousticness  danceability  energy  instrumentalness  \\\n",
       "13326            214289       0.19100         0.687   0.792          0.000000   \n",
       "13346            127946       0.01140         0.901   0.522          0.000000   \n",
       "13490            212500       0.15300         0.841   0.798          0.000003   \n",
       "13592            213309       0.01190         0.781   0.768          0.000005   \n",
       "13308            217925       0.05890         0.835   0.626          0.000060   \n",
       "13472            173799       0.55500         0.560   0.680          0.000000   \n",
       "13290            239835       0.34900         0.511   0.566          0.000000   \n",
       "11606            184560       0.17600         0.694   0.770          0.000011   \n",
       "13319            196400       0.01750         0.669   0.574          0.002940   \n",
       "13469            312820       0.00513         0.834   0.730          0.000000   \n",
       "13476            196373       0.69700         0.553   0.586          0.000000   \n",
       "13296            166605       0.25800         0.740   0.613          0.003720   \n",
       "13294            135090       0.55600         0.921   0.537          0.004040   \n",
       "13480            179404       0.08800         0.931   0.387          0.000000   \n",
       "10609            244679       0.06270         0.876   0.786          0.000000   \n",
       "13500            217822       0.17200         0.635   0.902          0.000000   \n",
       "13144            189466       0.21600         0.448   0.612          0.000000   \n",
       "14123            232959       0.02360         0.884   0.559          0.000000   \n",
       "13298            231266       0.35400         0.680   0.563          0.000000   \n",
       "13517            253390       0.09900         0.816   0.726          0.000000   \n",
       "\n",
       "       key  liveness  loudness  audio_mode  speechiness    tempo  \\\n",
       "13326    5    0.1670    -2.749           1       0.0452  100.015   \n",
       "13346    2    0.2590    -8.304           1       0.3300  104.053   \n",
       "13490    1    0.0618    -4.206           0       0.2290   95.948   \n",
       "13592   11    0.3250    -5.991           1       0.0394  123.070   \n",
       "13308    1    0.3960    -5.833           1       0.1250   91.030   \n",
       "13472    6    0.1160    -7.648           0       0.3210   89.391   \n",
       "13290    6    0.3400    -7.230           0       0.2000   83.903   \n",
       "11606    6    0.1180    -5.335           1       0.1490  125.905   \n",
       "13319    4    0.1460    -6.442           0       0.0286  120.013   \n",
       "13469    8    0.1240    -3.714           1       0.2220  155.008   \n",
       "13476   11    0.0813    -6.319           1       0.0362  126.684   \n",
       "13296    8    0.1230    -4.880           1       0.1450   75.023   \n",
       "13294    9    0.1020    -5.723           0       0.0804  128.009   \n",
       "13480    1    0.1360    -9.127           1       0.4120  125.978   \n",
       "10609   10    0.1270    -4.884           0       0.3060  153.068   \n",
       "13500    0    0.1250    -3.559           1       0.1090  102.063   \n",
       "13144    2    0.0800    -6.106           1       0.0708   97.773   \n",
       "14123    0    0.1010    -7.442           1       0.1200   97.994   \n",
       "13298   10    0.1360    -5.843           1       0.0454  145.028   \n",
       "13517    5    0.3720    -3.998           0       0.1290  136.048   \n",
       "\n",
       "       time_signature  audio_valence  \n",
       "13326               4          0.671  \n",
       "13346               4          0.329  \n",
       "13490               4          0.591  \n",
       "13592               4          0.486  \n",
       "13308               4          0.350  \n",
       "13472               4          0.319  \n",
       "13290               4          0.218  \n",
       "11606               4          0.163  \n",
       "13319               4          0.273  \n",
       "13469               4          0.446  \n",
       "13476               4          0.443  \n",
       "13296               4          0.473  \n",
       "13294               4          0.711  \n",
       "13480               4          0.376  \n",
       "10609               4          0.575  \n",
       "13500               4          0.286  \n",
       "13144               4          0.213  \n",
       "14123               4          0.342  \n",
       "13298               4          0.374  \n",
       "13517               4          0.650  "
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cleared.sort_values(by=[\"song_popularity\"], ascending=False).head(20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Zur Gegenprobe kann die Anzahl einzigartiger Liednamen ermittelt werden."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Heaven                      8\n",
       "Fire                        8\n",
       "You                         7\n",
       "Fall                        7\n",
       "Stay                        7\n",
       "                           ..\n",
       "Hallelujah I Love Her So    1\n",
       "Punches (with LP)           1\n",
       "Vibrate                     1\n",
       "3's & 7's                   1\n",
       "Est                         1\n",
       "Name: song_name, Length: 13070, dtype: int64"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cleared[\"song_name\"].value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Es ist erkennbar, dass weiterhin Lieder mit dem selben Titel mehrfach vorhanden sind. Jedoch ist es fraglich, ob sie vom selben Künstler stammen oder ob es auch die selbe Version eines Liedes ist, weil sie eine unterschiedliche Länge haben. Auffällig ist auch, dass sich unter den mehrfachvorkommenden Songtiteln vorallem generische Wörte wie \"Heaven\", \"Fire\", \"Fall\", \"Gone\" oder \"Stay\" befinden, was ein Indiz dafür sein kann, dass diese Lieder von unterschiedlichen Künstlern kommen könnten. Da es keine konkreten Anhaltspunkte gibt, werden keine weiteren Einträge entfernt."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2 Erweiterung des Datensatzes\n",
    "Zur Erweiterung des Basis-Datensatzes wird die Spotify Web API (https://developer.spotify.com/dashboard/) verwendet. Dazu wird ein kostenloser Spotify-Account benötigit, mit dem für den Anwendungszweck eine Client-ID und ein Client-Secret erstellt werden können. Leider ist nicht ganz ersichtlich, welche Rate-Limits vorliegen, sodass zwischen jeder Anfrage mindestens 100 Millisekunden gewartet wird. Zusätzlich wird der bereits verkleinerte Datensatz ohne die Redundanzen verwendet.\n",
    "\n",
    "Um das jeweilige Lied zu finden, wird neben den Liednamen auch die Länge des Liedes verwendet. In Kapitel 2.1 wurde bereits ersichtlich, dass es Lieder mit dem selben Titel gibt. Über diese Kombination kann relativ sicher gegangen werden, dass es sich definitiv um das selbe Werk handelt. Gefundene Lieder werden um die Künstlerin bzw. den Künstler ergänzt, wobei es sich hierbei auch um die Künstlergruppe handelt kann und um den Explicit-Status, also der Angabe, ob ein Lied unangemessene Inhalte enthält."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "CLIENT_ID = \"28f2619d8a6242ceae8160c565174771\"\n",
    "CLIENT_SECRET = \"5f6cb53e2614428380966f0e93e72c16\"\n",
    "\n",
    "sp = spotipy.Spotify(auth_manager=SpotifyClientCredentials(client_id=CLIENT_ID, client_secret=CLIENT_SECRET))\n",
    "\n",
    "expanded = cleared.copy()\n",
    "\n",
    "def expand_row(row):\n",
    "    time.sleep(0.1) # Sleep 100ms (=600 Anfragen pro min)\n",
    "    results = sp.search(q=row.song_name, limit=50, type=\"track\")\n",
    "\n",
    "    for _, track in enumerate(results[\"tracks\"][\"items\"]):\n",
    "        if track[\"duration_ms\"] == row.song_duration_ms:\n",
    "            row[\"artist\"] = track[\"artists\"][0][\"name\"]\n",
    "            row[\"explicit\"] = track[\"explicit\"]\n",
    "            return row\n",
    "    return row\n",
    "\n",
    "expanded = expanded.apply(expand_row, axis=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die Ausführung der Zelle hat circa $79$ Minuten gedauert. Im Verlauf davon wurden 14.468 Anfragen an Spotify gesendet und insgesamt wurden mit vorherigen Tests circa 20.000 Anfragen an Spotify gesendet."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'pandas.core.frame.DataFrame'>\n",
      "RangeIndex: 14468 entries, 0 to 14467\n",
      "Data columns (total 18 columns):\n",
      " #   Column            Non-Null Count  Dtype  \n",
      "---  ------            --------------  -----  \n",
      " 0   Unnamed: 0        14468 non-null  int64  \n",
      " 1   acousticness      14468 non-null  float64\n",
      " 2   artist            10503 non-null  object \n",
      " 3   audio_mode        14468 non-null  int64  \n",
      " 4   audio_valence     14468 non-null  float64\n",
      " 5   danceability      14468 non-null  float64\n",
      " 6   energy            14468 non-null  float64\n",
      " 7   explicit          10503 non-null  object \n",
      " 8   instrumentalness  14468 non-null  float64\n",
      " 9   key               14468 non-null  int64  \n",
      " 10  liveness          14468 non-null  float64\n",
      " 11  loudness          14468 non-null  float64\n",
      " 12  song_duration_ms  14468 non-null  int64  \n",
      " 13  song_name         14468 non-null  object \n",
      " 14  song_popularity   14468 non-null  int64  \n",
      " 15  speechiness       14468 non-null  float64\n",
      " 16  tempo             14468 non-null  float64\n",
      " 17  time_signature    14468 non-null  int64  \n",
      "dtypes: float64(9), int64(6), object(3)\n",
      "memory usage: 2.0+ MB\n"
     ]
    }
   ],
   "source": [
    "expanded.info()\n",
    "expanded.to_csv(\"song_data_expanded.csv\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Leider können bei circa 3900 Zeilen nicht zweifelsfrei Artist bzw. Explizit-Status ermittelt werden. Würde man jeweils auf das erste Ergebnis zurückgreifen, wenn mit gleicher Songlänge kein Lied gefunden würde, könnten alle Zeilen gefüllt werden. Aber es ist fraglich, ob das jeweilige Ergebnis richtig ist. Daher wird davon abgesehen und nur die zweifelsfei zugeordneten Lieder betrachtet."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die durch die Spotify-API erweiterten Daten wurden als eigene csv gecachet, um weitere Anfragen zu vermeiden. Die CSV enthält sowohl die bereinigten Daten als auch die Erweitertungen mancher Zeilen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "cleared = pd.read_csv(\"song_data_expanded.csv\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3 Visualisierung und Korrelationen zwischen den Features\n",
    "\n",
    "\n",
    "Zum Verständnis und der besseren Vorbereitung auf die Modellwahl, ist eine genaue Betrachtung der einzelnen Datenreihen sowie der Korrelationen zwischen ebendiesen unabdingbar.\n",
    "Erste Gedanken drehen sich dabei um die Audiofeatures. Im weiteren Verlauf werden anschließend die Künstlerinnen und Künstler genauer betrachtet, ob es mehr One-Hit-Wonder oder konsistent beliebte Künstler gibt."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Um die Gitterlinien hinter den Grafiken anzuzeigen, wird zunächst folgende Codezeile ausgeführt:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.rcParams[\"axes.axisbelow\"] = True"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.1 Popularität eines Liedes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cleared[\"song_popularity\"].hist(bins=14)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die Popularität eines Liedes ist mit Ausnahe des Intervalls $[0;10]$ normalverteilt. Wir können daher hier von einer annähernd normalverteilten Datenmenge reden.\n",
    "Was in diesem Diagramm gleich hervorsticht ist die Menge an sehr unbeliebten Songs. Ganz im Gegensatz zu den beliebtesten Songs, welche eine sehr geringe Menge aller Songs ausmachen.\n",
    "Dies könnte also ein Problem beim Training und der Testung der Modelle werden, da die Menge an populären Songs vielleicht einfach zu gering sein könnte um valide Ergebnisse zu erzielen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    14468.000000\n",
       "mean        48.593655\n",
       "std         20.282872\n",
       "min          0.000000\n",
       "25%         37.000000\n",
       "50%         52.000000\n",
       "75%         63.000000\n",
       "max        100.000000\n",
       "Name: song_popularity, dtype: float64"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cleared[\"song_popularity\"].describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.2 Länge eines Liedes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "count    1.446800e+04\n",
      "mean     2.189403e+05\n",
      "std      6.287834e+04\n",
      "min      1.200000e+04\n",
      "25%      1.836518e+05\n",
      "50%      2.117835e+05\n",
      "75%      2.448130e+05\n",
      "max      1.799346e+06\n",
      "Name: song_duration_ms, dtype: float64\n",
      "median: 211783.5\n"
     ]
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cleared[\"song_duration_ms\"].hist(range=[0, 500000], bins=15)\n",
    "\n",
    "print(cleared[\"song_duration_ms\"].describe())\n",
