Unsupervised Learning (K-mean and PCA).ipynb

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  {
   "cell_type": "markdown",
   "id": "6a257acb-a09e-462f-b78f-e926360d0dd4",
   "metadata": {},
   "source": [
    "## Digit Recongnition"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d7e28c0e",
   "metadata": {},
   "source": [
    "Model takes encoded handwritting images and tries to predict the digit displayed in the picture.  Data from: https://www.kaggle.com/c/digit-recognizer"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1062f7b9-e88a-4c35-a2ef-e321f4908886",
   "metadata": {},
   "source": [
    "### Import Libraries and Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "b91f048f-8213-4694-b763-4cfbb84ee13b",
   "metadata": {},
   "outputs": [
    {
     "ename": "ModuleNotFoundError",
     "evalue": "No module named 'utils'",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mModuleNotFoundError\u001b[0m                       Traceback (most recent call last)",
      "\u001b[1;32m~\\AppData\\Local\\Temp/ipykernel_15180/2630169644.py\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m      3\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mdatetime\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      4\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mnumpy\u001b[0m \u001b[1;32mas\u001b[0m \u001b[0mnp\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m----> 5\u001b[1;33m \u001b[1;32mimport\u001b[0m \u001b[0mutils\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m      6\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[0msklearn\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mpreprocessing\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mStandardScaler\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m      7\u001b[0m \u001b[1;32mfrom\u001b[0m \u001b[0msklearn\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mensemble\u001b[0m \u001b[1;32mimport\u001b[0m \u001b[0mRandomForestClassifier\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mModuleNotFoundError\u001b[0m: No module named 'utils'"
     ]
    }
   ],
   "source": [
    "#loading libraries\n",
    "import pandas as pd\n",
    "import datetime\n",
    "import numpy as np\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.ensemble import RandomForestClassifier\n",
    "from sklearn.model_selection import RepeatedStratifiedKFold\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.model_selection import RandomizedSearchCV\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.cluster import KMeans"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "a630e009-17af-42ab-b92a-c0ab7edb5482",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(42000, 785)\n"
     ]
    }
   ],
   "source": [
    "#loading training data\n",
    "df = pd.read_csv(\"train.csv\")\n",
    "print(df.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "4c330542-c8bb-48f0-81a7-9ec94296e19c",
   "metadata": {},
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     "metadata": {},
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    "df.head()"
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  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "6e19f034-e5dc-413b-818d-1e3aa88e7b72",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "(28000, 784)"
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     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "#loading test data\n",
    "df_test = pd.read_csv(\"test.csv\")\n",
    "df_test.shape"
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   "execution_count": 5,
   "id": "b6923af7-b5d6-45ea-b8d6-ced10938e9c6",
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     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "df_test.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6a1194bc-4c6b-4c15-bc07-d75fcbcf6a1d",
   "metadata": {},
   "source": [
    "### Management Question"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ea935c63-76d9-402f-972f-c88192406883",
   "metadata": {},
   "source": [
    "We would like to create a model that can accurately identify handwritten digits.  There are a number of business applications for being able to digitize handwritten numbers.  This includes bank wanting to have software that can automatically read amounts from a check image. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "390d1fce",
   "metadata": {},
   "source": [
    "### Standardizing the Independent Variables"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8a3ba935",
   "metadata": {},
   "source": [
    "We are going to do a PCA.  PCA is effected by scale so we standardize the data here and will use the standarized data throughout the entirity of the analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "a5bd845a",
   "metadata": {},
   "outputs": [],
   "source": [
    "#merge datasets together and then scale\n",
    "df_temp1 = df.drop(columns=['label'])\n",
    "df_temp1['source'] = 'train'\n",
    "df_temp2 = df_test\n",
    "df_temp2['source'] = 'test'\n",
    "join_list = [df_temp1,df_temp2]\n",
    "df_comb = pd.concat(join_list)\n",
    "df_comb.shape\n",
    "source = df_comb['source'].to_list()\n",
    "df_comb2 = df_comb.drop(columns=['source'])\n",
    "del df_temp1, df_temp2, df_comb"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "d9755c08",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(70000, 784)\n"
     ]
    },
    {
     "data": {
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       "      <th>pixel781</th>\n",
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       "      <th>pixel783</th>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>1.000007e+00</td>\n",
       "      <td>1.000007e+00</td>\n",
       "      <td>1.000007e+00</td>\n",
       "      <td>1.000007e+00</td>\n",
       "      <td>1.000007e+00</td>\n",
       "      <td>1.000007e+00</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>0.0</td>\n",
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       "      <td>-8.339086e-03</td>\n",