    "print(\"median:\", cleared[\"song_duration_ms\"].median())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die Länge der Lieder ist grundsätzlich normalverteilt, zeichnet sich aber auch durch Ausreißer auf der rechten Seite aus. Das arithmetische Mittel liegt bei circa $218,94$ Sekunden und der Median bei trotz der Ausreißer bei $211,78$ Sekunden. Die Abweichung zwischen diesen beiden Maßen ist durch Ausreißer bedingt, wobei der Median robuster gegenüber Ausreißern ist."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cleared[\"song_duration_ms\"].plot.box()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Der Boxplot stellt dar, wie deutliche Ausreißer besonders nach oben hin auftreten. Dies ist eventuell ein Indikator dafür, welches Intervall betrachtet werden sollte - gerade wenn Filtering nötig wird, um bessere Ergebnisse zu erzielen."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.3 Musikalische Eigenschaften (numerisch) eines Liedes\n",
    "Als erster Überblick über die musikalischen Eigenschaften, die numerisch skaliert sind, kann ein Histogramm über alle numerischen Features herangezogen werden. Auf die einzelnen Features wird im Detail in jedem Unterkapitel nochmal näher eingang."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1080x1080 with 9 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(nrows=3, ncols=3)\n",
    "fig.set_figheight(15)\n",
    "fig.set_figwidth(15)\n",
    "\n",
    "cleared[\"acousticness\"].hist(ax=axes[0,0])\n",
    "cleared[\"danceability\"].hist(ax=axes[0,1])\n",
    "cleared[\"energy\"].hist(ax=axes[0,2])\n",
    "\n",
    "cleared[\"instrumentalness\"].hist(ax=axes[1,0])\n",
    "cleared[\"liveness\"].hist(ax=axes[1,1])\n",
    "cleared[\"loudness\"].hist(ax=axes[1,2])\n",
    "\n",
    "cleared[\"speechiness\"].hist(ax=axes[2,0])\n",
    "cleared[\"tempo\"].hist(ax=axes[2,1])\n",
    "cleared[\"audio_valence\"].hist(ax=axes[2,2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3.3.1 Acousticness"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cleared[\"acousticness\"].hist()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die Akustik der Lieder ist mit Ausnahme des Intervalls $[0,0;0,2]$ nahezu gleichverteilt. Das bedeutet die meisten Lieder sind sehr stark elektronisch verstärkt bzw. ganz elektronisch produziert. Die restlichen Lieder verteilen sich hingegen sehr gut zwischen \"fast aussschließlich elektronisch\" verstärkt und \"rein akustisch\".\n",
    "Die Akustik liegt im Durchschnitt bei ca. $0,27$, was auf das Intervall $[0,0;0,1]$ zurückzuführen ist. Die Standardabweichung liegt hier bei ca. $0,3$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    14468.000000\n",
       "mean         0.273181\n",
       "std          0.299414\n",
       "min          0.000001\n",
       "25%          0.024300\n",
       "50%          0.142000\n",
       "75%          0.466000\n",
       "max          0.996000\n",
       "Name: acousticness, dtype: float64"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cleared[\"acousticness\"].describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3.3.2 Danceability"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cleared[\"danceability\"].hist(bins=14)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die Danceability scheint laut dem Diagramm ebenfalls nahezu normalverteilt. Hier liegt der Durchschnitt bei ca. $0,62$ und die Standardabweichung liegt bei ca. $0,16$.\n",
    "Allgemein lässt sich also sagen, dass die Mehrheit der Songs zum Tanzen geeignet sind."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    14468.000000\n",
       "mean         0.624570\n",
       "std          0.158247\n",
       "min          0.000000\n",
       "25%          0.524000\n",
       "50%          0.636000\n",
       "75%          0.740000\n",
       "max          0.987000\n",
       "Name: danceability, dtype: float64"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cleared[\"danceability\"].describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3.3.3 Energy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cleared[\"energy\"].hist(bins=12)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die Energie der Songs steigt innerhalb des Intervalls $[0,0;0,8]$ annäherd linear an. Der Durchschnitt liegt bei ca. $0,64$ und die Standardabweichung bei ca. $0,22$.\n",
    "Generell lässt sich sagen, dass eine Mehrzahl der Songs energetisch ist, jedoch der Anteil an besonders energetischen Songs geringer ausfällt. Ruhiger Lieder mit einer Energie von $0,2$ sind eher seltener."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    14468.000000\n",
       "mean         0.638505\n",
       "std          0.222621\n",
       "min          0.001070\n",
       "25%          0.494000\n",
       "50%          0.671000\n",
       "75%          0.817000\n",
       "max          0.999000\n",
       "Name: energy, dtype: float64"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cleared[\"energy\"].describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3.3.4 Instrumentalness"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cleared[\"instrumentalness\"].hist()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Der Großteil der Werte liegt in dem Intervall $[0;0,1]$, sodass die meisten Songs Vocals haben, das heißt: Sie beinhalten sowohl Musikinstrumente als auch menschliche Stimmen.\n",
    "Dieses Intervall wurde nochmal genauer betrachtet und es konnte festgestellt werden, dass auch diese, leicht gezoomte Grafik, fast die gleichen Eigenschaften aufweißt.\n",
    "Der Durchschnitt dieser Eingenschaft liegt bei ca. $0,09$, die Standardabweichung liegt bei ca. $0,24$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.000000    5057\n",
       "0.001050      13\n",
       "0.000001      13\n",
       "0.001030      12\n",
       "0.000105      11\n",
       "            ... \n",
       "0.009620       1\n",
       "0.702000       1\n",
       "0.737000       1\n",
       "0.272000       1\n",
       "0.000057       1\n",
       "Name: instrumentalness, Length: 3903, dtype: int64"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cleared[\"instrumentalness\"].hist(range=[0, 0.1], bins=20)\n",
    "cleared[\"instrumentalness\"].value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    14468.000000\n",
       "mean         0.093888\n",
       "std          0.242796\n",
       "min          0.000000\n",
       "25%          0.000000\n",
       "50%          0.000022\n",
       "75%          0.005482\n",
       "max          0.997000\n",
       "Name: instrumentalness, dtype: float64"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cleared[\"instrumentalness\"].describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3.3.5 Liveness"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cleared[\"liveness\"].hist(bins=12)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die meisten der Songs scheinen laut der Abbildung nicht Liveaufnahmen zu sein. Allerdings sieht man, das sich viele Songs nicht ganz links bei den reinen Studioaufnahmen befinden, sondern Spotify bei diesen automatisch gewisse Hintergrundgeräusche erkennt und sie somit weiter in Richtung Liveaufnahmen verschiebt.\n",
    "Die Songs liegen somit auch im Durchschnitt bei ca. $0,18$, wobei die Standardabweichung bei ca. $0,15$ liegt."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    14468.000000\n",
       "mean         0.180578\n",
       "std          0.145397\n",
       "min          0.010900\n",
       "25%          0.093100\n",
       "50%          0.121000\n",
       "75%          0.224000\n",
       "max          0.986000\n",
       "Name: liveness, dtype: float64"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cleared[\"liveness\"].describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3.3.6 Loudness"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAX0AAAD4CAYAAAAAczaOAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjUuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/YYfK9AAAACXBIWXMAAAsTAAALEwEAmpwYAAAQeklEQVR4nO3df6xkdX3G8fcjCDY0Crr0ShfqrnFrC2mqsEGMaXMjFRCNi4kaGlO3lmRrg6lNbCxIUqxIAm1aWlu12RYiGlMktgoBBCly2/QPfoj8UEDCFTXsBiWyiF1R2tVP/5jvkunu3L1zd+/ODH7fr+TmnvM9Z+Y+c+7uM2fOnDk3VYUkqQ/Pm3YASdLkWPqS1BFLX5I6YulLUkcsfUnqyKHTDrAva9asqXXr1u01/qMf/Ygjjjhi8oGWYa7xzWImMNdKzWKuWcwEk8111113fb+qjh65sKpm9uukk06qUW699daR49NmrvHNYqYqc63ULOaaxUxVk80FfKWW6FUP70hSRyx9SeqIpS9JHbH0Jakjlr4kdcTSl6SOWPqS1BFLX5I6YulLUkdm+jIMkjTKuvOu3/cKNy6zfMi3L3nTAaZ5bnFPX5I6YulLUkcsfUnqiKUvSR2x9CWpI5a+JHXE0pekjlj6ktQRS1+SOmLpS1JHLH1J6oilL0kdsfQlqSOWviR1xNKXpI5Y+pLUEUtfkjpi6UtSRyx9SeqIpS9JHfEPo0uaiGX/mLkmwj19SeqIpS9JHbH0JakjY5d+kkOS3J3kuja/PsntSRaTfDbJYW388Da/2JavG7qP89v4Q0lOX/VHI0nap5Xs6b8PeHBo/lLgsqp6BfAkcE4bPwd4so1f1tYjyfHA2cAJwBnAx5MccmDxJUkrMVbpJzkWeBPwz20+wOuBz7VVrgTOatOb2jxt+alt/U3AVVX1TFV9C1gETl6FxyBJGtO4e/p/C3wA+Fmbfwnwg6ra1ea3AWvb9FrgUYC2/Km2/rPjI24jSZqAZc/TT/Jm4PGquivJ/MEOlGQLsAVgbm6OhYWFvdbZuXPnyPFpM9f4ZjETmGulZjXXSkwq/6xsq3E+nPU64C1JzgReALwQ+DvgyCSHtr35Y4Htbf3twHHAtiSHAi8Cnhga3234Ns+qqq3AVoCNGzfW/Pz8XoEWFhYYNT5t5hrfLGYCc63UinLdOJsfzprUdp2V3+Gyh3eq6vyqOraq1jF4I/bLVfVO4FbgbW21zcA1bfraNk9b/uWqqjZ+dju7Zz2wAbhj1R6JJGlZB3IZhj8DrkryEeBu4PI2fjnw6SSLwA4GTxRU1f1JrgYeAHYB51bVTw/g50uSVmhFpV9VC8BCm36EEWffVNVPgLcvcfuLgYtXGlKStDr8RK4kdcTSl6SOWPqS1BFLX5I6YulLUkcsfUnqiKUvSR2x9CWpI5a+JHXE0pekjlj6ktQRS1+SOmLpS1JHLH1J6oilL0kdsfQlqSOWviR1xNKXpI5Y+pLUEUtfkjpi6UtSRyx9SeqIpS9JHbH0Jakjlr4kdcTSl6SOWPqS1BFLX5I6YulLUkcsfUnqiKUvSR2x9CWpI5a+JHXE0pekjlj6ktQRS1+SOrJs6Sd5QZI7ktyb5P4kf9HG1ye5Pcliks8mOayNH97mF9vydUP3dX4bfyjJ6QftUUmSRhpnT/8Z4PVV9ZvAq4AzkpwCXApcVlWvAJ4EzmnrnwM82cYva+uR5HjgbOAE4Azg40kOWcXHIklaxrKlXwM72+zz21cBrwc+18avBM5q05vaPG35qUnSxq+qqmeq6lvAInDyajwISdJ4Dh1npbZHfhfwCuBjwDeBH1TVrrbKNmBtm14LPApQVbuSPAW8pI3fNnS3w7cZ/llbgC0Ac3NzLCws7JVn586dI8enzVzjm8VMYK6VmtVcKzGp/LOyrcYq/ar6KfCqJEcCnwd+7WAFqqqtwFaAjRs31vz8/F7rLCwsMGp82sw1vlnMBOZaqRXluvH6g5plf01qu87K73BFZ+9U1Q+AW4HXAkcm2f2kcSywvU1vB44DaMtfBDwxPD7iNpKkCRjn7J2j2x4+SX4BeAPwIIPyf1tbbTNwTZu+ts3Tln+5qqqNn93O7lkPbADuWKXHIUkawziHd44BrmzH9Z8HXF1V1yV5ALgqyUeAu4HL2/qXA59OsgjsYHDGDlV1f5KrgQeAXcC57bCRJGlCli39qroPePWI8UcYcfZNVf0EePsS93UxcPHKY0qSVoOfyJWkjlj6ktQRS1+SOmLpS1JHLH1J6oilL0kdsfQlqSOWviR1xNKXpI5Y+pLUEUtfkjpi6UtSRyx9SeqIpS9JHbH0Jakjlr4kdcTSl6SOWPqS1BFLX5I6YulLUkcsfUnqiKUvSR2x9CWpI5a+JHXE0pekjhw67QCSZte6865ffqUbx1hHM8M9fUnqiKUvSR2x9CWpI5a+JHXE0pekjlj6ktQRS1+SOmLpS1JHLH1J6oilL0kdWbb0kxyX5NYkDyS5P8n72viLk9yc5OH2/ag2niQfTbKY5L4kJw7d1+a2/sNJNh+8hyVJGmWcPf1dwPur6njgFODcJMcD5wG3VNUG4JY2D/BGYEP72gJ8AgZPEsCFwGuAk4ELdz9RSJImY9nSr6rHquqrbfq/gQeBtcAm4Mq22pXAWW16E/CpGrgNODLJMcDpwM1VtaOqngRuBs5YzQcjSdq3FV1lM8k64NXA7cBcVT3WFn0XmGvTa4FHh262rY0tNb7nz9jC4BUCc3NzLCws7JVj586dI8enzVzjm8VMYK4eTWq7zsrvcOzST/KLwL8Cf1JVP0zy7LKqqiS1GoGqaiuwFWDjxo01Pz+/1zoLCwuMGp82c41vFjOBufbSwWWTJ7VdZ+Xf1lhn7yR5PoPC/0xV/Vsb/l47bEP7/ngb3w4cN3TzY9vYUuOSpAkZ5+ydAJcDD1bV3wwtuhbYfQbOZuCaofF3tbN4TgGeaoeBbgJOS3JUewP3tDYmSZqQcQ7vvA74PeBrSe5pYx8ELgGuTnIO8B3gHW3ZDcCZwCLwNPBugKrakeQi4M623oerasdqPAhJ0niWLf2q+i8gSyw+dcT6BZy7xH1dAVyxkoCSpNXjJ3IlqSOWviR1xNKXpI5Y+pLUEUtfkjpi6UtSRyx9SeqIpS9JHbH0Jakjlr4kdcTSl6SOWPqS1BFLX5I6YulLUkcsfUnqiKUvSR2x9CWpI5a+JHXE0pekjlj6ktQRS1+SOmLpS1JHLH1J6oilL0kdsfQlqSOWviR1xNKXpI5Y+pLUkUOnHUDS6lp33vXTjqAZ5p6+JHXE0pekjlj6ktQRS1+SOmLpS1JHLH1J6siypZ/kiiSPJ/n60NiLk9yc5OH2/ag2niQfTbKY5L4kJw7dZnNb/+Ekmw/Ow5Ek7cs4e/qfBM7YY+w84Jaq2gDc0uYB3ghsaF9bgE/A4EkCuBB4DXAycOHuJwpJ0uQsW/pV9Z/Ajj2GNwFXtukrgbOGxj9VA7cBRyY5BjgduLmqdlTVk8DN7P1EIkk6yPb3E7lzVfVYm/4uMNem1wKPDq23rY0tNb6XJFsYvEpgbm6OhYWFvdbZuXPnyPFpM9f4ZjETmKtHq/kJ5k+eccSSy2bld3jAl2GoqkpSqxGm3d9WYCvAxo0ba35+fq91FhYWGDU+beYa3yxmgp+TXDd6GYZp2dfvaFb+be3v2Tvfa4dtaN8fb+PbgeOG1ju2jS01LkmaoP0t/WuB3WfgbAauGRp/VzuL5xTgqXYY6CbgtCRHtTdwT2tjkqQJWvbwTpJ/AeaBNUm2MTgL5xLg6iTnAN8B3tFWvwE4E1gEngbeDVBVO5JcBNzZ1vtwVe355rAk6SBbtvSr6neXWHTqiHULOHeJ+7kCuGJF6SRJq8pP5EpSRyx9SeqIpS9JHbH0Jakjlr4kdcTSl6SOWPqS1BFLX5I6YulLUkcsfUnqiKUvSR2x9CWpI5a+JHXE0pekjhzwn0uUdODG+jut/hlErQL39CWpI5a+JHXE0pekjlj6ktQRS1+SOmLpS1JHLH1J6oilL0kdsfQlqSOWviR1xNKXpI5Y+pLUEUtfkjpi6UtSR7y0srSfxrocsjRj3NOXpI5Y+pLUEUtfkjpi6UtSR3wjVzNv4m+Y+rdo9XPMPX1J6sjESz/JGUkeSrKY5LxJ/3xJ6tlED+8kOQT4GPAGYBtwZ5Jrq+qBSebQaB5GkX7+TfqY/snAYlU9ApDkKmAT0FXpT+VDPRasdNAt+397Bf8Pv33Jmw4wzWiTLv21wKND89uA1wyvkGQLsKXN7kzy0Ij7WQN8/6AkPDDmGt8sZgJzrdQs5prFTLDCXLn0gH7Wy5ZaMHNn71TVVmDrvtZJ8pWq2jihSGMz1/hmMROYa6VmMdcsZoLZyTXpN3K3A8cNzR/bxiRJEzDp0r8T2JBkfZLDgLOBayecQZK6NdHDO1W1K8l7gZuAQ4Arqur+/birfR7+mSJzjW8WM4G5VmoWc81iJpiRXKmqaWeQJE2In8iVpI5Y+pLUkedk6Sd5f5JKsqbNJ8lH26Ud7kty4oTzXNR+7j1JvpTkl9v4fJKn2vg9Sf58BjJNe1v9VZJvtJ/9+SRHtvF1SX48tK3+cRZytWXnt+31UJLTJ5jp7UnuT/KzJBuHxqe9rUbmasumsq1GZPxQku1D2+jMKWaZrUvPVNVz6ovBKZ83Ad8B1rSxM4EvAgFOAW6fcKYXDk3/MfCPbXoeuG5K22mpTNPeVqcBh7bpS4FL2/Q64OtT/He1VK7jgXuBw4H1wDeBQyaU6deBVwILwMah8Wlvq6VyTW1bjcj4IeBPp7WNhnIc0rbDy4HD2vY5fpqZnot7+pcBHwCG34HeBHyqBm4DjkxyzKQCVdUPh2aP2CPbVOwj07S31ZeqalebvY3BZzWmbh+5NgFXVdUzVfUtYJHB5UQmkenBqhr1ifSp2keuqW2rGfbspWeq6n+A3ZeemZrnVOkn2QRsr6p791g06vIOaycWDEhycZJHgXcCw4dxXpvk3iRfTHLCDGSa+rYa8gcMXnXstj7J3Un+I8lvTSkT/P9cs7S9hs3Ktho2a9vqve1w3RVJjppShlnbJrN3GYYk/w68dMSiC4APMngZPnH7ylVV11TVBcAFSc4H3gtcCHwVeFlV7WzHFL8AbJhypoNuuVxtnQuAXcBn2rLHgF+pqieSnAR8IckJe7ximUaug2qcTCPMxLaatmW64hPARQxe4V4E/DWDJ/PuzVzpV9XvjBpP8hsMjhPemwQGL7+/muRkJnB5h6VyjfAZ4AbgwuH/hFV1Q5KPJ1lTVatyMaj9ycQMbKskvw+8GTi12oHPqnoGeKZN35Xkm8CvAl+ZZi4O8vZawe9w+DZT31ZLmOhlVsbNmOSfgOsOVo5lzNylZ54zh3eq6mtV9UtVta6q1jF4mXRiVX2XwaUc3tXOTDkFeKqqHptUtiTDe++bgG+08ZemPUO1J6fnAU9MMxPT31ZnMHhP5i1V9fTQ+NEZ/L0FkrycwSuiR6adi8H2OjvJ4UnWt1x3TCrXKNPeVvswM9tqj/ep3gp8fRo5mMFLz8zcnv5+uoHBWSmLwNPAuyf88y9J8krgZwzOKnpPG38b8EdJdgE/Bs4e2oOcVqZpb6t/YHB2x83t+fC2qnoP8NvAh5P8b8v8nqraMe1cVXV/kqsZ/M2HXcC5VfXTSQRK8lbg74GjgeuT3FNVpzPlbbVUrmluqxH+MsmrGBze+Tbwh9MIUat36ZlV42UYJKkjz5nDO5KkA2fpS1JHLH1J6oilL0kdsfQlqSOWviR1xNKXpI78Hy6CJuBNX3/yAAAAAElFTkSuQmCC",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cleared[\"loudness\"].hist(bins=16)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Da die optimale Dezibelzahl für gemasterte Songs bei maximal $-3$ Dezibel liegt, zeigt diese Songeigenschaft eine sehr gute Masterung der Songs im Datensatz. Alles Richtung $0$ db geht in die Richtung der Übersteuerung, alles unter ca. $-8$ db zwingt die Zuhöherinnen und Zuhöher häufig dazu, die Lautstärke am Ausgabegerät vermindern zu müssen.\n",
    "Der Durchschnitt liegt knapp über den $-8$ db, bei ca. $-7,72$ db, die Standardabweichung bei ca. $4,05$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    14468.000000\n",
       "mean        -7.718469\n",
       "std          4.046014\n",
       "min        -38.768000\n",
       "25%         -9.439250\n",
       "50%         -6.787500\n",
       "75%         -5.017750\n",
       "max          1.585000\n",
       "Name: loudness, dtype: float64"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cleared[\"loudness\"].describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3.3.7 Speechiness"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cleared[\"speechiness\"].hist(bins=16)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hier zeigt sich auch sehr schön, wie weiter oben bei der ```instrumentalness```, dass der Großteil der Songs Text beinhaltet. Der Anteil der Lieder ohne Text ist verschwindent gering.\n",
    "Der Durchschnitt ist wie erwartet bei ca. $0,1$, die Standardabweichtung liegt hier ebenfalls bei ca. $0,1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    14468.000000\n",
       "mean         0.099633\n",
       "std          0.103932\n",
       "min          0.000000\n",
       "25%          0.037200\n",
       "50%          0.054100\n",
       "75%          0.113000\n",
       "max          0.941000\n",
       "Name: speechiness, dtype: float64"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cleared[\"speechiness\"].describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3.3.8 Tempo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cleared[\"tempo\"].hist(range=[40, 240], bins=11)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die meisten Hip-Hop-Songs liegen zwischen $88$ und $121$ BPM, House-Songs liegen meist bei ca. $125$ BPM. Hier liegt ebenfalls eine annähernde Normalverteilung rund um die $125$ BPM vor, was den allgemeinen Schnitt wiederspiegelt.\n",
    "Der Durchschnitt liegt somit bei ca. $121,19$, die Standardabweichung liegt bei ca. $29,08$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    14468.000000\n",
       "mean       121.191691\n",
       "std         29.079174\n",
       "min          0.000000\n",
       "25%         98.227250\n",
       "50%        120.023500\n",
       "75%        139.956000\n",
       "max        242.318000\n",
       "Name: tempo, dtype: float64"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cleared[\"tempo\"].describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 3.3.9 Audio Valence"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<AxesSubplot:>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cleared[\"audio_valence\"].hist()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dieses Feature ist relativ gleichverteilt mit Ausnahme der niedrigeren Werte, wobei es sich um die negativeren Lieder handeln. Der größere Teil der Lieder geht doch in die positive Richtung, sodass es mehr Songs mit einer heiteren bzw. fröhlichen Stimmung gibt.\n",
    "Hier liegt der Mittelwert bei ca. $0,53$ sowie die Standardabweichung bei ca. $0,25$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    14468.000000\n",
       "mean         0.527793\n",
       "std          0.248473\n",
       "min          0.000000\n",
       "25%          0.332000\n",
       "50%          0.528000\n",
       "75%          0.730000\n",
       "max          0.984000\n",
       "Name: audio_valence, dtype: float64"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cleared[\"audio_valence\"].describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.4 Musikalische Eigenschaften (kategorisch) eines Liedes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.4.1 key (Tonart)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([<matplotlib.axis.XTick at 0x222502a8340>,\n",
       "  <matplotlib.axis.XTick at 0x222502a8310>,\n",
       "  <matplotlib.axis.XTick at 0x222502d8c10>,\n",
       "  <matplotlib.axis.XTick at 0x222502daa40>,\n",
       "  <matplotlib.axis.XTick at 0x222502db190>,\n",
       "  <matplotlib.axis.XTick at 0x222502db8e0>,\n",
       "  <matplotlib.axis.XTick at 0x222502db940>,\n",
       "  <matplotlib.axis.XTick at 0x22250314070>,\n",
       "  <matplotlib.axis.XTick at 0x2225028aad0>,\n",
       "  <matplotlib.axis.XTick at 0x22250314e50>,\n",
       "  <matplotlib.axis.XTick at 0x222503155a0>,\n",
       "  <matplotlib.axis.XTick at 0x22250315cf0>],\n",
       " [Text(0, 0, 'C'),\n",
       "  Text(1, 0, 'C#'),\n",
       "  Text(2, 0, 'D'),\n",
       "  Text(3, 0, 'D#'),\n",
       "  Text(4, 0, 'E'),\n",
       "  Text(5, 0, 'F'),\n",
       "  Text(6, 0, 'F#'),\n",
       "  Text(7, 0, 'G'),\n",
       "  Text(8, 0, 'G#'),\n",
       "  Text(9, 0, 'A'),\n",
       "  Text(10, 0, 'A#'),\n",
       "  Text(11, 0, 'B')])"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 864x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(12, 6))\n",
    "cleared[\"key\"].value_counts().sort_index().plot.bar()\n",
    "\n",
    "plt.grid()\n",
    "plt.xticks(range(0, 12), labels=[\"C\", \"C#\", \"D\", \"D#\", \"E\", \"F\", \"F#\", \"G\", \"G#\", \"A\", \"A#\", \"B\"], rotation=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In der Abbildung sind alle Tonarten der Songs kumuliert im Datensatz aufgeführt. Auffallend ist hier vor allem die Tonart \"D#\" auch \"dis\", welche generell sehr selten verwendet wird. Im Gegensatz dazu die Standardtonart \"C\" sowie \"G\", welche häufig mit der Modalität Dur gebraucht werden. Die Tonart \"D#\" wurde nur 427 mal in Liedern verwendet, während die Tonarten \"C\" sowie \"G\" 1674 bzw. 1601 mal vorkommen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0     1674\n",
       "7     1601\n",
       "1     1540\n",
       "9     1373\n",
       "2     1359\n",
       "5     1214\n",
       "11    1180\n",
       "4     1058\n",
       "6     1024\n",
       "8     1017\n",
       "10    1001\n",
       "3      427\n",
       "Name: key, dtype: int64"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cleared[\"key\"].value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.4.2 audio_mode (Modalität der Tonleiter)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([<matplotlib.axis.XTick at 0x22250333a60>,\n",
       "  <matplotlib.axis.XTick at 0x22250333a30>],\n",
       " [Text(0, 0, 'Moll'), Text(1, 0, 'Dur')])"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cleared[\"audio_mode\"].value_counts().sort_index().plot.bar()\n",
    "plt.grid()\n",
    "plt.xticks([0, 1], labels=[\"Moll\", \"Dur\"], rotation=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die Modalität eines Liedes spiegelt meist auch die Stimmung des Liedes wieder. \"Dur\" klingt dabei positiver, während \"Moll\" eher negativer und gedämpfter rüber kommt.\n",
    "Somit ist es nach der Betrachtung der ```audio_valence``` weiter oben nicht verwunderlich, dass tendenziell mehr Songs in die positive Richtung gehen, also die Modalität \"Dur\" haben."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.4.3 time_signature (Taktangabe)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([<matplotlib.axis.XTick at 0x222503a2860>,\n",
       "  <matplotlib.axis.XTick at 0x222503a2830>,\n",
       "  <matplotlib.axis.XTick at 0x222503be9b0>,\n",
       "  <matplotlib.axis.XTick at 0x222503bfa30>,\n",
       "  <matplotlib.axis.XTick at 0x222503bfd00>],\n",
       " [Text(0, 0, '7/4'),\n",
       "  Text(1, 0, '6/4'),\n",
       "  Text(2, 0, '5/4'),\n",
       "  Text(3, 0, '4/4'),\n",
       "  Text(4, 0, '3/4')])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cleared[\"time_signature\"].value_counts().sort_index().plot.bar()\n",
    "plt.grid()\n",
    "plt.xticks(range(0, 5), labels=[\"7/4\", \"6/4\", \"5/4\", \"4/4\", \"3/4\"], rotation=0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Der mit deutlichem Abstand meist verwendete Takt in den im Datensatz enthaltenen Liedern ist der 4/4 Takt (gesprochen: vier-viertel-Takt). Er ist der unkomplizierteste Takt, um mit den verschiedensten Notenwerten umzugehen, da diese von der selben Basis ausgehen. Identische Taktangaben wären also 2/2 oder 8/8, die jedoch seltener verwendet werden. Während in der Klassik auch häufiger auf den 3/4 Takt zurückgegriffen wird, ist im Pop, Rock, Hip-Hop, etc. der 5/4 Takt vorherrschend vor dem 3/4 Takt."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    14468.000000\n",
       "mean         3.953000\n",
       "std          0.316593\n",
       "min          0.000000\n",
       "25%          4.000000\n",
       "50%          4.000000\n",
       "75%          4.000000\n",
       "max          5.000000\n",
       "Name: time_signature, dtype: float64"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cleared[\"time_signature\"].describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3.5 Korrelationen zwischen den Datenwerten"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1440x864 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "matrix = cleared.corr()\n",
    "fig, ax = plt.subplots(figsize=(20, 12))\n",
    "sns.heatmap(matrix, annot=True, cmap=plt.cm.Blues)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vor dem Modelltraining war es noch wichtig zu schauen welche, Eigenschaften mit der Zielvariable ```song_popularity``` korrelieren. Dabei ist festzustellen, dass keine der Liedeigenschaften in einer relevanten Stärke mit der Zielvariable korreliert.\n",
    "Teilweise gibt es stärkere Korrelationen zwischen den Eigenschaften an sich.\n",
    "Die stärkste positive Korellation ist mit 0.77 zwischen ```loudness``` und ```energy```, was auch Sinn ergibt, da die Lautstärke bei energetischen Liedern meist sehr hoch ist. Die ```loudness``` korreliert gleichzeitig relativ stark mit der ```audio_valence```.\n",
    "Die stärksten negativen Korrelationen sind jeweils ```loudness``` und ```energy``` mit der ```acousticness```, ebenfalls sinnvoll, da die meisten Lieder mit rein akustischen Instrumenten weder sehr laut noch sehr energetisch sind."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3.6 Deskriptive Analyse des erweiterten Datensatzes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>acousticness</th>\n",
       "      <th>artist</th>\n",
       "      <th>audio_mode</th>\n",
       "      <th>audio_valence</th>\n",
       "      <th>danceability</th>\n",
       "      <th>energy</th>\n",
       "      <th>instrumentalness</th>\n",
       "      <th>key</th>\n",
       "      <th>liveness</th>\n",
       "      <th>loudness</th>\n",
       "      <th>song_duration_ms</th>\n",
       "      <th>song_name</th>\n",
       "      <th>song_popularity</th>\n",
       "      <th>speechiness</th>\n",
       "      <th>tempo</th>\n",
       "      <th>time_signature</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>explicit</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>False</th>\n",
       "      <td>8404</td>\n",
       "      <td>8404</td>\n",
       "      <td>8404</td>\n",
       "      <td>8404</td>\n",
       "      <td>8404</td>\n",
       "      <td>8404</td>\n",
       "      <td>8404</td>\n",
       "      <td>8404</td>\n",
       "      <td>8404</td>\n",
       "      <td>8404</td>\n",
       "      <td>8404</td>\n",
       "      <td>8404</td>\n",
       "      <td>8404</td>\n",
       "      <td>8404</td>\n",
       "      <td>8404</td>\n",
       "      <td>8404</td>\n",
       "      <td>8404</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>True</th>\n",
       "      <td>2099</td>\n",
       "      <td>2099</td>\n",
       "      <td>2099</td>\n",
       "      <td>2099</td>\n",
       "      <td>2099</td>\n",
       "      <td>2099</td>\n",
       "      <td>2099</td>\n",
       "      <td>2099</td>\n",
       "      <td>2099</td>\n",
       "      <td>2099</td>\n",
       "      <td>2099</td>\n",
       "      <td>2099</td>\n",
       "      <td>2099</td>\n",
       "      <td>2099</td>\n",
       "      <td>2099</td>\n",
       "      <td>2099</td>\n",
       "      <td>2099</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          Unnamed: 0  acousticness  artist  audio_mode  audio_valence  \\\n",
       "explicit                                                                \n",
       "False           8404          8404    8404        8404           8404   \n",
       "True            2099          2099    2099        2099           2099   \n",
       "\n",
       "          danceability  energy  instrumentalness   key  liveness  loudness  \\\n",
       "explicit                                                                     \n",
       "False             8404    8404              8404  8404      8404      8404   \n",
       "True              2099    2099              2099  2099      2099      2099   \n",
       "\n",
       "          song_duration_ms  song_name  song_popularity  speechiness  tempo  \\\n",
       "explicit                                                                     \n",
       "False                 8404       8404             8404         8404   8404   \n",
       "True                  2099       2099             2099         2099   2099   \n",
       "\n",
       "          time_signature  \n",
       "explicit                  \n",
       "False               8404  \n",
       "True                2099  "
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "explicit = cleared.groupby(\"explicit\")\n",
    "explicit.count().head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "explicit.count()[\"Unnamed: 0\"].plot.bar()\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Der Datensatz wurde in Kapitel 2.2 mit Hilfe der Spotify-API um die Künstler und den Explizit-Status erweitert. Leider konnten nur für 10.503 der 14.468 Lieder im Datensatz Explizit-Status sowie Künstler gefunden werden.\n",
    "Von diesen insgesamt 10.503 Liedern sind, mit einer Anzahl von 8404 Liedern, mehr als 80% als nicht explizit gekennzeichnet. Mit 2099 Liedern ist die Anzahl an unagemessenen Songs deutlich geringer.\n",