       "      <td>-5.342334e-03</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "      <th>25%</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>0.0</td>\n",
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       "      <th>50%</th>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>-3.295091e-02</td>\n",
       "      <td>-2.338733e-02</td>\n",
       "      <td>-1.675050e-02</td>\n",
       "      <td>-1.063784e-02</td>\n",
       "      <td>-8.339086e-03</td>\n",
       "      <td>-5.342334e-03</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>...</td>\n",
       "      <td>4.236282e+01</td>\n",
       "      <td>5.965323e+01</td>\n",
       "      <td>9.086908e+01</td>\n",
       "      <td>1.619808e+02</td>\n",
       "      <td>1.634635e+02</td>\n",
       "      <td>1.932091e+02</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "  </tbody>\n",
       "</table>\n",
       "<p>8 rows × 784 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        pixel0   pixel1   pixel2   pixel3   pixel4   pixel5   pixel6   pixel7  \\\n",
       "count  70000.0  70000.0  70000.0  70000.0  70000.0  70000.0  70000.0  70000.0   \n",
       "mean       0.0      0.0      0.0      0.0      0.0      0.0      0.0      0.0   \n",
       "std        0.0      0.0      0.0      0.0      0.0      0.0      0.0      0.0   \n",
       "min        0.0      0.0      0.0      0.0      0.0      0.0      0.0      0.0   \n",
       "25%        0.0      0.0      0.0      0.0      0.0      0.0      0.0      0.0   \n",
       "50%        0.0      0.0      0.0      0.0      0.0      0.0      0.0      0.0   \n",
       "75%        0.0      0.0      0.0      0.0      0.0      0.0      0.0      0.0   \n",
       "max        0.0      0.0      0.0      0.0      0.0      0.0      0.0      0.0   \n",
       "\n",
       "        pixel8   pixel9  ...      pixel774      pixel775      pixel776  \\\n",
       "count  70000.0  70000.0  ...  7.000000e+04  7.000000e+04  7.000000e+04   \n",
       "mean       0.0      0.0  ... -3.823623e-15 -1.137216e-15  2.825315e-15   \n",
       "std        0.0      0.0  ...  1.000007e+00  1.000007e+00  1.000007e+00   \n",
       "min        0.0      0.0  ... -3.295091e-02 -2.338733e-02 -1.675050e-02   \n",
       "25%        0.0      0.0  ... -3.295091e-02 -2.338733e-02 -1.675050e-02   \n",
       "50%        0.0      0.0  ... -3.295091e-02 -2.338733e-02 -1.675050e-02   \n",
       "75%        0.0      0.0  ... -3.295091e-02 -2.338733e-02 -1.675050e-02   \n",
       "max        0.0      0.0  ...  4.236282e+01  5.965323e+01  9.086908e+01   \n",
       "\n",
       "           pixel777      pixel778      pixel779  pixel780  pixel781  pixel782  \\\n",
       "count  7.000000e+04  7.000000e+04  7.000000e+04   70000.0   70000.0   70000.0   \n",
       "mean  -3.964385e-16  1.831964e-15  1.212366e-15       0.0       0.0       0.0   \n",
       "std    1.000007e+00  1.000007e+00  1.000007e+00       0.0       0.0       0.0   \n",
       "min   -1.063784e-02 -8.339086e-03 -5.342334e-03       0.0       0.0       0.0   \n",
       "25%   -1.063784e-02 -8.339086e-03 -5.342334e-03       0.0       0.0       0.0   \n",
       "50%   -1.063784e-02 -8.339086e-03 -5.342334e-03       0.0       0.0       0.0   \n",
       "75%   -1.063784e-02 -8.339086e-03 -5.342334e-03       0.0       0.0       0.0   \n",
       "max    1.619808e+02  1.634635e+02  1.932091e+02       0.0       0.0       0.0   \n",
       "\n",
       "       pixel783  \n",
       "count   70000.0  \n",
       "mean        0.0  \n",
       "std         0.0  \n",
       "min         0.0  \n",
       "25%         0.0  \n",
       "50%         0.0  \n",
       "75%         0.0  \n",
       "max         0.0  \n",
       "\n",
       "[8 rows x 784 columns]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#apply scaling to joined test and train data\n",
    "col_list = df_comb2.columns\n",
    "scaler = StandardScaler()\n",
    "model2=scaler.fit(df_comb2)\n",
    "df_standard=model2.transform(df_comb2)\n",
    "df_standard = pd.DataFrame(df_standard,columns=col_list)\n",
    "print(df_standard.shape)\n",
    "df_standard.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "7f499448",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(70000, 785)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_standard['source'] = source\n",
    "df_standard.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d0cadef",
   "metadata": {},
   "source": [
    "### Experiement Flaw"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "40304295",
   "metadata": {},
   "source": [
    "We should not be running our models on the full training data.  We apply a cross-validation approach.  I apply a 80/20 holdout approach below"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f36da996-c912-40b5-b59a-97ca101a0170",
   "metadata": {},
   "source": [
    "### Training Datasetup"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "6d02e287-0c74-4ca3-a0a6-82a719bfe8f0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(42000, 784)\n",
      "(42000,)\n"
     ]
    }
   ],
   "source": [
    "#splitting the dataframe into explanatory and dependent variables\n",
    "X = df_standard[df_standard['source'] == 'train']\n",
    "X = X.drop(columns=['source'])\n",
    "print(X.shape)\n",
    "y = df['label']\n",
    "print(y.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "cdba1610-2a8c-4548-8dfc-7b4695651153",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(33600, 784)\n",
      "(8400, 784)\n",
      "(33600,)\n",
      "(8400,)\n"
     ]
    }
   ],
   "source": [
    "#the assignment doesnt ask us to use a cross-validation approach, but I am going to anyway\n",
    "#I don't want to have to submit every model i produce to Kaggle to evaluate.  As a result, I am using a cross-validation approach so i can compare different models on my own\n",
    "X_train, X_ctest, y_train, y_ctest = train_test_split(X, y, test_size=0.2, random_state=0)\n",
    "print(X_train.shape)\n",
    "print(X_ctest.shape)\n",
    "print(y_train.shape)\n",
    "print(y_ctest.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "913af52d",