    "Als eine mögliche Hypothese könnte es damit erklärt werden, dass die beliebtesten Lieder meist auch im Radio gespielt werden müssen, um viel Aufmerksamkeit zu bekommen. Lieder mit Explizit-Status werden, wenn überhaupt, nur bei bestimmten Aktionen oder dem Wunsch eines Hörers im Radio gespielt. Außer der Künstler veröffentlicht eine zweite Version, in welcher die unangemessenen Inhalte ersetzt oder weggeschnitten wurden. Dennoch sind solche Songs generell auch altersbeschränkt auf Plattformen wie Youtube oder Spotify eingeschränkt verfügbar und haben es so meist schwerer eine ähnliche Popularität zu erreichen, wie es für \"normale\" Lieder möglich ist. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>count</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>min</th>\n",
       "      <th>25%</th>\n",
       "      <th>50%</th>\n",
       "      <th>75%</th>\n",
       "      <th>max</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>explicit</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>False</th>\n",
       "      <td>8404.0</td>\n",
       "      <td>50.524988</td>\n",
       "      <td>18.812325</td>\n",
       "      <td>0.0</td>\n",
       "      <td>40.0</td>\n",
       "      <td>53.0</td>\n",
       "      <td>64.0</td>\n",
       "      <td>100.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>True</th>\n",
       "      <td>2099.0</td>\n",
       "      <td>55.801810</td>\n",
       "      <td>19.874674</td>\n",
       "      <td>0.0</td>\n",
       "      <td>46.0</td>\n",
       "      <td>59.0</td>\n",
       "      <td>70.0</td>\n",
       "      <td>99.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           count       mean        std  min   25%   50%   75%    max\n",
       "explicit                                                            \n",
       "False     8404.0  50.524988  18.812325  0.0  40.0  53.0  64.0  100.0\n",
       "True      2099.0  55.801810  19.874674  0.0  46.0  59.0  70.0   99.0"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "explicit[\"song_popularity\"].describe().head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bei einer genaueren Betrachtung der Verteilung der Lieder mit und ohne unangemessenen Inhalten im Bezug zur ```song_popularity``` fällt jedoch auf, dass die Lieder mit unangemessenen Inhalten laut des Mittelwertes von ca. $55,8$ etwas beliebter sind als die nicht expliziten Lieder, mit einem Mittwelwert von ca. $50,52$. \n",
    "Anhand der Quantile fällt ebenfalls auf, dass deren Grenzen mit $46, 59$ und $70$ bei den Liedern mit unangemessenen Inhalten deutlich höher ausfallen als bei den nicht expliziten Liedern mit $40, 53$ und $64$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "explicit_song_popularity = explicit[\"song_popularity\"]\n",
    "explicit_song_popularity.mean().plot(kind=\"bar\", yerr=explicit_song_popularity.std(), capsize=6)\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True     51\n",
       "False    49\n",
       "Name: explicit, dtype: int64"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "top100 = cleared[[\"song_popularity\", \"explicit\"]].sort_values(by=[\"song_popularity\"], ascending=False).head(107)\n",
    "top100.count()\n",
    "top100[\"explicit\"].value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ebenfalls überraschend ist die Top 100 der beliebtesten Titel im Datensatz, wobei mit 51 Liedern zwei mehr mit unangemessenen Inhalten als ohne vertreten sind. Nach diesen Erkenntnissen ist davon auszugehen, dass die ```song_popularity``` nur auf die Beliebtheit der Titel bei Spotify zurückgreift und sonstige Einflüsse wie das Radio, wenn überhaupt, nur eine Nebenrolle spielen. Zusätzlich ist erkennbar, dass mit $51\\%$ in der Top 100 überdurchschnittlich viele Lieder mit unangemessene Inhalten vertreten sind, sodass die obengenannte Hypothese teilweise verworfen werden sollte."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Künstler"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "artist\n",
       "Lady Gaga      40\n",
       "Kanye West     38\n",
       "Drake          31\n",
       "Gucci Mane     21\n",
       "Eminem         20\n",
       "Ed Sheeran     19\n",
       "Khalid         19\n",
       "The Beatles    19\n",
       "Future         17\n",
       "The Weeknd     17\n",
       "Name: song_name, dtype: int64"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "artists = cleared.groupby(\"artist\")\n",
    "artists[\"song_name\"].count().sort_values(ascending=False).head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bei der Betrachtung der Künstler fällt auf, dass nur $3$ Künstler, nämlich Lady Gaga, Kanye West und Drake, mit mehr als $30$ Titeln im Datensatz vertreten sind. Bei diesen Künstlern ist dies durchaus gerechtfertigt, da sie schon viele Titel veröffentlicht haben. Es deutet jedoch auch auf eine ungleiche Verteilung hin, wenn Künstler wie die Beatles nur mit 19 Titeln im Datensatz vertreten sind. Generell sind mehr Musiker der 2000er und 2010er Jahre im Datensatz vertreten, was die These, dass der Datensatz von 2018 ist, weiter stützt."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-39-318b7715cf18>:1: FutureWarning: Indexing with multiple keys (implicitly converted to a tuple of keys) will be deprecated, use a list instead.\n",
      "  artists[\"song_popularity\", \"song_name\"].agg({\"song_name\":\"size\", \"song_popularity\":\"mean\"}).sort_values(by=\"song_popularity\", ascending=False).head(10)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>song_name</th>\n",
       "      <th>song_popularity</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>artist</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Dynoro</th>\n",
       "      <td>1</td>\n",
       "      <td>97.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Nio Garcia</th>\n",
       "      <td>1</td>\n",
       "      <td>94.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>XXXTENTACION</th>\n",
       "      <td>5</td>\n",
       "      <td>90.8</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Brytiago</th>\n",
       "      <td>1</td>\n",
       "      <td>90.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Dennis Lloyd</th>\n",
       "      <td>1</td>\n",
       "      <td>90.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Cassa Jackson</th>\n",
       "      <td>1</td>\n",
       "      <td>90.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Alex Rose</th>\n",
       "      <td>1</td>\n",
       "      <td>89.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>BlocBoy JB</th>\n",
       "      <td>1</td>\n",
       "      <td>89.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Kris Kross Amsterdam</th>\n",
       "      <td>1</td>\n",
       "      <td>89.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Ava Max</th>\n",
       "      <td>1</td>\n",
       "      <td>89.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                      song_name  song_popularity\n",
       "artist                                          \n",
       "Dynoro                        1             97.0\n",
       "Nio Garcia                    1             94.0\n",
       "XXXTENTACION                  5             90.8\n",
       "Brytiago                      1             90.0\n",
       "Dennis Lloyd                  1             90.0\n",
       "Cassa Jackson                 1             90.0\n",
       "Alex Rose                     1             89.0\n",
       "BlocBoy JB                    1             89.0\n",
       "Kris Kross Amsterdam          1             89.0\n",
       "Ava Max                       1             89.0"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "artists[\"song_popularity\", \"song_name\"].agg({\"song_name\":\"size\", \"song_popularity\":\"mean\"}) \\\n",
    "    .sort_values(by=\"song_popularity\", ascending=False).head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nun ist es von Interesse, ob es Künstlern gelungen ist mit vielen verschiedenen Titeln eine gleichmäßig hohe Beliebtheit zu erreichen oder die größte durchschnittliche Beliebtheit nur von One-Hit-Wundern erreicht wurde. \n",
    "Hier gab es eine Überraschung in der Form des Künstlers XXXTentacion, welcher es trotz 5 Titeln im Datensatz geschafft hat, eine durchschnittliche ```song_popularity``` von über 90 zu haben. Dies gelingt keiner anderen Personen in diesem Ausmaß."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-115-c24b59aa09e1>:1: FutureWarning: Indexing with multiple keys (implicitly converted to a tuple of keys) will be deprecated, use a list instead.\n",
      "  artists[\"song_popularity\", \"song_name\"].agg({\"song_name\":\"size\", \"song_popularity\":\"max\"}) \\\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>song_name</th>\n",
       "      <th>song_popularity</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>artist</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Marshmello</th>\n",
       "      <td>10</td>\n",
       "      <td>100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Kanye West</th>\n",
       "      <td>38</td>\n",
       "      <td>99</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>benny blanco</th>\n",
       "      <td>2</td>\n",
       "      <td>98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Drake</th>\n",
       "      <td>31</td>\n",
       "      <td>98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Calvin Harris</th>\n",
       "      <td>14</td>\n",
       "      <td>98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>DJ Snake</th>\n",
       "      <td>10</td>\n",
       "      <td>98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Lil Peep</th>\n",
       "      <td>9</td>\n",
       "      <td>97</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Juice WRLD</th>\n",
       "      <td>4</td>\n",
       "      <td>97</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Travis Scott</th>\n",
       "      <td>11</td>\n",
       "      <td>97</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Dynoro</th>\n",
       "      <td>1</td>\n",
       "      <td>97</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               song_name  song_popularity\n",
       "artist                                   \n",
       "Marshmello            10              100\n",
       "Kanye West            38               99\n",
       "benny blanco           2               98\n",
       "Drake                 31               98\n",
       "Calvin Harris         14               98\n",
       "DJ Snake              10               98\n",
       "Lil Peep               9               97\n",
       "Juice WRLD             4               97\n",
       "Travis Scott          11               97\n",
       "Dynoro                 1               97"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "artists[\"song_popularity\", \"song_name\"].agg({\"song_name\":\"size\", \"song_popularity\":\"max\"}) \\\n",
    "    .sort_values(by=\"song_popularity\", ascending=False).head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hier war es nun, anschließend zur vorigen Untersuchung zu der durchschnittlichen Beliebtheit, interessant zu sehen, ob die Künstler mit der tatsächlich höchsten ```song_popularity``` nur einen Hit gelandet haben, oder auch mehrere Songs veröffentlicht haben. \n",
    "Mit Außnahme von Dynoro und benny blanco haben alle Künstler, deren Titel die beliebtesten des Datensatzes sind mindestens 4 Titel im Datensatz. Marshmello, mit dem beliebtesten Titel des gesamten Datensatzes hat noch 9 andere Titel im Datensatz, Kanye West mit dem zweitbeliebtesten Titel sogar noch 37 andere. \n",
    "Anhand dessen lässt sich viel besser sehen, dass die meisten Künstlerinnen und Künstler mit einem beliebten Titel auch deutlich mehr Titel veröffentlich haben."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-40-66ed74aed6cc>:1: FutureWarning: Indexing with multiple keys (implicitly converted to a tuple of keys) will be deprecated, use a list instead.\n",
      "  artists[\"song_popularity\", \"song_name\"].agg({\"song_name\":\"size\", \"song_popularity\":\"sum\"}) \\\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>song_name</th>\n",
       "      <th>song_popularity</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>artist</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Kanye West</th>\n",
       "      <td>38</td>\n",
       "      <td>2464</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Drake</th>\n",
       "      <td>31</td>\n",
       "      <td>1931</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Lady Gaga</th>\n",
       "      <td>40</td>\n",
       "      <td>1873</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Ed Sheeran</th>\n",
       "      <td>19</td>\n",
       "      <td>1472</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Eminem</th>\n",
       "      <td>20</td>\n",
       "      <td>1321</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Gucci Mane</th>\n",
       "      <td>21</td>\n",
       "      <td>1224</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The Weeknd</th>\n",
       "      <td>17</td>\n",
       "      <td>1204</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Lil Wayne</th>\n",
       "      <td>15</td>\n",
       "      <td>1136</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Khalid</th>\n",
       "      <td>19</td>\n",
       "      <td>1132</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>The Beatles</th>\n",
       "      <td>19</td>\n",
       "      <td>1123</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             song_name  song_popularity\n",
       "artist                                 \n",
       "Kanye West          38             2464\n",
       "Drake               31             1931\n",
       "Lady Gaga           40             1873\n",
       "Ed Sheeran          19             1472\n",
       "Eminem              20             1321\n",