   "metadata": {},
   "outputs": [],
   "source": [
    "#and while we are at it also outputing the scaled test data\n",
    "df_test = df_standard[df_standard['source'] == 'test']\n",
    "df_test = df_test.drop(columns=['source'])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ec5dee9d-0c3c-46cc-958b-5bedd0c57301",
   "metadata": {},
   "source": [
    "### Accuarcy Function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "160a7f11-1c64-4127-ba31-57f65d2633a6",
   "metadata": {},
   "outputs": [],
   "source": [
    "#bulding a function to evaluate model accuracy\n",
    "def score(predict,actual):\n",
    "    return sum(predict == actual) / len(actual)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "71b46943-03d6-474e-ac6c-648ea9ae2243",
   "metadata": {},
   "source": [
    "### Random Forest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "c6afb0d9-adef-4ac7-89bf-27497ad2fbaf",
   "metadata": {},
   "outputs": [],
   "source": [
    "#training random forest with default hyperparameters\n",
    "rf = RandomForestClassifier()\n",
    "rf_start=datetime.datetime.now()\n",
    "rf.fit(X_train,y_train)\n",
    "rf_end=datetime.datetime.now()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "7cbd3a5f-5a85-4fba-a623-cef5fc6fc574",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0:00:21.230343\n"
     ]
    }
   ],
   "source": [
    "#time to fit random forest model\n",
    "print(rf_end-rf_start)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "d83fc2e9-7f1f-40b3-8936-b323ab692759",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9651190476190477"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#evaluate accuracy on holdout data\n",
    "rf_predict = rf.predict(X_ctest)\n",
    "score(rf_predict,y_ctest)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12486fc8-f0df-466b-9a6b-b91dd41f3637",
   "metadata": {},
   "source": [
    "Random Forest with default assumptions accurately predicted 96% of the observations in the holdout data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "7cd98b5f-dc07-4c9f-a4c4-51f9d5be241e",
   "metadata": {},
   "outputs": [
    {
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      ],
      "text/plain": [
       "   ImageId  Label\n",
       "0        1      2\n",
       "1        2      0\n",
       "2        3      9\n",
       "3        4      4\n",
       "4        5      3"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#generating a dataframe for kaggle submission\n",
    "rf_out = rf.predict(df_test)\n",
    "df_out = pd.DataFrame(data=rf_out,columns=['Label'])\n",
    "df_out['ImageId'] = df_out.index + 1\n",
    "df_out = df_out[['ImageId','Label']]\n",
    "df_out.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "6500ce9d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(28000, 2)\n"
     ]
    }
   ],
   "source": [
    "#checking the shape of the dataframe and creating the csv \n",
    "print(df_out.shape)\n",
    "df_out.to_csv(\"RandomForest.csv\",index=False)"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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f+7tB30osXJEZj4Q8g5hywsiZwfButl/j8VQkfFokIk7L602s7edqufYJlPJPsWDLa0hpSILYwq/3LDwz+mH4Odtqy1phLEdW+mtY+o16w6tsETJsG17yu4pJlMPRGBAUr80002sM3kxZjYDOyiGYyuIfhUMbAsUtdLVVYPMMP4RlarPNPbUFJ8K8tJlrr2JHOKavy8egp9cjesLVrx0iIiIiIrr+GQ/H4tE/rkF+jbaggQ4jX0vHhj/8PP8obBTx4UQRHxZp8ybuIk5LE3GaTpu/RFkq5gQsRvpZbd7Ezh/R6XGYYlYdxqNr8PhjschtVnf6CSuR9rdJcLGURDm7GwtHzEOK8h2xzyyxz77KGqCuAllrlmBObDZkWuSS9eZa289VJhMo1+4tPJWfY7l58qSLJ54Zuh5/D5nStuSJpHOGX0As9gYsRUjDnVCLhC/m4u38Wm3+KvKNQFpODo7IT1Y63nzSTb2g0anahf+/LSROO3fzzwIvbe11oqYC+UcLcPqSByMREREREf0yFSNhmUye6DAyIgVHCgtx4ptCHEmJwEg7IzKWvoKU5omEnwNjNqL+KJMnbghNyFHO6UROAkJFmFr07hOIymzS7cOMAemvL1OSJ96LtjTUx+dR/tDVZCLs2cTGBgt1BYhbLJMnbiIezMB/5LY5W7BEhIGGHcuw+jNLkbDY/4rFSBH1rbPTFjWoQMpsP0yLzYXL1ECM1JZa1tp+Ose1SaD8VI6UlJeQYJY8eXHMa3jut64tZ8Raobv9IbwUHIvnGr5cgjc+exUZldrs1aLToU8vPfTy09cNAYsWI0Au35GLHLN7s+JwMqLmBGBigPiELEZMagEMddpK5CFOLg+IR25dGTKi56nbzYlGSsGlN1/FgXgsDJHbhyDio2K09CugNNtaru0rYB4ikrJR0XBMoWI3wuS68N2oqMhG3JIQZds5b2vbie83LItORZGFBITOQTt384/ZjWwoSEWMto9Lz1ttHSLXhe0oQ+neaMxRprVRcOoMyE+N1c41ANOWxCOjuFl9NNtm4pxIJBwwjaJTgfTwAExfma3MZa2cpWwTl6fMWnbJMWMvvQYyO5oUqZT1km2MeVgVJJdHNsvclmGzcv1DkVCsLSIiIiIiomvjVC6ylf+XB2P+kx4N3U709wQj/LW5mP+MO3TmYUCzGGDO8kRkndLWmbQhlsh9V10XlyeHRViMacq0trL5MaKTkWt+DGV9LBKyWx411LA3GQkybpsWhiXDtX4tvXyx5E/BYsKIhG37LP+h3yjqI1VGljOxZK5XQ324TA1D+D1iIi9ZxGLqMuP+ZMSIad2TEQgf1Q86uW0vL8x/bbWot5lwsnAEY6aoF7F/lxkRWDJUW2jmom4MItOykBYVCHdtmSXW9tMZrkkCxXBwPV763tRCxBUhv16O0LuvsMuN3hvPPLwUAaYz+ukzPP/ZwZYTDFeDzhYOykQVjNqBSz8KxYigcMQd0hYU7caqZwMw4uXshrJVHC1A/tFcJCwehxnJeThdLOZ3xWPhxCCsKtA2EoqSQjAiJBopB4pxuq4KO1eIX6x1l0bkxrw1mPhgCCKS9ontxIKKfUhYHoKh46Ibm1mJ75+Wxy1Jx18fD8GqzHylpUZ6bAgefz0WEeL7q7KLUCSXvbsYE5fttvzL1oKK1HkYMXExVm3LV87TmJ+qnPfQ2ckoNSVRtNYhpbtWYkZoPNLFtNpSpAIpz47ExGfXIF1re1a4KxozRgch6rCp1ozIfT1I20YHd/d+MB5KRETISMzY1p6hiBuPmZIrv2/EsW1rxDUYibBd2pnXlWHz7JGYJh+YNf3EMXWiXHKbIMTkiXLpPODtWSzOKRHp2Wa1VZyJ93eJuj7rBR83bRkREREREV0bTu5wV/7wm4hV7zX9I6/7hEVYsmgRxplGuZB/JA1QY4D0MvF//roKZCRFYtqDAYhriNXMYol8JfrRYgk/zPioTN1EqpRxXwFy/74Cjy9PRZaYVv54bXaMLCUeMiLr3XA8+mAoNmtfN3wWK9avQcS0eOSqiy5R9K9U5edIb88mDRN03r7qH/pTcy/p2qMwnGtoYdK1SfcbPXTKS1pEmb9W45v8vGTlZ8gYX+jkOCjvxiImNhYJJ90QukDUXfPxMGuyEfPnRBj7zUT0Yn8LY3Y6YcrfViPEw8pAJlb30zk6P4HyUyE2534mbjGVt+sLeNHPWZtrh58qkfvPfDW4d34Ir//24YZxQCq+W49PTmozV5uxArnvrkGCnPbyhqdyRctQdKIHfIYvwsf705GWkoK0/VuwRNxThveSkdEkI7EbhsEp+E9OFg4dyUHSDHnjFWPVLi0leTYVMctl0kXcmFtycCgtRWyXDv+65oORiCD/5VjkiwA/NEHsS2yXlpWDj58SkXtxPBbGm2VkpOw89IlQu9+cSA+Dt1hU9O526N4Ry7Ky8J/Po5RmVMZUUd5meYnNy9TsaONnDXKVB0A2VikJF39EZuRgjzjvPYcyED1KB+PecETtaHLiyNp7Dk+kqU3MNvzBCcYDa/CC2Eb38Ers3y/KL75/KF2Uw64YcYvjka884GRiRyaPZmKDqNM3Y1Zjz/4EhA4fA/ezReL+csK4qBRsXOwrN4bf4vXKfkJb6GFkOia8FiHtUJbYNh1HMiLEuRuw+a+JUIYMrsjGrr3igegbhbQ9q8Uxt+BQShTGjRXHKJOtgXTweyhYeVil7DrYkHAqPbhd+b7nzLHwVBcREREREdG1YuOFJ16TrR2MyIgMwOCBPhgtW8x/lI2ipqEKSj96BTEF4n/6IjY5dEjEdGkixkqYCZeaAkStU//I3BBL+Efgc7mNjCVkHNVCd6D0AgeszVK7yYQPaTyG9yIR9+yR8U86Dm2ZCXfZfUYbHkI/2B8hwz3gt6ilmKIChcfVKXeXZmM/6p3QR5koRmHzljOSkxu8lbzHLqRnm/5gLZTswi4t3DTUyOUVKBXlBDygOx6N0X5BonxrsOrtNYgIHdf0j+UKI3LXRSKuTIeQvyyCX0vdbiyNmdJEG/fTCTo9gWI4uAkv/6DN3PQgFvy2aXbssvxUiayPFuLhQ3Pxu4TPlRtLNyQEyxvSUYVYeugqtkLJDMfQ2wdigPzc7YdHY/MAOw/MXxYIF2WDfhj5/EokJcyFt84Iw1kDKk4Wa8mjc6hq0i3GH2MnuKl1YaOH36ixylJTSxb8Jx/p8uekxZg/RKsxm36YEiKbY5kpE0G+zLncMxNBpmZbYq/ewTPhJ6ZKkzPVZECDsRhn2u4Ob/goE2bL+vlC5geki01+GcS1lC1ljpp/8lAoTy53n9Z0bBqmmDK3sqwz1LKmf9aYXFBMndEk45iTmSiumRNCH34AOoNBqTdDd38EPSxWlh3EsXJ1O7XfWya2bxIPulMGGHW+CE9YifAZvg1JtLZSjwmEPDMTnqZfSNdgrP0qB0dSguEuz92mq7r8SDK2pBag9Kz4hlsg1q6NwJJJ4iEi13mNRYj8fmq21o2rAll75QXxQpA/m58QEREREV0PXCZEYU/WFkQ/NQaefY0oOpCKVUtDMPq+ccoQA6oyZO2Q/5f3QPjcSQ1vW9UPD8MeOf7jigeUlhANsUSIiANNyYB+gZg1VU7sRoZ563TBb+ZMjGwY+NR0jDEImtAPRhn7iI/RbTKChojFO/JxTMYifccgMiEFSc+0MhBsu3kgJGyS2G8Z4qaJuHZJNGKWh2LoQ4nAKA9tG5UaExZg1evFDX8EN42BIv9YHmHeG6AgHi+8XQzdpJVY4n8Fpe6o/XSATk6gVCOn6DNtGvB2eQR+t2gzl0tLnjz2XYkyW3FmOZ5OLRQ3riPGeTW2QsF3B5FjSth0NDsneN7jIT5uWhMif0R+moIlpgSHYChIRkSQH+4aOAiDfXwwdPQybG7L2Cw3aT81Fd9pXXWcnZo0V9L9ql/TfmKnipElf/bWad2JNP3c1UxlmfhlVBa0lTiXFu7R0C1q1rTxo46A3FDW7g5NvzrATR0U6FxV0zLcqCUmFBUo/Ub9uSrER6kz9eOHOUlyeTaKlaypF+b/fRG8exVj83LxoPPzEXXsg9Fz1iCrWUsZ60zHFKdq3/RkdXp1bBelb5/TJETGiAcn8pTuSPf7DMKAQeIBszy5cYwYGy8EPC3Tt8nI/FKc5dmDyJRZW6/JGHkN3xZORERERETN9PXClLDVSMs6hhPHMvDxS7JViogv5i9GghJmVqBYGVKxD3Td5c9GOmUMSBk7tBxLDLzLX/mptt5opLvRfDvTMXYjbLR5/BOAqMNyeTFK2xTf6NHnVnXKWN0s4qu7qE30Q59e2mQz8g06+5MWYZwbkLstEZu/7oH572/BEm81+eNysxqFmrr4eD4f1vhHcDkGyrKZSuyXseugOCOhrhgJy2NRZOePV5eNaX+Xm47aTwfp3ASK8Rj+eUabhism3N3O1ifNkieS9y0v4bWHBir70903Gk82nNk25PxHm+xoQxdho+yWIz5rn5RHzsT7O8y6yJxNxQsTw5FQ0A+hf0vB5zk5+E9hBiLbMeCNzq6HOvGj6ebXGCqa9mOz06utX8TvTJMtK8os93e7Closa3mZmtxplQ4OytfdsGSL2rWo+UdmNyXdkLn4+NAxHNqzBRteE7/Aw4GiXbGY9vgarZtPW5mOKVhJtrnIpntHjuHzlAS8+dJMBNwmB4AKbzJGjKe/bIFkxOYDBTBkZygth0Y+NlZrlURERERERNeS8VQBsg5kI+u4WcsQu37wnhaFyBlyJg+ZX8o0gA56pWuLCK5+lD8taTmWKC1VX2jROtMxJuHNzy3FPzH4fZua1+vg4q62Fsn4d7NxMk9qf2S/xw0uLQTgsuWL7q6ZWLtHtioRMdaWlQjxMuLYl7I1jj887pJfdIKLh7qDPt2bpTJ6aX/YNyVr8pIRIRvWIB9xT5uGfJiFmENyWTZiZon5d5UNWtdR++kgnZtAKSlsDKBv+g182vMX+RaSJ29NvR8uprPpMhA+Zi1bcv6r9fm4anTwe1qOlyEC+NdjsdnUr6xY63YTvEzp4uEiWzL8WIQC5WJfHr2ntzI+CTbtRkZD1x8jstJ3adMaNy+MlF1Isncjy2y8IsPBdGTIiUnerY5s3BEayrp7nzYIkir/wHal5YnLrz1b6WKjh+dQL/GzGBn5FWZv+NGh9MAu5OQX47R8eJ0VD4G9yYjbXgy9POc/zETkxlUIlbsozsOxZlla44/NsrDi+/kNb/UxHRNI2JGplFFRk4mIQbKLVjSy6sQ+yvKQlZqIuP0GuNzji4BpYXjznQila5TRfECme/wRJB6CxsT38ecdciCnMQgYdbmdioiIiIiI6GrQVWYiLCQE0+ataXzJhlRX1tCaRG1x4QbvUTJhkI0te82SEsWJeFQO4zAtGaVmsUT63sYXhcjX/WZtk3P94O3RWixgOsZu5BbpGuMfvQE5e/fhmIiJjFqrDzmEQvMxWsy5+05WYr3SD7ebxWEiZvwwXhnGwf0h34ZYsOm+yrB5lmz1Mg5RZmOgGA/HY73Smv4B+GldjrwfnKv8YThDxE3m453k71DHjWyI9Wy03hpuVxgHddR+OkjnJlAunGscf6Oba4vZrxa1JXmisIWL40BtWtxAF6q1qauobyCWPC/HuBBB92otCHcSvyzyZ+IriEnNRpbsVxe6BJvlssvlOhmhk0SF1SRiTtBiRMXGIurZIMzZp2vaskHni1kr/KET5QiTrzpOSsbm2Hl49NndYqUbljzdCc2eXAPxJzlobVk8ZoiyxnyUjITwIDwaWwbYTUL41Kb96JpzeXiZ8q7y3MggTItORoaotzhxro8+G44ZseIOkveN3WnsEvNRSxZj4bupom4zsfmVWG0Q38ZfcFNrmKzXwxERm4hc+ZCoy0PUiHGYONoPMVqy0nRMY9J8cZxoxMRGY2HQfGUsF/dnxsJHPLR0dfmIeTYSUfPnIeqjTOV6xv01XkkK6p58wGwwJw+MmynOsSYVKTvE7IRxGNlCUzkiIiIiIupkd07GPJm0KI7HoyIumLM8FjEvL8ajQ0ciTCYM3OYiwFcGHTr4zYxQ/kCtxCZyu9hITAuKRK5YN/IP/kosZoolSjeEilgiFps/SkTYY0GIEeGPbtIyhLQa/piOYUTC/CA1ttmbjKjpAZixdDFm7D2thD84HI2howMw2i+2xbfw4I5gvKrFYdNGiFhQxIwRIX6YtkHGYcEIDxbrpEv21Q9TnpEvw2gcAyVizjgMDYpHkYgh579oGuNTuEfEvbLuMsMxOsAUlwaIWK+4aaznNVPpqdH0s157/bAvlqwX80+piadWddR+OkinJlAqKhsTH7iph3ojmCk99Bnyz2szzbU5eaLqepPyviVF0dnypoOWXiWeT4YpA4gak6LVV1q5BuPNVYEisJZjZoRgWsgKZA9f1s53Vusx7pUURE5yAgpE4P72Gmw+OxkfrJ55SYsSlz+sQtpr4rjGbCQsD0fY27tR2tcf4eJmm9967qKD6OD9/PtIWuQLnSjrqqXhiNiUB51XMNamr8Q4a8kEOy+Ef5CAJcOhvL5rRoj4xUwthvukCKS9H6z+8soBY7dGIcSrAunRi0XdhiJsQwH0o8Lw8UZtG0E/djHWil9i3VlRF29Hq+8vt9HD6TZx99l5o5+jul3jMXXIT43HqrfjkVIgHmaLEvDBAm2gJnE930lahJH6AsQtDRXHFOXaVQHvaSux50VxrsqOVO7+gWryTAiYoA4uRURERERE1wH5got30rHhKX84GYuRnrQGqzakIvesHt4PR+DjjxfB2/Sf+36BWCvijikeRmTJ7d5ORJbRA1NeS8Hah7VWEU1iiTUIWxqJzYdFTDRtNfasbMMfsE3HuK0YKTK2CQ1H3AHA76m4xjhD76S8elk3uF8rrfnVOGzDU17QK/HPGiQcMECvxGFqIkhhYV86/whlDBS/XgbkbotHwq5iGD0CEZ0mB4g1j3ScEPBOhoj1/KE/qcalcakF0A1fhKTP2hDr/czdcLzoZP1At84Z3bIi4wUM+eqgOtP7JRwNub/hZir9xwt4+MhBVOimYNuTc+FtPkjPZSZPpNaO1enqjDAYjMqApMpgpFfKaIDBqINeb34jWyb7shl1euhNvyydTTt3OTZLG4p7KXmuNeIXurW6a8s2shw/ijozlUHMy9cOW9y+LfurkdfAyjZERERERHTdU2Im8dPq/+2VGEB2s2klsGlLLNGa1uIM+YpWXRuDKlMc1lIs2Mq+jAZRHze2IYa80ljvZ6awuKRzW6A4OZolan4419A/zJi/Hn+UyRNlZjMefu995JsG4GlH8kS6+EPDaLXw7OV8bVsA2Kh92Tos0Ja/BG28Q5XRoa9V8kTSzr3dv1DyXK3VXVu2keUwL4OYb3H7tuxPPiSsbUNERERERNc99Y06bfi/vRIDWAls2hJLtKa1OKOtyRPJFIe1FAu2si+ZvGlTDHmlsd7PUKcmUNCtR+M4EYYSlGqTOs9Z+Pt9v2lsimRcjwlxMonSvuQJUIvSykJtGujTzV6bIiIiIiIiIiK6fJ2bQHEdqLyxRPU5co5rk4LLyFexrXkSZdXD7UieCD8VIue/2jSc4XNL43goRERERERERESXq3MTKLpB+G1DLqMc6/7d8E4exSVJFDNtTp4Ixq/24L2ftBnldcm22gwRERERERER0eXr3AQK7OHj/qA2DVR8sxUZzV6PoyRRBjdNolxO8gSoRHreNnU8FcGzz28wiK9AISIiIiIiIqIr0MkJFEDv8wieu0mbwWd4/rOmrVAkl981JlEuL3kCGA8n4KWGpIwnnhz6G75CloiIiIiIiIiuSKcnUKDzxFSzFiYVJQuxPKtam2skkyibfvvqZSVPUP4pnv9nY+sT71um4ne3aTNERERERERERO3U+QkUwem3C7G8p2lcklokfDEXcV9rs2bch/6m7ckTQy7e3vYaUkxjn+gewoKR91scT4WIiIiIiIiI6HJckwQKujgjIGA5QhqOXoKXd4RgeVa5Nn95jN98iuWJi/CGUVvQZSCe+c1cjHTW5omIiIiIiIiIrsC1SaBIjvfjpaClCDBLoiR8MRXD4zcj93ttkTXGcmSlLMKolNeQYEqewBUhv34Jz3nba/NERERERERERFfm2iVQJOeH8FbQSwjRafNCqWENHt44GqPefQkJ/ywU87XaGpWxuhJF+Z8hIXEuRr0zFY99k4tSbR26eOKZEa/iJb+r3/Sk+uudWL04GDOCg/HsnzYi95S2wopj64Ox6ag2015FSZgxdgX2VamztdXVqK1TpxV1tai+oE1froqdeDVyJyq1WXMdUnaprhqFO2Pwoqi7GcGz8ZeNX6DSrPwddpxWzqXDVRVhT8zzyv0wY/afsCmrbTdE5c4VeHXnlZawCJsem4BX92pjCTW//nK+uunvUdtVYl+kuNdMAwuZqd67AqOCNqJEm2+PS+5dIiIiIiKi69S1TaBIzvfjpdBNWHfLQLPxSmpRdP4zLD80C8PjR8M19oGGzx1xD2PU7pewvCIfRabxTgQX/RT8/ZE1eG5IJ/TbKViH2cvz4L3wHbwT9w4iptli04w/YV9b4uDqUzjT0FqmnQYEIGL1bDzgIGdOYfcL4dhtHuDmrcP4dXnazGUSwfaZ0y0E2x1R9rpTSFsUhJVFXgh94x28tTocj+AjTA/eiEJTIN0Rx5FaO5eOVFeAhNBwHLvvGbwVtwFvrZgG200z8JfdbbghLlTizIUrLaM7Jka9hVB/rdVV8+tfsRN/eaG9iaRanDtdiXMWkhz2/rOx4dVAuGrzl8/CvUtERERERHSdsnlmwcIVvR17arPXiE0PuN8zGU/eNhh9/luGopoKNLyJuFW2cO85GWG+K/DKuN+JaW3xVVa5PwFHBi3AjN84wuYmW3Rzuhc+Q+xh170fenYDyne/jdwuw3BbL3V78/nTBxNQ0v8R3HIkCcnpX6Hcxhl3/EoNfKvzkpF93hU/fJGErekFuMH1XjjXFWFPYhL+kVsJvdtA9O4qNuxyCkeSvoZumBNKNm3E9uyjKKmswMnzzvDpkoO4D3bjyPFS1JVVQneXJ/rI75zKQ9qmj7Dvn0Wo7XM7XHqZBvEVTn2BrRu34UDRefyqdy0OfgEMf+guiFNposWy14oyrtmPn+69C71Nr6gu2om4rBtwzx2ijrRFUu0/38Li/wXjvecfQG97W9h2dUAfrzEYcjoSH1ZNxANutupx+o7BjZ9vRNq+AlT2HAi3mxvLW/n1Tuz8MB0Hjp6C7ld3oY+WNyjfnYySrjoc2ZKEIzd44u4eJ7Dnc7NzaaUOKg+nIOXjPciWdXD7APQwqx6rTmch6fC9mD9/GBxusoGtvRPuHjIMPey6wdmxm3Jd00654m5ndafm8xf+vRMHMAI+hhQkbtuHkmpnuLg6wFZJbX6LfZu+gf7mb7FTXJ8jlb1x2+2OqD6YhMRPxLZ1Yh8u6smf+TIJ/75R3GPf/6Pp9f9VLQ4kbcWBghM4UyHPW7sv607h2CfJSPnsQLNjqutyP5R1L7Z37oML/xQ3xAPjcYdWzw3OFeIfmZVwGeSM2lbOUbq0fqtxrPm966ZkBBs0/X0Q95utK+5wNrsrLV1P5V78AjcOGYie8nwqxb29/jh6DhPHVL5zAJt2nsFtns7i6UFERERERNQ2lWerroMWKGZ0zt4ICV6DA3M3Ycdvl+Il5/vh180VLtp6JWGiG4hxTlPw0n2vYsfUT7F3+kJMuc8Zuk48E3unvji6Mxm53zW2HHC8cxhcHdXpMwUpOHZGnZaazx9b/xb22Y7AowH3oXb7c1i6Ve3uUXtiP+LeWIejTqMw0acScbNn49k398N5TAB8sROzX94JtZPGGRzbmi/+tUXvOz3gam8PV4+h8LldRLgO/eFzZ2+gjwd8fNzRW0aJ36Vg6aIU1N4XgEfHOyI3fDbi8rSyF6xD8IKdgG8AJnqdw9bYJJxU11hksey2/dG7eh3SDjfWx7G0t1EtytI8SD2e8w9MHD38kuUD536CP49pjND3bUzG//MSZfK1R+7yBdj6rbq8MmUBpr1RBOfxgXjUrxZbFzS2/DlTkITolxJxbsBQ3NGn2RFaqYPq3X/Cc9sBn8DpmNj3IJ5fkIzLGs7YoTecT+zEx1mnGrujOLnD2129IeR1PXii8VXdzedP7nwbH57wwMTA8XAuiMKCt/Oglkxc500xWLX1PHwCRsF+33N4fvaf8GHVMEwc746SN2cjQevq1HCPNb/+3Z1xh4cr7O1dMchnKG6TOQqlFdBz+LT2PuWYPXLCsWCNdkzZmuaxBdhjMxwTA7xwZtMb2PSdXGHBhW9xcP+3yvdaO0fL9Wvh3m1G+X1Y/gayxe/Do+P7ovCVGVhtuseaXE9nHIuaLdaJ49n2he1367BPe6tX9eHtiN26Adkn1PnKrC3YV9cblx6NiIiIiIiodddVAqWBzhmeQx9CyNSX8OHsBBxYtA8lymcP9s5dj3XBcxEy8jfw1P663dlsR4QjaZY90pYHYfzvg/FijAhe2zgGimQcFoSQUe5w7O+FR5bNhvO6ZBzTAu/eo6bhkSH94ewXiIdurcYDIdMxqH9/DJo1HY8cLmqW3LCFs5cXXB0c4TpkmBqwO4rA3aM/cKsHvP284NytFrkJSRgUvkLZr6P7eMxbMQrZmw+gWoS+2VtT4LtUXefsEYB580Zp+7bMctlt4T16PHYfOKQG4RcOYM/u4XhgSPPrcwonC93h2k+bbcUDs57BRHEezkMCERJoi4OH1Qp2nPgGUt55Br7ufeHoEYiJQ77AsW+UVUI1fKeLcxk1DINuNT92a3UAnPw6D3cOH4WBfe3hPCociXGBsNQRrPbbPBz7tjFJ0KDbcCx6bzp6fBqOwEm/x4zFMUjTytsW5c6jEDpVXKu+7vB9JhwTD2/EbtPXq7ww8enfwbW/Byb+YRSOuY5H6Hh3OItzeHJqfxwrbHac5tffsS8GDXHHzQ7u8PFTk3y1WRuw6a5wvKAdc/SSFRjzxUfIrhLr9n+C9/yWqevkMZcswBht1+1luX4t3LsW9H5kNkK0axY6yxP7corEUnk918F5brh2PX+H0OUBOLZmJ8phD58HBiLzsMy41eLooXOibl1xME/WU7WYr8ToYaJ+iIiIiIiILtP1mUD5GXAcNh1/3vAJdm55C6H3fYvVMxZgTxtjZh8Pd21K6OaOge6FOKmNA6Ez7+8CR9g270dz2Srx/8qq8XGUOuCt8lmRgpJz50R4WYkz5c0SGk59cZs2aUmLZfcahce++Bw5F0TYelj8nPh7eF9Sdkf0di5CSVuad5jVg87GLBly4RRyNsXgL7PFeTwWjMhMbblJk/ozaa0OgEGPPAdsDELAY88jdn0KjlkcLKQWx5L+hGc35SvfuYTTMEz96wakpG7BG3O9UL5uBpamtO2G8L7Hw6xFTn/cMaQAJWXarFhja35O9t3Ntm2f6opTKN8d1VgXT67AhxXncE5cu+rKU/Dpb5Y+snGE463adDu1rX4tM/99sHfsi/ILcnAceT3FvTfQrCb6u2PQiVOQjXDsvYbj5i/yUFmXj9xvhuGBgKHAoQJUX/gKuWXj4TNA/QoREREREdHlYAKlHZq8OcTWEa6jnsGfp9dizxdtiwzPVJm3YqhFbVUP9LjiRElr+iP0jURsSNQ+H36CvasDoHUwAcwHCK2rRWvjt7ZYdhsP+I45hIOiDo4d+ApjRniomzRhizs9PLBPBLPNlW8VwbXVQVerse+153DQKRCL35LnkYi/trl5RCt1cOvv8MKHO5CyYQkeGfAtVgdHIfeStxjZwnvZDuxdOuzSBEZtdeNbb2xs1RYRK6bDuPeLNg3cWl5pvlUtzlXbo4edNnuVDJr2RmNdiE/Krrcwsa+6zth8wFiLGaPL0Kb6vVyX3rcNF6avF35z4RCOZh3CsWFecO07DPefO4ijX+QhZ4SY1zYjIiIiIiK6HEygtENJQjCeTZBdCTR13yI78xQG3a51QxBBdEmRNmhH1RfY16yVxJ6UnSjXgr/aL5KxyXk4fJqOn3kZbKGzqUS19kpjhY1YWnlWi3v7wmdELT7d3Vje2sMbEZtcJNar6zYlm8bcEOe2eydytWlLWiv7wPGBOJq8ApvyA/DAPeqy5hzHT8fozBWI3dvYOqP66yTErreF9xDL3TgaVePcGUcM9OwPexks1xUgN0td07rW6qAax9ZHIU2OkdGtL1z9x+MBp1M4Y6GnTotE+WfM24gSs4C+fP9+lN81UE3QiOtxsqgE1XK9uFcy9zZNIJXvFHVuOt53Kdh2eDx879Tm26PJ9RdkK46qxjfpOA4ZgVpxzIbyVudh08vJKBRfUNYlJ+OYqTxf78SnZrd6i1o8x9bq18K92yaX3rflKUlI8/fCHcpcf/j4l2B1zF4M8pGJvL64Z1gRVq/Jwxg/S4k9IiIiIiIi65hAaYeBIW9g9NfPKeOfyC4QAZMW4NiINzBVSxrILgu9U2Zj1IQJCHj5FFz91OUmU/1tEad0nwhC4JvnMG/h+CsY1NIRvoFe2L3o95iToAWt947HvNNvIOD3UdgnglPnwChM/XYFAh7VjhlTAm8/d+UP9nLdk6ciESjXPToDm/oHYKq6F4taLfuAEZh4oQDnJo5o+a/83bwQunoJeifPwIgJQZjx+wkIjCrB/bHL8IC1/IkIhMdM98TWeeJ7sgyhe3HuLm2VFS3XgT3uGOaMPaL+lH0GheN4wHMiyNe+2Bb3TMPrY4qwQI5/Ivchzmn2VyPweogarDuOmo1HvonE+EnifghOge2QpkG8b4A7chbIcol7ad5eeL80DQNl0qO9ml1/OI3Aw/fuxWx5feUt0j8Qf55agshH1XoMDo5BydARUHrEyHXTTuFPoo5kPc1JcsVDAXKnrWv5HFurXwv3bhvJ6xlaFaPet4/9HrN3e+GtZxoHJ3YdIe7Lqvvg7anNDxmG2ioveDN/QkRERERE7XTD8aKT9QPd2Ki9XbSuG7b29k3HqWiLulrlu/ZKU4pOIo9Zawt7S92FLlSj1raN59Fi2b/F1hlvwDaqsTtIq+R+6kR5LrcK5PeqxfEd2lF3rdRBreye1J5raaKUqxboZn/55yTUVtXCtj3ndAVaPGYr9dTgRBJmrHPGW9G/a1MC8Irr1xL5O1gn6vuqdoEjIiIiIqJfusLiErZAuSK2InBzaGdAaCOC085MnkjymC0FmiLob/N5WCh7dcEBpL0dhbjbgzCmLckTSe6nPVUgv9feREMrdWDb3mtpopSrfckTqbOTJ1KLx2ylnhSVedj0dgp097m3ufXUFdevJfJ3kMkTIiIiIiLqBGyBQh2iuugLHD/njDvu7Q/7jg6S6fpTWYTcEltebyIiIiIi+kWQLVCYQCEiIiIiIiIiagW78BARERERERERtQETKEREREREREREVjCBQkRERERERERkBRMoRERERERERERWMIFCRERERERERGQFEyhERERERERERFYwgUJEREREREREZAUTKEREREREREREVjCBQkRERERERERkBRMoRERERERERERWMIFCRERERERERGQFEyhERERERERERFYwgUJEREREREREZAUTKEREREREREREVjCBQkRERERERERkBRMoRERERERERERWMIFCRERERERERGQFEyhERERERERERFYwgUJEREREREREZAUTKEREREREREREVjCBQkRERERERERkBRMoRERERERERERWMIFCRERERERERGQFEyhERERERERERFYwgUJEREREREREZAUTKEREREREREREVtxwvOhk/UA3V232+nC+5gIqz36PKsM5ZdpoNKKu7ifU19drWxARteyGG26AjU0X6HQ6dLfrBgd9Dzj26qlMExERERERXa7C4pLrK4FSfuo0yv9bgQsXLqK3Y084OOjRo7sdunbViWDIRgmKiIiskcnWuro6XLxoxLnzNaiqMuBM5ffo1q0rnG9xgnPfPtqWRERERERE1l03CZSK/53BNyVl6Kqzxa3OfXFz717aGiKijvO/M2fxXfkpXDTW4nbXfnC6ube2hoiIiIiIqGXXRQLl68Jv8H2VAW4DXJk4IaJOIRMpxSdK0NNBjzsH3q4tJSIiIiIiskwmUK7ZILLG2lrkHslXmtoP9RnM5AkRdRr5vJHPHfn8kc8h+TwiIiIiIiJqzTVJoMhg5auj/4ZjLwfcdYcbxzYhok4nnzvy+SOfQ/J5xCQKERERERG15pokUPL/XYhbnHrjtv79tCVERNeGfA7J55F8LhEREREREbWk0xMocswTu25dmTwhouuGfB7J55J8PhEREREREVnSqQkU+bYdOWAsB20kouuNfC7J55N8ThERERERETXXqQkU+api+bYdjnlCRNcb+VySzyf5nCIiIiIiImqu0xIo5adOo6vOlm/bIaLrlnw+yeeUfF4RERERERGZ67wEyn8rcKtzX22OiOj6JJ9T8nlFRERERERkrlMSKOdrLuDChYtXr/XJqWTMuH0gpm26Ck3vjQYYzopPjTZPHa9Gq2OjNn811BnVY1zpQTpqPx3lOihP6Y5ITJsTj/xWfkeMR+MxJyQS6T+D3jHyOSWfV/K5RUREREREZNIpCZTKs9+jt2NPbe7npSJ1CQb7+GDwW3nakuuD4Xg2sg5kI7fsOgnkr0DuW6J+RR0vTL2Kf/XPi1Wv48LtuKKjdNR+Oso1L08FcrclImtXLNK/VpdYujfzPxPrDyRiy5c/j5Yd8nkln1tEREREREQmnZJAqTKcg4ODXpujjlC0NQTTQkKw6qBBW0J0LTghICYdH6dkYImXusTSvem9IANpW9Lx5mQnbcn1TT6v5HOLiIiIiIjIxOaZBQtXXO3WISe+LUM/51tga2urLelg1QVIid+LulF/xKODOjZRU1OQirg9JwGfQCwc7ozSXbFYn3oQRTd5YvCvdGILA3KT1uCDvQdh+JUv3Hua5ovR9S5nnNj6BqLe2I6vb3SHz52OOJudiNeilmPLF3VwvOdeuHSXu8hDwppN+OzgOfTxNGJ/7Ao8l3QYP/YUx+gvN2hKluGd1C/x9Smg7icjKs85YNC9zpClgaEYGR+9i7+98TpScmtwXu+CQb+6dB/G46l4J2EH9h/vikH3ad+tK0b6395DysECYIA3XOzFslN52PzBu1j9lw34rPg8dLfehgGOytZAyW7EbNyO7G/EPrTjGw4nYtXmvcg2uMDPXd9QX4Y+7jj90XKE/a0Cgx++F47qHhTlB97GlhxxyNEzEeChlbXZcfV3iLqS5TGpq0DWh+9i/dporM8oQWWtIwa6O0FnSgkq60XdL0/Glzf9Cj7di/HO1jzgtlEIDfCEcpQ6A4oykvHO6jfw6if/wvn6Po37MF0TcW4uXQ9j9YtL8Vm3hzCy65f4W7K6nyeGGZDyajRe+/Q4fhTnN8jZrJ6b7/uiA/rf6YzuZilLg7i3Etatw8qY7fjXqbPQDTCdo9k9JG6QQ2uW47m93THR/zbo2nJeJmbXZ2Cfk/gg4k9YufskbnTxxF1O2jWU2lDWigOJeCduHaL+tgNfn6uBw62ecDaV9aNNyDj6L+X+131h+d48veddpOR8jVJb0++N0JZ7S9xHPjfl4oOY10U9HxX3850YrPzSXF3yPWHfnTqNfr/iuE1ERERERCR71lQBx4tO1l9t+/75Rf0PP/ygzV0F5Vvqpw9wr3/8w1JtQcc5nTyr/jax79teyVXmc14R02J+evJpZV5sUb9purrsr1+azz9R/+yCsep3lY9n/fTnF9WPaJgXnwdX1x/7UXxFK/9tAwLrH3nEbL34zuOJRXKnTZjK0PCZvkUcVajMqP/zg+qyO33H1v/aU51+UJT9ovJNMxez6v+srF9Uv7NKW5a/Wi3f5PfrC+V80fv1j2j7uPfBsfX3ynXyPJK1ev7yFWVdw/GFlupr9ry56vIBr9TnKGsaXVKnpaI+lON61v/6IdNxx4r61c7iYm79G9p53vvg5PqHfD2V6TsX7KpXTuXH0vpNs9Rlps+DovzKdENZL4rjasu8xzbuY9aW+m/Nr8njc+tnj1D3oZTPdM6TZ9VP15arH8/6Zz81VWRV/T9e1Pbt6Vv/oLbv2x4U535e3eL01ln1d2rrH5rceI5v5ytrG+6h2fP81e/KcrfpvMw0lFXcV9p1VD/e9X/eb7ojrJf12BqzejKV1XNW/Sflcm3T+7+le/OSa9zWe2veovpnm5R9bP0buZfczR1OPq/kc4uIiIiIiEiSuZNO6cJTV/cTbGxstLkrVJOHmIk+mPGRldEoy3YjbPRIRB24Vl1cslHq/gqOFBbi85f8xbwRGQf7IPqrQpz4Kg4hdmJRcTIytHEjVBXwWZSDE98U4kjCTLiI72QtT0RGs2FOvMMK8fFT6vTI17JwYkMgZMeI3HXzkVAMuD+1BUey0nEoKwGh/YCid5ch4bi6fQOdN8YGyr/2pyI7Vz1A0Ze7UCp+egf5w12UZfNfI5FboxPHyMCRPek4khGBkfI8VqxB+mVWa/rXLkjKOob/HFsEb22ZZQakRIcjo8YNoVtycChNHPfzKIy0K0bcK8lK+YzF4tpPmIv5r6Xg0J4UpO2PQ6hcnirqs0L8zI5HxF5xTv1mIknWd2EOIh9oVolH47Hw3WLoRkXh80PpSMvKEXXqBuPeSKzPNts2ex+Mc0UZjh3D2klm3U+OlsJ95THlWn0e5Q+dqJeU6ETky3WH12BOkrgQbjPx8aEs7NmfhaQZ4kIUx+OFRLFc1G3hWQ+EPhOGDelZSEsRx4/yFcuLsWqX+Vg72eLaz8Wer0S9rZoMfVvOy5KjDgj4VGwvy6rciwYkvJ6MIrnOalnzkL5a/vRC5FZRTlHW/VsiMH+mB6rKLr0JWro3m7qMeyvzHHxTRD2Lc90gy6XUUYG67iqSzyv53CIiIiIiIjLplARKh/rxIoxGAzKWjms5iSKTJ9PnYXOxTkRC2rJrwMfXC3pxfJc73dQF7m4YKHsY6T3hMVQuKGv2dp+xGDdc7YKkHz4ZQTJeRCbyZfxqVQGydshg2gNPBHqpXXL0vhg3QU4UI/tfzQfv1MHvoWBlu82yy44IanP2yZ9eCBguDmzIQ3am3C4QT0xSCgK4jsVYGX/XJCO3eULGipFPz4RfXx10dloXjZYYDiJjh5zQ4/T+NYiJjUVMsiiX7POTtw+54jR0HpOwZG4wAm6rQnqSWL9iLTbLrwgX64DS4lwRiot6f2wy/GR12ujFuU5W60STf0BNxvQR9bblLbGP2DXIqJAbG7H5S/MAPRjzp7pBL8qtM9+B70w8MURd4PLwNEyRE2V5KBLly/9yl3J8z+BAeMtEmTz+uLFyCxQdzBU17QS/GYsw/xFf6L5ORlxsNGISc5X1xmb5kJCnA+GuV+utLedlkf8YjHdVJ10mBSJAThzNRZGhLWV1g+cEeYQ8RD0WhIUvx2NnlTeC5i5CyBD1Xr1sl3NvDR2D37mJ44tyjRyllouIiIiIiOha6JQEio1NF9TVici2I+h9EZ6yBaFuRstJlLJUzAmQyRM3hCZtQbhvO4O8a04PJxf5s3mSpSVGGJSq6ANdW4eI8JqM+SJ+Ne7IRr4pqBXLRspgu6YKakMAHRysRugdqOG4xcjPzESG8snF6V4e8LzHSU0WFCfiUR8/jA4KxV8/zEQRboa78h2VoVLNOMmkRwO9U5NtjFXqfXM6P1c7hvgUGcUxPODelvoTu+6qTULn0JDEkAkc0777dG/p3jMgY/k43DUyANOWxiMl7zS6OlsfXLUt52VV9x7iDpHOoUrcV9bLqse4FSl485lJyngrKRuiERYagPt9ArAqr1m2p63ae2/dpP3sBPJ5JZ9bREREREREJp0SIeh0Oly82M5gyxI7r6ZJlL8XK39Fv/h1IuYELEb62XYmTyp2IywgABMDYpGlFfd0udLRAX63NQ1wTxu0fgZ1BhjOqJNXLhfHSrTJs3nIzJYT/vDUWg+0zg3ek+TPTOTlm+q6DMe+VKdcbrZQFzYeGBnYT2y2CxnvZSNFLBr52FgoeZu+nvBWGgdkI8fUIsBYhIJDcsID/XopS1RnDKjS8mNVhtPqRHv1dYenbAmBsQj/MAVpKfKzBR+sex8f/D0MIx1FLW2PRq4I/qfEyS4+KVi7IhA+ypdVLrfJ7jCydUWBFqiLS5u3T+1eo3G5UzZ3ANxnrdSOIT7vr8fGv4vjBGuvk2nNoQIcMyW2juciS5lwg4u4TdzvVS4EMg7lK/elVPq12sIEtzpBX7EP78tuM/eEYY/sPpSwEvNGKbXeqracl0WirIWmghTkIV3+tPPAwL5tKGudEQajE7wfnIe1e3KUrjRJz3gANQWIaW9Xmsu5t64R+bySzy0iIiIiIiKTTkmgdLfrhnPn29SMou3MkyjvxisBbO578e1PnkhOHvC4sQD5R9dgTmgkYl6eh4Wx8i/0Xhjrq3Y1MAWc+S8H4dElizFjxDy8f1ZZ1AEKEDVvHqJio7HwiWVKoKubFIiRFhon6BzU8mRtiUVMUp4IqPUYOVWOmwJsfvYJRH2UjLhnxb7kkBpuixA0wnIw6OkfKL4jguHYRDE3BgGjTAfzQMBcmWRQyxQn9hcVOh8J4jLqJs3D72WvpDu8te4g0Xg0aDEWhvphzt9NoX17eSHgeZnASMacP0Zj895MbH75CQz188HgWdtx2kYcv6taxpwD25F1IBubX4lGgrJE5STOKUAmYXYsw+PPRovruBjTX8luaCUiOY2dpoxDky+u8Zx3U5GVGo85j/phqI8fYrQxYVqXjIXinKNiIzHtsWglieHy1Fj4iPLpxfHl2DP4aD4efzkZm99djDmvKBcCSx7zVwJz5e4sPoj0zGxk7Y1H1OtKtqxVbTkvy0RdPhEurrEo6x9jla5L7vPGKmPRWC0ripEQ5IP7AwIwPVbUU/Y+ZGerLWG8ZbbIgkvvzebacG9dY/J5JZ9bREREREREJp2SQHHQ90BV1ZUG1hY0JFG0eRH0XVm3nX4I+dtqhHjpYTiQiFUbdqOoly+WJIllWisQ/djFWDvVQwSWBuRu2wfjH1ciUhlnpCMEI3KuA7Li45FSYIR+eBg+fmWMGmw34zk1CqEeOhgPJ2PVK7Ibiwg+fcOQtCoY3ro8xC0NR1RqAXTDFyHpg7nwbGksmHv8tbFWhAnjMNLsr/8uU1chLcwfTuW7ESX2F3fAqBw3zVQm/RgsWRWotBgx5KUiwzgTb0Zc+TgV7sHr8bE4rr4gHmGhoQjbUAD9KFEXG4OVBJHnkyuxRFyjovfCMS0kFO93D8YStUGJqtcYvPphGPx6GZGfGo9V24wIXRUBP221ws4fkZ+uFNe6AunRizHt2WikV3qJ65+OyOFtaHkwNAyvPvI/bH47EVlndXCaFIENC7SxZ+x8Ef6BvI90yN0QjrDoVOTr5H30PuZ7iPWy3mImwQmZiAkNwbSluRj3/Ez5zda15bwsGboIf3mwDAlaWT2nrsaGp2RBBGtltfHA/I3a+rdFPYUsxqoCPUYuSsA7U003TlOW7s3mrN5b15h8XsnnFhERERERkckN8lU8A93a1Eek3c7XXMBX/yrAb39j3tGiA9XkISpgGfCXDhzzxGiAwaiDXt+GYPpKnUrGDL9wZGAmPv4mDN5KtwlxbKUrixU1RhEEX1pG41kDjHZ6WC++ASnzfbBwBzDubzlYO8lC/cnyGIzQ6fXQdeagvNpx0dJ51Ihz1LVeJqOoH6sD14r9KPXdqx3XWpbxR/Hdlr4q9y3XW9pAfvc82nWPtem8DkdjQFA84B+FQ/JtOFdSVkn+TshWIm29D1q4N5u4VveWFf88mIP77vVgKxQiIiIiIlIUFpd0Xheebt264n9nOqyvS1OyJcqe9I4dMFYE5p2SPLHERgSxbUmeSC0EqLpe1pMnFdsWY+LokUryBG5zETqmhfqT5RH76/QAVztui+dhZ71MVpMMkkzQtCd5IskytvZVue+WNpDfbec91qbzau5KyirJ34nLuQ/aUsZrdW+1Qj6n5POKyRMiIiIiIjLXaa+ZcL7FCd+Vn9LmqAkbB/S5R33LTOcxovBksQhy+8FzrOzmswje7Yvl6Xpl46S8Vcizr4O2gNpCPqfk84qIiIiIiMhcp3ThMfki5wjcbuuPm3tfB6/ZICJqRrY+KT75LYb5DNaWEBERERERdWIXHpPbXfuh+EQJ6uvrtSVERNcH+VySzyf5nCIiIiIiImquUxMoTjf3Rk8HPb4u/EZbQkR0fZDPJfl8ks8pIiIiIiKi5jo1gSLdOfB21Fy4iJPflmlLiIiuLfk8ks8l+XwiIiIiIiKypNMTKJLn3QPx34ozTKIQ0TUnn0PyeSSfS0RERERERC25JgkUna0t7rvnblSercJ/jhdzTBQi6nTyuSOfP/I5JJ9H8rlERERERETUkmuSQJFksOI92BM33HADDuUcUd5+QUTUGeTzRj535PNHPoeYPCEiIiIiIms69TXGLan43xl8U1KGrjpb3Orcl685JqKrQiZOvis/hYvGWuVtOxwwloiIiIiI2kK+xvi6SKCYlJ86jfL/VuDChYvo7dgTDg569Ohuh65ddbCxsVH+WkxEZI3snlNXV4eLF404d74GVVUGnKn8Ht26dYXzLU5w7ttH25KIiIiIiMi66y6BYnK+5gIqz36PKsM5ZdpoNIpg6CeOlUJEbSKTrTY2XaDT6dDdrhsc9D3g2KunMk1ERERERHS5rtsEChERERERERHR9UImUK7ZILJERERERERERD8XTKAQEREREREREVnBBAoRERERERERkRVMoBARERERERERWcEEChERERERERGRFUygEBERERERERFZwQQKEREREREREZEVTKAQEREREREREVnBBAoRERERERERkRVdBNTV1WmzRERERERERERkInMmMnfS5aabbsQPP/yoLSYiIiIiIiIiIhOZM5G5ky5ddToYa2u1xUREREREREREZCJzJjJ30qVrVx1qai5qi4mIiIiIiIiIyETmTGTupIt9926oPl/DcVCIiIiIiIiIiMzIXInMmcjciTKIrIO+B6oM1dpqIiIiIiIiIiKSuRKZM1EGkZULHBzscfb7KrZCISIiIiIiIiISZI5E5kpkzkRSEig6W1s46PX4X+X3ykIiIiIiIiIiol8ymSORuRKZM5GUBIp0c++eMBprUWU4py0hIiIiIiIiIvrlkbkRmSORuRKThgSKdEuf3vjfme9xrvq8toSIiIiIiIiI6JdD5kRkbkTmSMzdUC9o04qLF434rvy0kmWRA6UQEREREREREf0SyJYnMnlyq3Mf5dXF5i5JoEjG2lr89/QZ6HS2uNmxJ2xsbLQ1RERERERERET/t8gBY+WYJ7Lbjmx5Yhr3xJzFBIqJzLpUGQzo1dMBDnp7JlKIiIiIiIiI6P8MmTiRrypW3raj1zcZ86S5VhMokmyNUlVVrTRjse9uBzu7rkom5qabbmRChYiIiIiIiIh+NmTC5IcfflRyHTU1F1F9vkYZvkS+qthSqxNzVhMoJj/99JPY8QVljJSLRqNyQLmMiIiIiIiIiOjnoEuXLkqDkK46nTLGiX33bsqytmhzAoWIiIiIiIiI6JcJ+P/nMzIZRkw2mQAAAABJRU5ErkJggg=="