       "Gucci Mane          21             1224\n",
       "The Weeknd          17             1204\n",
       "Lil Wayne           15             1136\n",
       "Khalid              19             1132\n",
       "The Beatles         19             1123"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "artists[\"song_popularity\", \"song_name\"].agg({\"song_name\":\"size\", \"song_popularity\":\"sum\"}) \\\n",
    "    .sort_values(by=\"song_popularity\", ascending=False).head(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Darüber hinaus wird nun die kumulierten Beliebtheiten der Künstler im Datensatz betrachtet. Zum einen hat Kanye West mit 38 Titeln in Summe die größte Beliebtheit, zum anderen schafft es Drake mit 31 Titeln auf Platz 2, vor Lady Gaga mit 40 Titeln. \n",
    "Diese ist dann auf Platz 3, dicht gefolgt von Ed Sheeran auf Platz 4, mit weniger als der Hälfte der Titel, was für eine durchschnittlich deutlich höhere Beliebtheit der einzelnen Titel spricht. Insgesamt ist diese Betrachtung jedoch ungerecht, da Künstlerinnen und Künstler mit vielen Titeln einen deutlichen Vorteil haben."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-27-b8eb99767d2c>:1: FutureWarning: Indexing with multiple keys (implicitly converted to a tuple of keys) will be deprecated, use a list instead.\n",
      "  artists[\"song_popularity\", \"song_name\"] \\\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "song_name        size     7.590000\n",
       "song_popularity  mean    72.076428\n",
       "                 amax    90.710000\n",
       "dtype: float64"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "artists[\"song_popularity\", \"song_name\"] \\\n",
    "    .agg({\"song_name\":\"size\", \"song_popularity\":[np.mean, np.max]}) \\\n",
    "    .sort_values(by=(\"song_popularity\", \"amax\"), ascending=False).head(100).mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Zum Schluss wird nun die durchschnittliche Titelanzahl der Top 100 Künstler (nach ihren beliebtesten Titeln) mit ihrer durchschnittlichen ```song_popularity``` und der durchschnittlichen Beliebtheit der jeweils beliebtesten Songs aller Künstler aus den Top 100 betrachtet. \n",
    "In den Top 100 haben die Künstler im Durchschnitt ca. $8$ Titel, eine Beliebtheit im Mittel von ca. $72,08$ über alle Songs und eine insgesamte Beliebtheit im Mittel von ca. $90,71$ über die jeweils beliebtesten Songs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "<ipython-input-28-24525b998a97>:1: FutureWarning: Indexing with multiple keys (implicitly converted to a tuple of keys) will be deprecated, use a list instead.\n",
      "  artists[\"song_popularity\", \"song_name\"] \\\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "song_name        size     4.590000\n",
       "song_popularity  mean    68.768154\n",
       "                 amax    81.320000\n",
       "dtype: float64"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "artists[\"song_popularity\", \"song_name\"] \\\n",
    "    .agg({\"song_name\":\"size\", \"song_popularity\":[np.mean, np.max]}) \\\n",
    "    .sort_values(by=(\"song_popularity\", \"amax\"), ascending=False).head(500).mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Zum Vergleich zu den Top 100 wurden noch die Top 500 betrachtet. \n",
    "Hier haben die Künstler im Durchschnitt ca. 5 Titel, eine Beliebtheit im Mittel von ca. $68,77$ über alle Songs und eine Beliebtheit im Mittel von ca. $81,32$ über die jeweils beliebtesten Songs. \n",
    "Es lässt sich erkennen, dass die durchschnittliche Beliebtheit sowohl aller Titel als auch der jeweils beliebtesten Titel abnimmt. Ebenso wie die durchschnittliche Gesamtanzahl an Titeln eines Künstlers."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4 Datentransformation und Preprocessing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die Datenaufbereitung ist ein entscheidender Schritt für Data Analytics und Machine Learning, wobei sich die Art der Aufbereitung unterscheidet, je nachdem ob die Daten innerhalb von Data Analytics ausgewertet werden sollen oder über Machine Learning Modelle auf ihnen trainiert werden sollen (vgl. Jafari 2020, Kap. 3). Durch die Aufbereitung der Daten kann neben einer verbesserten Performance auch schnellere Berechnungen der Modelle erreicht werden (vgl. Bishop 2016, S. 2f.). Im folgenden werden verschiedene Ansätze verwendet, um die Daten in ein möglichst passendes Format für die Algorithmen zum Machine Learning zu überführen."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.1 Auswahl der Features\n",
    "Das hier vorliegende Supervised Learning zeichnet sich dadurch aus, dass sowohl der Eingangsvektor $X$ als auch der Zielvektor $y$ von Anfang an bekannt sind (vgl. Bishop 2016, S. 3). Konkret setzt sich der Eingangsvektoren aus allen numerischen bzw. kategorischen Features des Basisdatensatzes zusammen, im nachfolgenden Sourcecode als \n",
    "$X$ bezeichnet, mit Ausnahme der Song-Popularitätswerte, die den Zielvektor bilden und als $y$ bezeichnet werden. Als abhängige Variable soll die Popularität eines Songs durch die Modelle angenährt werden. Die Features \"Artist\" und \"Explicit\", die über die Erweiterung in Kapitel 2.2 in den Datensatz aufgenommen wurden, werden hierbei nicht betrachtet, da sie nicht für jeden Eintrag gefunden werden konnten. Durch die daraus entstehenden Null-Werte müssten die entsprechenden Einträge entfernt werden, sodass der Datensatz um fast 30% reduziert worden wäre."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = cleared[[\"song_duration_ms\", \"acousticness\", \"danceability\", \"energy\", \"instrumentalness\", \"key\", \"liveness\", \"loudness\", \"audio_mode\", \"speechiness\", \"tempo\", \"time_signature\", \"audio_valence\"]]\n",
    "y = cleared[\"song_popularity\"]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Bei der Auswahl der Features ist es wichtig, über Feature Engineering eine Selektion so zu treffen, dass nur für das Machine Learning nützliche Features verwendet werden (vgl. Géron 2019, S. 27). Beim Tainieren der Modelle kam es zu keinen positiven Effekten, wenn Features aus $X$ heraus gelassen wurden. Dadurch wird $X$ nachfolgend mit dieser Kombination an Features beibehalten."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.2 Trainings- und Testdatensatz Split\n",
    "Um die Performance der einzelnen Modelle zu messen, wird der Datensatz in zwei disjunkte Teildatensätze unterteilt. Als Trainingsdaten $X_{train} \\subset X$ wird die erste Teilmenge zum Erstellen der Modelle verwendet. Als Testdatensatz $X_{test} \\subset X$ wird die zweite Teilmenge in Kombination mit $y_{test}$ ausschließlich zur Validierung verwendet (vgl. Mohammed 2017, Kap. 1.2.6).\n",
    "\\begin{align}\n",
    "X_{train} \\cap  X_{test} = \\emptyset\n",
    "\\end{align}\n",
    "Die Gleichung zeigt, dass keine Elemente sowohl im Trainingsdatensatz $X_{train}$ als auch im Testdatensatz $X_{test}$ gleichzeitig vorkommen dürfen. In Kapitel 2.1 wurde beschrieben, dass alle Redundanzen entfernt wurden. Wären doppelte Einträge nicht entfernt worden, wäre es an dieser Stelle wichtig gewesen, dass jede Gruppe von gleichen Einträgen entweder ausnahmslos im Trainigs- oder nur im Testdatensatz vorgekommen wären."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Kardinalität des Trainingsdatensatzes: 11574 bzw. des Testdatensatzes: 2894\n"
     ]
    }
   ],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(X, y, random_state=7, test_size=0.2)\n",
    "print(\"Kardinalität\", \"des Trainingsdatensatzes:\", len(X_train), \"bzw. des Testdatensatzes:\", len(X_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Zum Aufteilen des Datensatzes in die entsprechenden Trainigs- und Testdatensätze wird die Methode ```train_test_split()``` verwendet. Dabei wird über den Parameter ```test_size=0.2``` das Verhältnis von 80% Trainingsdatensatz und 20% Testdatensatz bestimmt und über den Parameter ```random_state=7``` ein Seed gesetzt, sodass die Aufteilung immer gleich erfolgt (vgl. Géron 2019, S. 51ff.). Der Trainingsdatensatz $X_{train}$ bzw. $y_{train}$ besteht dadurch aus 11574 Elementen und der Testdatensatz $X_{test}$ bzw. $y_{test}$ aus 2894."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4.3 Normalisierung und Standardisierung der Features\n",
    "Die Skalierung der Features beeinflusst maßgeblich die Performance der Modelle, sowohl in ihrer Zuverlässigkeit der Ergebnisse als auch in der Performance (vgl. Géron 2019, S. 69ff.). Ein erster Ansatz war dabei, die Features zu skalieren, die sich besonders durch Ausreißer auszeichnen (siehe Kapitel 3). Die Skalierung wird anhand $X_{train}$ angepasst und anschließend auf $X_{train}$ und $X_{test}$ angewendet. Der ```RobustScaler``` nutzt dafür statistische Verfahren, die gegen Ausreißer robust sind, um die Features zu zentrieren bzw. skalieren (vgl. Sklearn Doku 2022). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "scaler = RobustScaler()\n",
    "scaler.fit(X_train)\n",
    "\n",
    "X_train = pd.DataFrame(scaler.transform(X_train), columns = X_train.columns, index = X_train.index) \n",
    "X_test = pd.DataFrame(scaler.transform(X_test), columns = X_test.columns, index = X_test.index)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Während der Validierung der Ergebnisse konnte die Performance durch den RobustScaler nicht verbessert werden, sodass er nicht weiter verwendet wurde. Das Ergebnis der Skalierung würde folgendermaßen aussehen:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
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       "      <td>1.774047</td>\n",
       "      <td>-0.616822</td>\n",
       "      <td>-1.910836</td>\n",
       "      <td>7.568351</td>\n",
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       "      <td>0.0</td>\n",
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       "      <th>2334</th>\n",
       "      <td>-1.192741</td>\n",
       "      <td>-0.307101</td>\n",
       "      <td>0.845794</td>\n",
       "      <td>-0.557276</td>\n",
       "      <td>-0.004112</td>\n",
       "      <td>-0.500000</td>\n",
       "      <td>0.341615</td>\n",
       "      <td>-0.559376</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3.653280</td>\n",
       "      <td>-1.028338</td>\n",
       "      <td>0.0</td>\n",
       "      <td>-0.068182</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       song_duration_ms  acousticness  danceability    energy  \\\n",
       "8299          -1.153702     -0.027223      0.355140 -0.507740   \n",
       "14414          0.264873      1.774047     -0.616822 -1.910836   \n",
       "7823          -1.950843      1.578947      1.042056 -1.628483   \n",
       "6754           1.486085     -0.320417     -0.855140  0.801858   \n",
       "2334          -1.192741     -0.307101      0.845794 -0.557276   \n",
       "\n",
       "       instrumentalness       key  liveness  loudness  audio_mode  \\\n",
       "8299           8.818351 -0.666667 -0.023292 -0.870165         0.0   \n",
       "14414          7.568351 -0.666667 -0.108696 -3.815426         0.0   \n",
       "7823         172.821975 -0.166667 -0.100932 -0.934178         0.0   \n",
       "6754           0.883569  0.666667  1.855590  0.666139         0.0   \n",
       "2334          -0.004112 -0.500000  0.341615 -0.559376         0.0   \n",
       "\n",
       "       speechiness     tempo  time_signature  audio_valence  \n",
       "8299      0.165997  0.453859             0.0       0.560606  \n",
       "14414    -0.247657 -0.993670             0.0      -0.050505  \n",
       "7823      3.693440 -0.887396             0.0       0.631313  \n",
       "6754      0.238286  0.070411             0.0      -0.893939  \n",
       "2334      3.653280 -1.028338             0.0      -0.068182  "
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Neben dem RobustScaler wird ein ```StandardScaler``` zur Standardisierung der unabhängigen Features verwendet. Der StandardScaler skaliert die Werte anhand ihrer Standardabweichung, sodass sie nicht in einem festen Intervall liegen. Die Skalierung funktioniert auch mit Features, die Ausreißer besitzen (vgl. Géron 2019, S. 69f.). \n",
    "\n",
    "Es werden hierbei nicht alle Features des Datensatzes skaliert, da bei manchen Werten die Skalierung zu schlechteren Ergebnissen geführt hat, insbesondere diskrete Werte werden nicht über den StandardScaler skaliert. Um nur konkrete Features, die in ```scaled_columns``` definiert sind, zu skalieren, wird ein ```ColumnTransformer``` verwendet. Der entsprechende StandardScaler wird wie der RobustScaler nur auf $X_{train}$ trainiert und anschließend auf die angegebenen Spalten angewendet. Da die nicht skalierten Spalten ans Ende der jeweiligen Zeile verschoben werden, müssen die Spaltennamen neu zugewiesen werden."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "scaler = StandardScaler()\n",
    "scaler.fit(X_train)\n",
    "\n",
    "scaled_columns = [\n",
    "    \"acousticness\", \n",
    "    \"danceability\", \n",
    "    \"energy\", \n",
    "    \"instrumentalness\", \n",
    "    \"liveness\", \n",
    "    \"speechiness\", \n",
    "    \"tempo\", \n",
    "    \"audio_valence\"\n",
    "]\n",
    "\n",
    "ct = ColumnTransformer([\n",
    "    (\"scaler\", scaler, scaled_columns)\n",
    "], remainder=\"passthrough\")\n",
    "\n",
    "ct.fit_transform(X_train)\n",
    "\n",
    "column_names = scaled_columns\n",
    "for col in X_test: # Fehlende Spaltennamen hinzufügen\n",
    "    if col not in column_names:\n",
    "        column_names.append(col)\n",
    "\n",
    "X_train = pd.DataFrame(ct.transform(X_train), index = X_train.index, columns = column_names)\n",