    }
   },
   "cell_type": "markdown",
   "id": "ae6b2281",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f0507368",
   "metadata": {},
   "source": [
    "### Principle Component Analysis"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "75a54712",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(70000, 332)\n"
     ]
    }
   ],
   "source": [
    "#running pca on test + train data\n",
    "#recording time to run pca\n",
    "df_pca = df_standard.drop(columns=['source']) #we already have combined test + train that has been standardized: df_standard\n",
    "pca_start=datetime.datetime.now() #start timer\n",
    "pca = PCA(n_components=0.95) #retain 95% of varability\n",
    "pca_reduced = pca.fit_transform(df_pca)\n",
    "print(pca_reduced.shape)\n",
    "pca_end=datetime.datetime.now()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "6653ec93",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0:00:05.201944\n"
     ]
    }
   ],
   "source": [
    "#PCA time\n",
    "print(pca_end-pca_start)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f8513b62",
   "metadata": {},
   "source": [
    "### Rebuilding Cross-validation datasets and Test Datasets on PCA database"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "8c516cb0",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(70000, 333)\n"
     ]
    }
   ],
   "source": [
    "#add back to PCA data a source identifier\n",
    "pca = pd.DataFrame(data=pca_reduced)\n",
    "pca['source'] = source\n",
    "print(pca.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "a946b6b5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(42000, 332)"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#build training dataset\n",
    "XC = pca[pca['source'] == 'train']\n",
    "XC = XC.drop(columns=['source'])\n",
    "XC.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "08722441",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(33600, 332)\n",
      "(8400, 332)\n",
      "(33600,)\n",
      "(8400,)\n"
     ]
    }
   ],
   "source": [
    "#build cross-validation pca data\n",
    "XP_train, XP_ctest, yp_train, yp_ctest = train_test_split(XC, y, test_size=0.2, random_state=0)\n",
    "print(XP_train.shape)\n",
    "print(XP_ctest.shape)\n",
    "print(yp_train.shape)\n",
    "print(yp_ctest.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "417b4bc8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(28000, 332)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#building the evaluation data\n",
    "pca_test = pca[pca['source'] == 'test']\n",
    "pca_test = pca_test.drop(columns=['source'])\n",
    "pca_test.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6199114d",
   "metadata": {},
   "source": [
    "### Random Forest with PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "b790a166",
   "metadata": {},
   "outputs": [],
   "source": [
    "#training random forest with default hyperparameters\n",
    "rf_pca = RandomForestClassifier()\n",
    "rf_pca_start=datetime.datetime.now()\n",
    "rf_pca.fit(XP_train,yp_train)\n",
    "rf_pca_end=datetime.datetime.now()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "5715c778",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0:00:57.733329\n"
     ]
    }
   ],
   "source": [
    "#time to fit random forest model\n",
    "print(rf_pca_end-rf_pca_start)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "46011d5f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9271428571428572"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#evaluate accuracy on holdout data\n",
    "rf_pca_predict = rf_pca.predict(XP_ctest)\n",
    "score(rf_pca_predict,yp_ctest)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "3ad1a26d",
   "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>ImageId</th>\n",
       "      <th>Label</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   ImageId  Label\n",
       "0        1      2\n",
       "1        2      0\n",
       "2        3      4\n",
       "3        4      4\n",
       "4        5      3"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#generating a dataframe for kaggle submission\n",
    "rf_pca_out = rf_pca.predict(pca_test)\n",
    "df_out_2 = pd.DataFrame(data=rf_pca_out,columns=['Label'])\n",
    "df_out_2['ImageId'] = df_out_2.index + 1\n",
    "df_out_2 = df_out_2[['ImageId','Label']]\n",
    "df_out_2.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "212f978e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(28000, 2)\n"
     ]
    }
   ],
   "source": [
    "#checking the shape of the dataframe and creating the csv \n",
    "print(df_out_2.shape)\n",
    "df_out_2.to_csv(\"RandomForest_wPCA.csv\",index=False)"
   ]
  },
  {
   "attachments": {
    "image.png": {
     "image/png": 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"
    }
   },
   "cell_type": "markdown",
   "id": "5ad80cd8",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a0432a6d",
   "metadata": {},
   "source": [
    "### K-Means Clustering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "id": "ba510f3d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "KMeans(n_clusters=10)"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#applying a k-means with 10 clusters \n",
    "n_digits = len(np.unique(y_train))\n",
    "km = KMeans(n_clusters=n_digits)\n",
    "km.fit(X_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "id": "8225547c",
   "metadata": {},
   "outputs": [],
   "source": [
    "#function to create label dictionary\n",
    "def retrieve_info(cluster_labels,y_train):\n",
    "    reference_labels = {}\n",
    "\n",
    "    for i in range(len(np.unique(km.labels_))):\n",
    "        index = np.where(cluster_labels == i,1,0)\n",