    "X_test = pd.DataFrame(ct.transform(X_test), index = X_test.index, columns = column_names)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Im Datensatz $X_{train}$ ist nun erkennbar, dass die Werte um den Wert $0$ skaliert sind, wobei die jeweils fünf letzten Werte nicht skaliert wurden."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>acousticness</th>\n",
       "      <th>danceability</th>\n",
       "      <th>energy</th>\n",
       "      <th>instrumentalness</th>\n",
       "      <th>liveness</th>\n",
       "      <th>speechiness</th>\n",
       "      <th>tempo</th>\n",
       "      <th>audio_valence</th>\n",
       "      <th>song_duration_ms</th>\n",
       "      <th>key</th>\n",
       "      <th>loudness</th>\n",
       "      <th>audio_mode</th>\n",
       "      <th>time_signature</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>8299</th>\n",
       "      <td>-0.476747</td>\n",
       "      <td>0.550390</td>\n",
       "      <td>-0.589291</td>\n",
       "      <td>-0.188043</td>\n",
       "      <td>-0.424744</td>\n",
       "      <td>-0.318291</td>\n",
       "      <td>0.608465</td>\n",
       "      <td>0.888722</td>\n",
       "      <td>141093.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>-10.663</td>\n",
       "      <td>1.0</td>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14414</th>\n",
       "      <td>2.179352</td>\n",
       "      <td>-0.768994</td>\n",
       "      <td>-2.625220</td>\n",
       "      <td>-0.216334</td>\n",
       "      <td>-0.500373</td>\n",
       "      <td>-0.614464</td>\n",
       "      <td>-1.466805</td>\n",
       "      <td>-0.085712</td>\n",
       "      <td>228013.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>-23.684</td>\n",
       "      <td>1.0</td>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7823</th>\n",
       "      <td>1.891664</td>\n",
       "      <td>1.482838</td>\n",
       "      <td>-2.215519</td>\n",
       "      <td>3.523809</td>\n",
       "      <td>-0.493498</td>\n",
       "      <td>2.207327</td>\n",
       "      <td>-1.314443</td>\n",
       "      <td>1.001466</td>\n",
       "      <td>92250.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>-10.946</td>\n",
       "      <td>1.0</td>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6754</th>\n",
       "      <td>-0.909082</td>\n",
       "      <td>-1.092497</td>\n",
       "      <td>1.310970</td>\n",
       "      <td>-0.367629</td>\n",
       "      <td>1.239082</td>\n",
       "      <td>-0.266533</td>\n",
       "      <td>0.058730</td>\n",
       "      <td>-1.430591</td>\n",
       "      <td>302840.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>-3.871</td>\n",
       "      <td>1.0</td>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2334</th>\n",
       "      <td>-0.889446</td>\n",
       "      <td>1.216424</td>\n",
       "      <td>-0.661168</td>\n",
       "      <td>-0.387720</td>\n",
       "      <td>-0.101605</td>\n",
       "      <td>2.178572</td>\n",
       "      <td>-1.516507</td>\n",
       "      <td>-0.113898</td>\n",
       "      <td>138701.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>-9.289</td>\n",
       "      <td>1.0</td>\n",
       "      <td>4.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       acousticness  danceability    energy  instrumentalness  liveness  \\\n",
       "8299      -0.476747      0.550390 -0.589291         -0.188043 -0.424744   \n",
       "14414      2.179352     -0.768994 -2.625220         -0.216334 -0.500373   \n",
       "7823       1.891664      1.482838 -2.215519          3.523809 -0.493498   \n",
       "6754      -0.909082     -1.092497  1.310970         -0.367629  1.239082   \n",
       "2334      -0.889446      1.216424 -0.661168         -0.387720 -0.101605   \n",
       "\n",
       "       speechiness     tempo  audio_valence  song_duration_ms  key  loudness  \\\n",
       "8299     -0.318291  0.608465       0.888722          141093.0  1.0   -10.663   \n",
       "14414    -0.614464 -1.466805      -0.085712          228013.0  1.0   -23.684   \n",
       "7823      2.207327 -1.314443       1.001466           92250.0  4.0   -10.946   \n",
       "6754     -0.266533  0.058730      -1.430591          302840.0  9.0    -3.871   \n",
       "2334      2.178572 -1.516507      -0.113898          138701.0  2.0    -9.289   \n",
       "\n",
       "       audio_mode  time_signature  \n",
       "8299          1.0             4.0  \n",
       "14414         1.0             4.0  \n",
       "7823          1.0             4.0  \n",
       "6754          1.0             4.0  \n",
       "2334          1.0             4.0  "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5 Maschinelles Lernen (Regression)\n",
    "In diesem Kapitel werden die sechs Modelle vorgestellt, die zu diesem Datensatz erstellt wurden. Als Basis werden die aufbereiteten und skalierten Daten verwendet, wie sie zuvor beschrieben wurden, wobei keiner der Modelle mit einer ausreichenden Güte die Song-Popularität anhand der Audiofeatures vorhersagen kann. Die Ergebnisse über $X_{test}$ setzen sich folgendermaßen zusammen:\n",
    "\n",
    "| Kapitel | Modell | R²-Score | MSE | RMSE |\n",
    "| --- | --- | --- | --- | --- |\n",
    "| 5.1 | Multiple Lineare Regression | 0,018 | 402,40 | 20,06 |\n",
    "| 5.2 | Multiple Lasso Regression | 0,002 | 408,85 | 20,22 |\n",
    "| 5.3 | Random Forest Regression | 0,05 | 388,88 | 19,72 |\n",
    "| 5.4 | Gradient Boosting Regression | 0,036 | 394,42 | 19,86 |\n",
    "| 5.5 | Support Vector Machine | -0,01 | 414,53 | 20,36 |\n",
    "| 5.6 | Neuronales Netz | -0,014 | 416,57 | 20,37 |\n",
    "\n",
    "Im Rahmen des maschinellen Lernens konnte der R²-Score von circa $0,02$ auf $0,05$ gesteigert werden. Hierbei ist das beste Modell die Random Forest Regression."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.1 Multiple lineare Regression\n",
    "Als grober Anhaltspunkt und um erste Einblicke zu bekommen, wird zunächst eine lineare Regression über die Klasse ```LinearRegression``` trainiert. Die Basisfunktion bei der linearen Regression hat folgende Gestalt, wobei $\\hat{y}$ die abhängige Variable annähert, hier die Song-Popularität, und $\\phi_{j}(x)$ sich aus den unabhängigen Eingangswerten zusammensetzt (vgl. Bishop 2016, S. 137ff.):\n",
    "\\begin{align}\n",
    "\\hat{y} = \\hat{\\beta}_{0} + \\sum \\limits _{j=1} ^{M-1} \\hat{\\beta}_{j} \\phi_{j}(x)\n",
    "\\end{align}\n",
    "Die jewiligen $\\hat{\\beta}_i$ sind die Koeffizienten, die innerhalb der linearen Regression so bestimmt werden sollen, dass die $y$ Werte möglichst genau angenähert werden. Die Summe erfolgt dabei bis $M - 1$, da der erste Wert $\\hat{\\beta}_0$ als Achsenabschnitt interpretiert wird (vgl. Bishop 2016, S. 138ff.). Die lineare Regression wird mit $X_{train}$ und $y_{train}$ trainiert."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R² score: 0.017543325504641882\n",
      "RMSE error: 20.055951744388004\n",
      "******************************\n",
      "Koeffizienten: [-7.98820024e-01  1.17087144e+00 -1.87614540e+00 -1.73662922e+00\n",
      " -4.96504082e-01 -2.53340581e-01 -3.53999509e-01 -1.62597274e+00\n",
      " -8.65986732e-07  1.81440183e-02  3.95728616e-01  7.06922513e-01\n",
      "  1.47110178e+00]\n"
     ]
    }
   ],
   "source": [
    "reg = LinearRegression()\n",
    "reg.fit(X_train, y_train)\n",
    "\n",
    "score = reg.score(X_test, y_test)\n",
    "rmse = mean_squared_error(y_test, reg.predict(X_test), squared=False)\n",
    "\n",
    "print(\"R² score:\", score)\n",
    "print(\"RMSE error:\", rmse)\n",
    "\n",
    "print(\"*\" * 30)\n",
    "print(\"Koeffizienten:\", reg.coef_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Als Ergebnisse über $X_{test}$ und $y_{test}$ kommt ein R²-Score von $0,0175$ bzw. ein RMSE von $20.056$ heraus. Die linare Regression ist unter Umständen ungeeignet, da die abhängige Zielvariable $p$, die die Song-Popularität eines Liedes angibt, folgende Eigenschaften besitzt:\n",
    "\\begin{align}\n",
    "p \\in \\{x\\in\\mathbb{N} \\mid x \\geq 0 \\wedge x \\leq 100\\}\n",
    "\\end{align}\n",
    "Da die lineare Regression auch Werte außerhalb dieser Menge abbildet, besonders $p < 0$ oder $p > 100$, könnte die lineare Regression ungeeignet sein. Zudem könnten auch die Beziehungen zwischen den Features und der Song-Popularität nicht linear sein."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.2 Lasso Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die _Least Absolute Shrinkage and Selection Operator_ (Lasso) Regression erweitert die lineare Regression, indem sie einen Regulierungsterm zu der Kostenfunktion hinzufügt. Eine besondere Eigenschaft der Lasso Regression ist, dass sie den Einfluss unwichtigerer Features über die Gewichtung minimiert (vgl. Géron 2019, S. 137ff.). Über die Klasse ```LassoCV``` kann die Lasso Regression trainiert werden und über Kreuzvalidierung die Hyperparameter entsprechend optimiert werden. Dabei wird ein Teil des Trainingsdatensatzes als Validierungsmenge verwendet, um die entsprechenden Hyperparameter zu prüfen (vgl. Géron 2019, S. 31f.)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Alphawert: 2.3326707155336455\n",
      "R² score: 0.0015540444968926703\n",
      "RMSE error: 20.218496320541508\n"
     ]
    }
   ],
   "source": [
    "reg = LassoCV(cv=5, random_state=7, max_iter=10000)\n",
    "reg.fit(X_train, y_train)\n",
    "\n",
    "print(\"Alphawert:\", reg.alpha_)\n",
    "\n",
    "score = reg.score(X_test, y_test)\n",
    "rmse = mean_squared_error(y_test, reg.predict(X_test), squared=False)\n",
    "\n",
    "print(\"R² score:\", score)\n",
    "print(\"RMSE error:\", rmse)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ähnlich zur linearen Regression, fallen auch hier die Ergebnisse mit einem R²-Score von $0,0016$ und einem RMSE von circa $20.2185$ mangelhaft aus. Entsprechend der linearen Regression ist auch bei der Lasso Regression eventuell ein Problem, dass eine lineare Beziehung angenommen wird und die Regression auch Werte außerhalb der eigentlichen Zielmenge hervorbringt. Daher werden nachfolgend auch Modelle trainiert, die keinen linearen Zusammenhang zwischen der Song-Popularität und den Features annehmen."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.3 Random Forest Regression\n",
    "Der Random Forest Algorithmus ist ein Ensemble Verfahren, wobei er sich aus $n$ vielen Entscheidungsbäumen zusammensetzt und die Ergebnisse der einzelnen Entscheidungsbäume über Bagging kombiniert werden (vgl. Géron 2019, S. 197ff.). Im Detail werden die Entscheidungsbäume mit einem jeweils zufällig gewählten Teil der Features bei jedem Knoten erzeugt. Über ein Fehlermaß wie beispielsweise dem Mean-Squared-Error (MSE) werden anschließend die optimalen Features ausgewählt. Schließlich werden die Ergebnisse der einzelnen Entscheidungsbäume über den Durchschnitt oder der Anzahl der Stimmen zu einem Ergebnis zusammengeführt. Über den Zufall wird versucht den Bias zu verringern, um eine bessere Generalisierung auch bei zuvor unbekannten Daten wie zum Beispiel dem Trainingsdatensatz $X_{test}$ zu erzielen (vgl. Alshare et al. 2022, S. 232ff.).\n",
    "\n",
    "Um die optimalen Hyperparameter des Random Forests zu finden, wird Random Search über die Klasse ```RandomizedSearchCV``` verwendet. Zum Random Search wird ähnlich wie beim Grid Search ein ```random_grid``` übergeben, das die möglichen Hyperparameter festlegt, mit dem Unterschied, dass nur ein Teil der möglichen Kombinationen zufällig getestet wird (vgl. Géron 2019, S. 76ff.). "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting 7 folds for each of 100 candidates, totalling 700 fits\n",
      "Optimale Parameter: {'n_estimators': 726, 'min_samples_split': 7, 'min_samples_leaf': 5, 'max_features': 'sqrt', 'max_depth': 30}\n"
     ]
    }
   ],
   "source": [
    "rf = RandomForestRegressor()\n",
    "random_grid = {\n",
    "    \"n_estimators\":      list(range(1, 1000)),\n",
    "    \"max_features\":      [\"auto\", \"sqrt\"],\n",
    "    \"max_depth\":         list(range(6, 121, 6)),\n",
    "    \"min_samples_split\": list(range(2, 15)),\n",
    "    \"min_samples_leaf\":  list(range(2, 15)),\n",
    "}\n",
    "\n",
    "search = RandomizedSearchCV(estimator=rf, param_distributions=random_grid, n_iter=100, cv=7, verbose=2, random_state=7, n_jobs=-1)\n",
    "search.fit(X_train, y_train)\n",
    "\n",
    "print (\"Optimale Parameter:\", search.best_params_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Über das Random Search-Verfahren kam heraus, dass die optimalen Parameter bei ```{'n_estimators': 726, 'min_samples_split': 7, 'min_samples_leaf': 5, 'max_features': 'sqrt', 'max_depth': 30}``` liegen. Die Suche hatte dabei circa $30$ Minuten gedauert.\n",
    "Anschließend wird der RandomForestRegressor auf den gesamten Trainingsdatensatz $X_{train}$ bzw. $y_{train}$ trainiert."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R² score: 0.05037487317279821\n",
      "RMSE error: 19.71799131546703\n"
     ]
    }
   ],
   "source": [
    "rf = RandomForestRegressor(n_estimators=726, min_samples_split=7, min_samples_leaf=5, max_features=\"sqrt\", max_depth=30, random_state=7)\n",
    "rf.fit(X_train, y_train)\n",
    "\n",
    "score = rf.score(X_test, y_test)\n",
    "rmse = mean_squared_error(y_test, rf.predict(X_test), squared=False)\n",
    "\n",
    "print(\"R² score:\", score)\n",
    "print(\"RMSE error:\", rmse)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die Random Forest Regression ist mit einem R²-Score von $0.0504$ und einem RMSE von $19.718$ das Modell mit der besten Performance."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.4 Gradient Boosting Regressor\n",
    "Der Gradient Boosting-Regressor ähnelt dem Random Forest, da er ebenfalls als Ensemble Verfahren die Ergebnisse mehrere Entscheidungsbäume kombiniert. Dabei werden sequenziell Entscheidungsbäume hinzugefügt, die ihre jeweiligen Vorgänger korrigieren, indem die Nachfolger anhand der vorherigen Residuen trainiert werden (vgl. Géron 2019, S. 203ff.).\n",
    "\n",
    "Ähnlich zum Random Forest wird auch zum Optimieren der Hyperparameter des Gradient Boosting-Regressors das Random Search-Verfahren über die Klasse ```RandomizedSearchCV``` verwendet."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Fitting 5 folds for each of 100 candidates, totalling 500 fits\n",
      "Optimale Parameter: {'n_estimators': 168, 'min_samples_split': 5, 'min_samples_leaf': 7, 'max_features': 'sqrt', 'max_depth': 60, 'learning_rate': 0.01}\n"
     ]
    }
   ],
   "source": [
    "gbr = GradientBoostingRegressor()\n",
    "random_grid = {\n",
    "    \"learning_rate\":     list(np.arange(0.01, 0.9, 0.01)),\n",
    "    \"n_estimators\":      list(range(1, 1000)),\n",
    "    \"max_features\":      [\"auto\", \"sqrt\"],\n",
    "    \"max_depth\":         list(range(6, 121, 6)),\n",
    "    \"min_samples_split\": list(range(2, 15)),\n",
    "    \"min_samples_leaf\":  list(range(2, 15)),\n",
    "}\n",
    "\n",
    "search = RandomizedSearchCV(estimator=gbr, param_distributions=random_grid, n_iter=100, cv=5, verbose=2, random_state=7, n_jobs=-1)\n",
    "search.fit(X_train, y_train)\n",
    "\n",
    "print (\"Optimale Parameter:\", search.best_params_)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Über das Random Search-Verfahren kam heraus, dass die optimalen Parameter bei ```{'n_estimators': 168, 'min_samples_split': 5, 'min_samples_leaf': 7, 'max_features': 'sqrt', 'max_depth': 60, 'learning_rate': 0.01}``` liegen. Die Suche hatte dabei circa $115$ Minuten gedauert.\n",
    "Anschließend wird der Gradient Boosting-Regressor nochmal auf den gesamten Trainingsdatensatz $X_{train}$ bzw. $y_{train}$ trainiert."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R² score: 0.03638379534735259\n",
      "RMSE error: 19.862715387244634\n"
     ]
    }
   ],
   "source": [
    "gbr = GradientBoostingRegressor(n_estimators=168, min_samples_split=5, min_samples_leaf=7, max_features=\"sqrt\", max_depth=60, learning_rate=0.01, random_state=7)\n",
    "gbr.fit(X_train, y_train)\n",
    "\n",
    "rmse = mean_squared_error(y_test, gbr.predict(X_test), squared=False)\n",
    "r2score = gbr.score(X_test, y_test)\n",
    "\n",
    "print(\"R² score:\", r2score)\n",
    "print(\"RMSE error:\", rmse)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Der Gradient Boosting-Regressor ist mit einem R²-Score von $0.0364$ und einem RMSE von $19.863$ das Modell mit der zweit besten Performance."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.5 Support Vector Regression\n",
    "Die Suppport Vector Regression ist ein robustes Verfahren, bei dem der Abstand zwischen den Entscheidungsgrenzen möglichst maximiert werden soll. Je nach Kernel können auch nicht lineare Zusammenhänge abgebildet werden (vgl. Bishop 2016, S. 325ff.). Über die Klasse ```SVR``` kann eine Support Vector Regression durchgeführt werden. Als Kernel wird der radiale Basisfunktionskernel (RBF) gewählt, da er die beste Performance sowohl in der Laufzeit als auch bei den Ergebnissen zeigte."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "R² score: -0.01273102631743317\n",
      "RMSE error: 20.362618747225284\n"
     ]
    }
   ],
   "source": [
    "svr = SVR(kernel=\"rbf\")\n",
    "svr.fit(X_train, y_train)\n",
    "\n",
    "score = svr.score(X_test, y_test)\n",
    "mse = mean_squared_error(y_test, svr.predict(X_test), squared=False)\n",
    "\n",
    "print(\"R² score:\", score)\n",
    "print(\"RMSE error:\", mse)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die Ergebnisse der Support Vector Regression fallen mit einem R²-Score von $-0.013$ und einem RMSE von $20.363$ mangelhaft aus."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 5.6 Künstliches neuronales Netz\n",
    "Als letztes Modell wird ein neuronales Netz trainiert. Dabei ist der Fokus eher auf dem grundsätzlichen Ausprobieren, sodass das Optimieren des neuronalen Netzes weniger im Vordergrund steht. Ein Neuronales Netz besteht aus verschiedenen Schichten, wobei jedes Neuron eine Aktivierungsfunktion besitzt (vgl. Bishop 2016, S. 225ff.). Das neuronale Netz besteht aus sechs Schichten, wobei die Inputlayer aus 13 Neuronen besteht, da jedes Element von $X_{train}$ aus 13 Werten besteht, und die Outputlayer aus einem Neuron, da die Song-Popularität als einzelner Wert bestimmt werden soll. Die erste und die fünfte Schicht nutzen zur Aktivierung die Sigmoindfunktion, während alle anderen Schichten lineare Funktionen nutzen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch 1/8\n",
      "400/400 [==============================] - 1s 2ms/step - loss: 17.9947 - val_loss: 15.8668\n",
      "Epoch 2/8\n",
      "400/400 [==============================] - 1s 1ms/step - loss: 15.9550 - val_loss: 15.9404\n",
      "Epoch 3/8\n",
      "400/400 [==============================] - 0s 1ms/step - loss: 15.9514 - val_loss: 15.9253\n",
      "Epoch 4/8\n",
      "400/400 [==============================] - 0s 1ms/step - loss: 15.9721 - val_loss: 15.8670\n",
      "Epoch 5/8\n",
      "400/400 [==============================] - 0s 1ms/step - loss: 15.9647 - val_loss: 15.8679\n",
      "Epoch 6/8\n",
      "400/400 [==============================] - 0s 1ms/step - loss: 15.9629 - val_loss: 15.8682\n",
      "Epoch 7/8\n",
      "400/400 [==============================] - 0s 1ms/step - loss: 15.9509 - val_loss: 15.8910\n",
      "Epoch 8/8\n",
      "400/400 [==============================] - 0s 1ms/step - loss: 15.9625 - val_loss: 15.8742\n"
     ]
    }
   ],
   "source": [
    "model = keras.Sequential([\n",
    "    keras.layers.Dense(units=13, activation=\"sigmoid\"),\n",
    "    keras.layers.Dense(units=13),\n",
    "    keras.layers.Dense(units=13),\n",
    "    keras.layers.Dense(units=13),\n",
    "    keras.layers.Dense(units=13, activation=\"sigmoid\"),\n",
    "    keras.layers.Dense(units=1)\n",
    "])\n",
    "\n",
    "model.compile(optimizer=keras.optimizers.Adam(learning_rate=0.1), loss=\"mean_absolute_error\")\n",
    "\n",
    "history = model.fit(\n",
    "    X_train,\n",
    "    y_train, \n",
    "    epochs=8, \n",
    "    steps_per_epoch=400,\n",
    "    validation_data=(X_test, y_test), \n",
    "    validation_steps=2\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die besten Ergebnisse konnten nach $8$ Epochen erreicht werden. Als Optimizer wird dazu Adam genutzt und als Loss-Funktion der durchschnittliche absolute Fehler."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "91/91 [==============================] - 0s 852us/step\n",
      "91/91 [==============================] - 0s 885us/step\n",
      "******************************\n",
      "R² score: -0.013510916116246552\n",
      "RMSE error: 20.37045772028239\n"
     ]
    }
   ],
   "source": [
    "rmse = mean_squared_error(y_test, model.predict(X_test), squared=False)\n",
    "r2score = r2_score(y_test, model.predict(X_test))\n",
    "\n",
    "print(\"*\" * 30)\n",
    "print(\"R² score:\", r2score)\n",
    "print(\"RMSE error:\", rmse)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Das neuronale Netz erzielt auf dem Testdatensatz $X_{test}$ einen R²-Score von $-0,017$ bzw. einen RMSE von $20,411$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6. Transformation des Regressionsproblems in ein Klassifikationsproblem\n",
    "Als weiterer Ansatz könnte das Regressionsproblem in ein Klassifikationsproblem umgewandelt werden, um somit die Komplexität der Vorhersage zu verringern. Dazu kann die Song-Popularität in vier Klassen $K_i$ unterteilt werden. Anfangs war die Idee, die Unterteilung anhand der Quartile vorzunehmen, sodass alle Klassen $K_i$ gleichverteilt sind bzw. $|K_0| = |K_1| = |K_2| = |K_3|$ gilt."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.0, 37.0, 52.0, 63.0]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def get_bins(n, feature):\n",
    "    step, bins = 1 / n, []\n",
    "\n",
    "    for i in range(n):\n",
    "        q = feature.quantile(step * i)\n",
    "        bins.append(q)\n",
    "\n",
    "    return bins\n",
    "\n",
    "quartil_bins = get_bins(4, cleared[\"song_popularity\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die Quartile befinden sich bei $0, 37, 52$ und $63$, sodass die Interpretation im Sachkontext nicht ganz eindeutig ist, da die Klassen unterschiedlich große Bereiche abdecken. Deswegen wurde dieser Ansatz verworfen und die Einträge anhand ihrer Song-Popularität in fünfundzwanziger Schritten in die vier Klassen eingeteilt. Die Mengenbeschreibungen für Klassen $K_i$ sehen folgendermaßen aus: \n",
    "\\begin{align}\n",
    "K_0 = \\{x\\in\\mathbb{N} \\mid x \\geq 0 \\wedge x < 25\\}\\\\\n",
    "K_1 = \\{x\\in\\mathbb{N} \\mid x \\geq 25 \\wedge x < 50\\}\\\\\n",
    "K_2 = \\{x\\in\\mathbb{N} \\mid x \\geq 50 \\wedge x < 75\\}\\\\\n",
    "K_3 = \\{x\\in\\mathbb{N} \\mid x \\geq 75 \\wedge x \\leq 100\\} \n",
    "\\end{align}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Zum Unterteilen in die Bins wurde anfangs die Methode ```np.digitize(x, bins)``` verwendet. Dabei hat sich ein unoffensichtlicher Fehler eingeschlichen, da ```np.digitize()``` den Index verändert, sodass die Indizes für $X_{train}$ nicht mehr den Indizes von $y_{train,class}$ entsprechen und so dem Input nicht mehr der richtige Output zugeordnet werden kann."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "bins = [0, 25, 50, 75]\n",
    "y_train_class, y_test_class = y_train.copy(), y_test.copy()\n",
    "\n",
    "y_train_class = np.digitize(y_train, bins)\n",
    "y_train_class = pd.DataFrame(y_train_class)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Daher wurde von diesem Ansatz abgesehen und eine eigene Methode geschrieben, die eine Integer-Division vornimmt und darüber die Werte in die jeweiligen Klassen unterteilt. Die Methode wird hierzu sowohl auf $y_{train}$ als auch auf $y_{test}$ über die ```apply()``` Funktion auf das jeweilige DataFrame angewendet."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "count    14468.000000\n",
      "mean        48.593655\n",
      "std         20.282872\n",
      "min          0.000000\n",
      "25%         37.000000\n",
      "50%         52.000000\n",
      "75%         63.000000\n",
      "max        100.000000\n",
      "Name: song_popularity, dtype: float64\n",
      "****************************************\n",
      "Klassenverteilung Training: 2    5472\n",
      "1    3643\n",
      "0    1634\n",
      "3     825\n",
      "Name: song_popularity, dtype: int64\n",
      "****************************************\n",
      "Klassenverteilung Test: 2    1359\n",
      "1     907\n",
      "0     395\n",
      "3     233\n",
      "Name: song_popularity, dtype: int64\n"
     ]
    }
   ],
   "source": [
    "print(cleared[\"song_popularity\"].describe())\n",
    "print(\"*\" * 40)\n",
    "\n",
    "def bin_to(x):\n",
    "    x = x // 25\n",
    "    if x == 4:\n",
    "        x = 3\n",
    "    return x\n",
    "\n",
    "y_train_class = y_train.apply(bin_to)\n",
    "y_test_class = y_test.apply(bin_to)\n",
    "\n",
    "print(\"Klassenverteilung Training:\", y_train_class.value_counts())\n",
    "print(\"*\" * 40)\n",
    "print(\"Klassenverteilung Test:\", y_test_class.value_counts())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Es ist nun erkennbar, dass in dem Datensatz $y_{train,class}$ nur noch die Werte $0, 1, 2, 3$ enthalten sind, die für die jeweilig Klasse $K_i$ stehen."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2    5472\n",
       "1    3643\n",
       "0    1634\n",
       "3     825\n",
       "Name: song_popularity, dtype: int64"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train_class.value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Außerdem sieht man, dass die Klassen unterschiedlich verteilt sind. Die Klasse $K_3$ besitzt lediglich 825 Einträge, während zu der Klasse $K_2$ 5472 Einträge zugewiesen werden können. Im weiteren Verlauf wird daher ein Downsample auf je 825 Elemente vom Trainingsdatensatz $X_{train}$ bzw. $y_{train,class}$ vorgenommen, damit die Klassen gleichverteilt sind. Dazu wird die folgende Methode ```down_sample(x, y, n)``` verwendet:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def down_sample(x, y, n):\n",
    "    random.seed(7) # Reproduzierbare Ergebnisse\n",
    "\n",
    "    for i in range(0, y.nunique()): # Jede Klasse durchgehen\n",
    "        y_class = y[y == i]\n",
    "\n",
    "        # n Indizes, die behalten werden sollen, auswählen\n",
    "        # Dazu über random.sample() zufällig Indizes aus verfügbaren wählen\n",
    "        indices = random.sample(list(y_class.index.values), len(y_class) - n)\n",
    "\n",
    "        x = x[~x.index.isin(indices)] # Die Zeilen entfernen deren\n",
    "        y = y[~y.index.isin(indices)] # Index nicht in indices enthalten ist\n",
    "    \n",
    "    return x, y\n",
    "\n",
    "X_train_sampled, y_train_class_sampled = down_sample(X_train, y_train_class, 825)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Nun ist erkennbar, dass von jeder Klasse $K_i$ exakt 825 Elemente vorhanden sind."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2    825\n",
       "3    825\n",
       "0    825\n",
       "1    825\n",
       "Name: song_popularity, dtype: int64"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train_class_sampled.value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 7. Maschinelles Lernen (Klassifikation)\n",
    "Im Rahmen der Klassifikation werden in Kapitel 7.1 einerseits ein Random Forest-Klassifikator und in Kapitel 7.2 eine logistische Regression trainiert. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 7.1 RandomForestClassifier\n",