    "        num = np.bincount(y_train[index==1]).argmax()\n",
    "        reference_labels[i] = num\n",
    "        \n",
    "    return reference_labels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "id": "227fd8df",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{0: 2, 1: 4, 2: 7, 3: 3, 4: 1, 5: 0, 6: 2, 7: 5, 8: 7, 9: 6}\n"
     ]
    }
   ],
   "source": [
    "#digit dictionary\n",
    "reference_labels = retrieve_info(km.labels_,y_train)\n",
    "dict = {}\n",
    "for i in reference_labels:\n",
    "    dict[i] = reference_labels[i]\n",
    "print(dict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "id": "9b63f621",
   "metadata": {},
   "outputs": [],
   "source": [
    "#making prediction and labeling\n",
    "km_predict = km.predict(X_ctest)\n",
    "km_labeled_predict = np.vectorize(dict.get)(km_predict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "id": "4c7a9e7c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5273809523809524"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#evaluating accuracy\n",
    "score(km_labeled_predict,y_ctest)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "db111781",
   "metadata": {},
   "source": [
    "A pretty bad accruarcy to start.  We also observe from our label dictinary that no predictions are being made for the 8 and 9 digits.  We need to pre-parametrize the model and then re-run"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "id": "42fc86b7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.5282142857142857\n",
      "0.5919047619047619\n",
      "0.6798809523809524\n",
      "0.7323809523809524\n",
      "0.7645238095238095\n",
      "0.8210714285714286\n"
     ]
    }
   ],
   "source": [
    "cluster_number = [10,20,50,75,150,300]\n",
    "\n",
    "for i in cluster_number:\n",
    "    km = KMeans(n_clusters = i)\n",
    "    km.fit(X_train)\n",
    "\n",
    "    reference_labels = retrieve_info(km.labels_,y_train)\n",
    "    \n",
    "    dict = {}\n",
    "    for y in reference_labels:\n",
    "        dict[y] = reference_labels[y]\n",
    "    \n",
    "    km_predict = km.predict(X_ctest)\n",
    "    km_labeled_predict = np.vectorize(dict.get)(km_predict)\n",
    "    \n",
    "    print(score(km_labeled_predict,y_ctest))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3080ef0f",
   "metadata": {},
   "source": [
    "I run 6 different k-means models each with an increasing number of nodes.  I fit each model to the training data.  I then make a prediction against our holdout data.  I then measure the accuracy on the holdout data.  We observe that as the number of nodes is increased the accuracy on the holdout data increases.  Given the improvement between 150 and 300 clusters, I run a second set of models testing larger number of clusters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "id": "0ebbd6b1",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.8123809523809524\n",
      "0.848452380952381\n",
      "0.8764285714285714\n"
     ]
    }
   ],
   "source": [
    "cluster_number = [300,500,1000]\n",
    "\n",
    "for i in cluster_number:\n",
    "    km = KMeans(n_clusters = i)\n",
    "    km.fit(X_train)\n",
    "\n",
    "    reference_labels = retrieve_info(km.labels_,y_train)\n",
    "    \n",
    "    dict = {}\n",
    "    for y in reference_labels:\n",
    "        dict[y] = reference_labels[y]\n",
    "    \n",
    "    km_predict = km.predict(X_ctest)\n",
    "    km_labeled_predict = np.vectorize(dict.get)(km_predict)\n",
    "    \n",
    "    print(score(km_labeled_predict,y_ctest))"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f975c8db",
   "metadata": {},
   "source": [
    "Accuracy continues to increase as the number of clusters is increased all the way up to 1000.  We should test models with more than 1000 clusters, but given compute constraints we accept 1000 nodes as our final model"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6caec43a",
   "metadata": {},
   "source": [
    "### K-Means Clustering - with 1000 Clusters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "id": "8ab2ab54",
   "metadata": {},
   "outputs": [],
   "source": [
    "km = KMeans(n_clusters = 1000)\n",
    "km.fit(X_train)\n",
    "\n",
    "reference_labels = retrieve_info(km.labels_,y_train)\n",
    "    \n",
    "dict = {}\n",
    "for y in reference_labels:\n",
    "    dict[y] = reference_labels[y]\n",
    "    \n",
    "km_predict = km.predict(X_ctest)\n",
    "km_labeled_predict = np.vectorize(dict.get)(km_predict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "id": "9c9288a7",
   "metadata": {},
   "outputs": [],
   "source": [
    "km_predict = km.predict(df_test)\n",
    "km_labeled_predict = np.vectorize(dict.get)(km_predict)\n",
    "km_labeled_predict = np.vectorize(dict.get)(km_predict)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "id": "9d69fa94",
   "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>ImageId</th>\n",
       "      <th>Label</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   ImageId  Label\n",
       "0        1      2\n",
       "1        2      0\n",
       "2        3      7\n",
       "3        4      9\n",
       "4        5      3"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#generating a dataframe for kaggle submission\n",
    "df_out_3 = pd.DataFrame(data=km_labeled_predict,columns=['Label'])\n",
    "df_out_3['ImageId'] = df_out_3.index + 1\n",
    "df_out_3 = df_out_3[['ImageId','Label']]\n",
    "df_out_3.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "id": "c0b3e198",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(28000, 2)\n"
     ]
    }
   ],
   "source": [
    "#checking the shape of the dataframe and creating the csv \n",
    "print(df_out_3.shape)\n",
    "df_out_3.to_csv(\"Kmeans.csv\",index=False)"
   ]
  },
  {
   "attachments": {
    "image.png": {
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"
    }
   },
   "cell_type": "markdown",
   "id": "9ed477b1",
   "metadata": {},
   "source": [
    "![image.png](attachment:image.png)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}