    "Da der zielführendste Ansatz bei der Regression der Random Forest war (siehe Kapitel 5.3), wird bei der Klassifikation ebenfalls der Random Forest Algorithmus verwendet. Dazu wird statt der Klasse ```RandomForestRegressor``` die Klasse ```RandomForestClassifier``` verwendet. Um einen schnellen Überblick zu bekommen, wurden die Hyperparameter nicht nochmal gesondert über Random Search optimiert."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Durchschnittliche Genauigkeit (accuracy): 0.30545957152729786\n"
     ]
    }
   ],
   "source": [
    "rf = RandomForestClassifier(n_estimators=400, random_state=7)\n",
    "rf.fit(X_train_sampled, y_train_class_sampled)\n",
    "\n",
    "accuracy = rf.score(X_test, y_test_class)\n",
    "print(\"Durchschnittliche Genauigkeit (accuracy):\", accuracy)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Der Random Forest klassifiziert $X_{test}$ mit einer durchschnittlichen Genauigkeit von $30,55\\%$, was relativ nahe bei der A-priori-Wahrscheinlichkeit von $\\frac{1}{4} = 25\\%$ liegt. Um das Ergebnis besser einzuordnen, wird im Anschluss eine Konfusionsmatrix erstellt. Jede Zeile der Konfusionsmatrix stellt die tatsächliche Klasse dar, während jede Spalte die vorhergesagte Klasse zeigt. Bei einer perfekten Vorhersage würden abseits der Hauptdiagonalen nur Werte um 0 stehen (vgl. Géron 2019, S. 90ff.)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[114 106  75 100]\n",
      " [235 296 169 207]\n",
      " [315 303 340 401]\n",
      " [ 35  23  41 134]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1152x504 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_pred_test = rf.predict(X_test)\n",
    "\n",
    "matrix = confusion_matrix(y_test_class, y_pred_test)\n",
    "matrix = matrix.astype(\"float\") / matrix.sum(axis=1)[:, np.newaxis]\n",
    "\n",
    "plt.figure(figsize=(16,7))\n",
    "sns.heatmap(matrix, annot=True, annot_kws={\"size\":10}, cmap=plt.cm.Blues, linewidths=0.2)\n",
    "\n",
    "plt.xlabel(\"Vorhergesagte Klasse\")\n",
    "plt.ylabel(\"Annotierte Klasse\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Innerhalb der Konfusionsmatrix ist erkennbar, dass besonders die Klassen $K_0$ und $K_2$ nahezu zufällig vorhergesagt werden. Ein Lichtblick ist die Klasse $K_3$, die zu fast $60\\%$ korrekt vorhergesagt wird."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 7.2 Logistische Regression\n",
    "Da vor allem die Popularität der beliebtesten Lieder ($p \\geq 75$) aus Klasse $K_3$ etwas zuverlässiger vorhergesagt werden konnten, wird eine gezielte logistische Regression verwendet, um eine Vorhersage zu treffen, ob ein Lied grundsätzlich das potential hat, beliebt zu werden. Dazu wird die Zielvariable $y$ in zwei Klassen unterteilt, wobei alle Lieder mit einer Beliebtheit $< 66$ in eine Klasse $K_0$ und alle Lieder $\\geq 66$ in die Klasse $K_1$ eingeteilt."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "def is_popular(x):\n",
    "    if x >= 66:\n",
    "        return 1\n",
    "    return 0\n",
    "\n",
    "y_train_binary = y_train.apply(is_popular)\n",
    "y_test_binary = y_test.apply(is_popular)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ähnlich wie in Kapitel 6 wird dazu die ```apply()``` Methode auf $y_{test}$ bzw. $y_{train}$ angewendet."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    9195\n",
       "1    2379\n",
       "Name: song_popularity, dtype: int64"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train_binary.value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Da die beiden Klassen ebenfalls ungleichverteilt sind, wird hier nochmals die ```down_sample()``` Methode aus Kapitel 6 verwendet, um die Klassen auf je 2379 Einträge zu reduzieren."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0    2379\n",
       "1    2379\n",
       "Name: song_popularity, dtype: int64"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_train_sampled, y_train_binary = down_sample(X_train, y_train_binary, 2379)\n",
    "y_train_binary.value_counts()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Es ist nun erkennbar, dass die beiden Klassen gleichverteilt sind, sodass mit $X_{train}$ bzw. $y_{train,binary}$ die logistische Regression trainiert werden kann."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Genauigkeit: 0.5224602626123013\n"
     ]
    }
   ],
   "source": [
    "logReg = LogisticRegression()\n",
    "logReg.fit(X_train_sampled, y_train_binary)\n",
    "\n",
    "score = logReg.score(X_test, y_test_binary)\n",
    "print(\"Genauigkeit:\", score)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Die logistische Regression klassifiziert $X_{test}$ mit einer Genauigkeit von $52,25\\%$ gleich den annotierten Ergebnissen in $y_{test}$. Um das Verhältnis von richtigen zu falschen positiven Vorhersagen zu visualiseren, kann eine Receiver Operating Characteristic-Kurve (ROC) erstellt werden. Eine gute Klassifikation zeigt sich, indem sich der Graph soweit wie möglich in die obere linke Ecke erstreckt (vgl. Géron 2019, S. 97ff.). Dazu kann die Methode ```roc_curve()``` verwendet werden."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "A priori: ROC AUC = 0.5\n",
      "Logistische Regression: ROC AUC = 0.5781822787828212\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "y_scores = logReg.predict_proba(X_test)\n",
    "y_scores = y_scores[:, 1]\n",
    "\n",
    "auc_score = roc_auc_score(y_test_binary, y_scores)\n",
    "fpr, tpr, _ = roc_curve(y_test_binary, y_scores)\n",
    "\n",
    "print(\"A priori: ROC AUC = 0.5\")\n",
    "print(\"Logistische Regression: ROC AUC =\", auc_score)\n",
    "\n",
    "plt.plot([0, 1], [0, 1], linestyle=\"--\", label=\"A priori\")\n",
    "plt.plot(fpr, tpr, label=\"Logistische Regression\", color=\"#FFCC00\")\n",
    "\n",
    "plt.xlabel(\"False Positive Rate\")\n",
    "plt.ylabel(\"True Positive Rate\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In der Abbildung ist erkennbar, dass der gelbe Graph über dem gestrichteln Graph liegt und somit das Modell besser als der Zufall die Klassen vorhersagt. Die logistische Regression kommt auf einen Area under Curve-Wert (AUC) von $0,5782$. Damit fällt die Performance dieser Klassifikation ebenfalls eher mäßig aus. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 8 Diskussion"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Im Verlauf des Projektes wurden unterschiedliche Modelle trainiert, wobei keiner der Modelle mit einer ausreichenden Güte die Song-Popularität anhand der Audiofeatures vorhersagen kann. Einerseits könnte das darauf zurück zu führen sein, dass die Modelle eine zu geringe Komplexität aufweisen, um die Song-Popularität ausreichend abbilden zu können. Dafür können die geringen Ergebnisse der linearen Regression sprechen (siehe Kapitel 5.1), die von einem linearen Zusammenhang ausgeht und damit eine geringe Komplexität besitzt. Dagegen spricht, dass das neuronale Netz einer der schlechtesten Ergebnisse aufweist. Hierbei muss jedoch beachtet werden, dass das neuronale Netz größere Spielräume für Optimierungen lässt und unter Umständen die Features nicht in ein passendes Format gebracht worden waren.\n",
    "\n",
    "Darüber hinaus ist unklar nach welchen Kriterien die Lieder in dem Datensatz ausgewählt wurden. Es kann davon ausgegangen werden, dass unter Umständen eine Stichprobenverzerrung vorliegt, sodass besonders Lieder aus dem Jahr 2018 eine höhere Beliebtheit als ältere Lieder haben oder manche bekannten Lieder nicht Teil des Datensatzes sind. Dies würde sich besonders auf die deskriptiven Analysen in Kapitel 3.6 auswirken. Generell ist fraglich, welche Bedeutung die Popularität genau hat. Besonders aktuelle Lieder sind übermäßig beliebt, wobei sich die Audiofeatures dieser Lieder nicht verändern. Zwischen der Beliebtheit und dem Erscheinungsjahr eines Lieder könnte somit für die Popularität in diesem Datensatz eine deutlich höhere Korrelation als mit den Audiofeatures bestehen. Erschwerend ist die Beschaffenheit des Datensatzes als Momentaufnahme, da nur die aktuelle Beliebtheit relativ zum beliebtesten Lied dargestellt wird und saisonale Effekte oder Trends gar nicht berücksichtigt werden können.\n",
    "\n",
    "Besonders Trends werden innerhalb der Modelle nicht berücksichtigt, obwohl sie einen größeren Einfluss haben könnten. Beispielsweise waren verschiedene Genres besonders beliebt zu verschiedenen Zeitpunkten oder es sind saisonale Lieder wie zum Beispiel Weihnachtslieder besonders beliebt zur Weihnachtszeit. \n",
    "\n",
    "Abschließend ist fraglich, wie zuverlässig die Audiofeatures sind und wie statistisch signifikant die Ergebnisse der jeweiligen Features sind. Fehlerhafte Ausprägungen der Features beeinflussen die Modelle als Entscheidungsvariablen besonders stark. Die niedrigen Ergebnisse der Modelle könnten eventuell darauf hindeuten, dass die Audiofeatures nur eine geringe Aussagekraft besitzen. \n",
    "\n",
    "Zusätzlich wurde beim Erstellen der Modelle beobachtet, dass wenn Redundanzen nicht entfernt werden, die Ergebnisse besonders beim Random Forest auf einen R²-Score bis zu 0.40 anstiegen. In vergleichbaren Arbeiten, die diesen Datensatz behandelt haben, konnten diese Ergebnisse erreicht werden, wobei diese ebenfalls nicht die Redundanzen entfernt haben. Wieder andere Arbeiten konnten nur ähnliche Ergebnisse wie in dieser Arbeit erreichen, sodass die Theorie weiter bekräftigt wird, dass der Datensatz nicht genügend oder nicht ausreichend genaue Informationen zur Beantwortung des Regressionsproblems besitzt."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 8.1 Limitationen"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Aus der vorherigen Diskussion ergeben sich die folgenden Limitationen. Einerseits wird auf bereits ermittelte Audiofeatures zurükgegriffen, über deren Genauigkeit nur wenig bekannt ist. Falsche Ergebnisse bei den Audiofeatures wirken sich auch unter Umständen auf die Modelle die im Rahmen dieser Ausarbeiten aufgestellt wurden aus. Zusätzlich wurde in der Diskussion die Bedeutung von Trends oder saisonalen Effekten aufgezeigt. Innerhalb des Datensatz ist das Erscheinungsdatum nicht enthalten, sodass darüber keine detaillierteren Aussagen getroffen werden können und es nicht in den Modellen berücksichtigt werden kann.\n",
    "\n",
    "Ein weitere Limitation ergibt sich dadurch, dass in dem Datensatz neben Liedern auch Podcasts und Reden enthalten sind. Abschließend wurden nicht für alle Modelle die Hyperparameter optimiert. Besonders für das neuronale Netz in Kapitel 5.6, die Support Vector Machine in Kapitel 5.5 und die Klassifikationsmodelle in Kapitel 7 könnten die Ergebnisse noch verbessert werden."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 8.2 Konklusion"
   ]
  },
  {
   "cell_type": "markdown",
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    "Zusammenfassend können die Modelle dieser Arbeit das Regressionsproblem nicht mit einer ausreichenden Güte anhand der Audiofeatures lösen. Ein Grund dafür ist, dass Musik vom subjektiven Geschmack bzw. von einer Vielzahl an Faktoren abhängt und ganz individuell empfunden wird. Mit den hier gegebenen Audiofeatures kann nicht zweifelsfrei ermittelt werden, ob ein Lied das potential hat, beliebt zu werden.\n",
    "\n",
    "Zusätzlich haben sich weitere Punkte in der Diskussion in Kapitel 8 gesammelt, die nicht beantwortet werden konnten. Eine weitere Forschung kann sich mit Genres und deren Beliebtheit im zeitlichen Verlauf beschäftigen, beispielsweise Rock in den 70ern oder anderen historischen oder saisonalen Verknüpfungen. Außerdem können vermutlich mit Assoziationsanalysen oder Clustering weitere Erkenntnisse gewonnen werden, indem Personengruppen nach Genres oder ähnlichem Musikgeschmack geclustert werden und auf dieser Basis Empfehlungen oder mögliche Vorhersagen über die Beliebtheit getroffen werden. Abschließend sollte der gegebene Datensatz um weitere Audiofeatures oder Songtexte erweitert werden, die zusätzliche Informationen bereit halten. Besonders das Erscheinungsjahr könnte ein wichtiger Faktor für die Beliebtheit darstellen."
   ]
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   "source": [
    "## Quellenverzeichnis\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- Alshare, Somaya; Abdullah, Malak; Quwaider, Muhannad (2022): Increasing Accuracy of Random Forest Algorithm by Decreasing Variance. In: International Conference on Information and Communication Systems (ICICS), S. 232–238.\n",
    "- Bishop, Christopher M. (2016): Pattern Recognition and Machine Learning. New York, NY: Springer New York (Information Science and Statistics).\n",
    "- Géron, Aurélien (2019): Hands-on machine learning with Scikit-Learn and TensorFlow. Concepts, tools, and techniques to build intelligent systems. Unter Mitarbeit von Rebecca Demarest. 2. Auflage, Sebastopol (Clif.) [etc.]: O'Reilly.\n",
    "- Grünewald-Schukalla, Lorenz; Jóri, Anita; Schwetter, Holger (Hg.) (2022): Musik et Marken. 1. Auflage, 2022. Wiesbaden: Springer Fachmedien Wiesbaden; Springer VS (Jahrbuch für Musikwirtschafts- und Musikkulturforschung).\n",
    "- Jafari, Roy (2022): Hands-On Data Preprocessing in Python. Learn How to Effectively Prepare Data for Successful Data Analytics. Birmingham: Packt Publishing, Limited.\n",
    "- Mohammed, Mohssen; Khan, Muhammad Badruddin; Bashier, Eihab Bashier Mohammed (2017): Machine learning. Algorithms and applications. Boca Raton, FL: CRC Press.\n",
    "- Nusca, Andrew; Abril, Danielle; Barrett, Eamon; Bellstrom, Kristen; Clifford, Lee; Decarlo, Scott et al. (2019): SPOTIFY SAVED THE MUSIC INDUSTRY. NOW WHAT? (cover story). In: Fortune 180 (5), S. 84–92.\n",
    "- Sklearn Doku (Hg.). Online verfügbar unter https://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.RobustScaler.html, zuletzt geprüft am 30.07.2022.\n",
    "- Spotify (Hg.): Spotify Web API - Dokumetation. Online verfügbar unter https://developer.spotify.com/documentation/web-api/, zuletzt geprüft am 30.07.2022.\n"
   ]
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