PCA_Iris.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "\n",
    "# load Data\n",
    "\n",
    "iris = pd.read_csv('C:/Users/aryan.singh/PythonNotebooks/Machine_Learning_Python/DimensionalityReduction/iris.data',names=['sepal length','sepalwidth','petal length','petal width','target'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sepal length</th>\n",
       "      <th>sepalwidth</th>\n",
       "      <th>petal length</th>\n",
       "      <th>petal width</th>\n",
       "      <th>target</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5.1</td>\n",
       "      <td>3.5</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.9</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>4.7</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.3</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.6</td>\n",
       "      <td>3.1</td>\n",
       "      <td>1.5</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5.0</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.4</td>\n",
       "      <td>0.2</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   sepal length  sepalwidth  petal length  petal width       target\n",
       "0           5.1         3.5           1.4          0.2  Iris-setosa\n",
       "1           4.9         3.0           1.4          0.2  Iris-setosa\n",
       "2           4.7         3.2           1.3          0.2  Iris-setosa\n",
       "3           4.6         3.1           1.5          0.2  Iris-setosa\n",
       "4           5.0         3.6           1.4          0.2  Iris-setosa"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "iris.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Scaling the data before performing PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "features = ['sepal length','sepalwidth','petal length','petal width']\n",
    "\n",
    "#Separate out features from the target\n",
    "\n",
    "x = iris.loc[:, features].values\n",
    "\n",
    "y = iris.loc[:, ['target']].values\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Before Scaling  [[5.1 3.5 1.4 0.2]\n",
      " [4.9 3.  1.4 0.2]\n",
      " [4.7 3.2 1.3 0.2]\n",
      " [4.6 3.1 1.5 0.2]\n",
      " [5.  3.6 1.4 0.2]]\n",
      "After Scaling  [[-0.90068117  1.03205722 -1.3412724  -1.31297673]\n",
      " [-1.14301691 -0.1249576  -1.3412724  -1.31297673]\n",
      " [-1.38535265  0.33784833 -1.39813811 -1.31297673]\n",
      " [-1.50652052  0.10644536 -1.2844067  -1.31297673]\n",
      " [-1.02184904  1.26346019 -1.3412724  -1.31297673]]\n"
     ]
    }
   ],
   "source": [
    "# Standardizing the features\n",
    "\n",
    "print('Before Scaling ',x[0:5,:])\n",
    "\n",
    "x = StandardScaler().fit_transform(x)\n",
    "\n",
    "print('After Scaling ',x[0:5,:])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PCA Projection to 2D For Visualization"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "\n",
    "pca = PCA(n_components=2)\n",
    "\n",
    "principal_components = pca.fit_transform(x)\n",
    "\n",
    "principal_df = pd.DataFrame(data = principal_components, columns = ['principal_component_1','principal_component_2'])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\n",
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       "        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>principal_component_1</th>\n",
       "      <th>principal_component_2</th>\n",
       "      <th>target</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-2.264542</td>\n",
       "      <td>0.505704</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-2.086426</td>\n",
       "      <td>-0.655405</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-2.367950</td>\n",
       "      <td>-0.318477</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-2.304197</td>\n",
       "      <td>-0.575368</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-2.388777</td>\n",
       "      <td>0.674767</td>\n",
       "      <td>Iris-setosa</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   principal_component_1  principal_component_2       target\n",
       "0              -2.264542               0.505704  Iris-setosa\n",
       "1              -2.086426              -0.655405  Iris-setosa\n",
       "2              -2.367950              -0.318477  Iris-setosa\n",
       "3              -2.304197              -0.575368  Iris-setosa\n",
       "4              -2.388777               0.674767  Iris-setosa"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "final_df = pd.concat([principal_df, iris['target']], axis = 1)\n",
    "final_df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Visualise 2-D projection"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xd826c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "fig = plt.figure(figsize=(8,8))\n",
    "ax = fig.add_subplot(1,1,1)\n",
    "ax.set_xlabel('Principal Component 1', fontsize = 15)\n",
    "ax.set_ylabel('Principal Component 2', fontsize = 15)\n",
    "ax.set_title('2 component PCA', fontsize = 20)\n",
    "\n",
    "targets = ['Iris-setosa', 'Iris-versicolor', 'Iris-virginica']\n",
    "colors = ['r', 'g', 'b']\n",
    "\n",
    "for target,color in zip(targets,colors):\n",
    "    indices_to_keep = final_df['target'] == target\n",
    "    ax.scatter(final_df.loc[indices_to_keep, 'principal_component_1'], final_df.loc[indices_to_keep, 'principal_component_2']\n",
    "    , c = color, s = 50)\n",
    "ax.legend(targets)\n",
    "ax.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we know that PCA is a variance maximization algorithm with a goal to minimise the sum of squared difference between the projected datapoints and the original ones. Take a look at the explained variance of each principal component to visualise how much variance is captured by them:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.72770452, 0.23030523])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.explained_variance_ratio_"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thus first principal component explains 72.7 % of variance whereas the second component explains 23.03 of the variance, so in total our PCA transformation explains around 95% of the variance of original dimensions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.datasets import fetch_mldata\n",
    "mnist = fetch_mldata('MNIST original',data_home='D:/upgrad/DimensionalityReduction/mnist')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(mnist.data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Split into training and test dataset\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "train_img, test_img, train_lbl, test_lbl = train_test_split(mnist.data, mnist.target, test_size=1/7.0, random_state=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(60000, 784)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_img.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10000, 784)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_img.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(60000,)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_lbl.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10000,)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "test_lbl.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "D:\\ProgramData\\Anaconda3\\lib\\site-packages\\sklearn\\utils\\validation.py:475: DataConversionWarning: Data with input dtype uint8 was converted to float64 by StandardScaler.\n",
      "  warnings.warn(msg, DataConversionWarning)\n"
     ]
    }
   ],
   "source": [
    "# Apply Standardisation on the data\n",
    "\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "scaler = StandardScaler()\n",
    "\n",
    "# Fit for the training data only\n",
    "scaler.fit(train_img)\n",
    "\n",
    "# Apply the transform to both the training and test dataset\n",
    "\n",
    "train_img = scaler.transform(train_img)\n",
    "\n",
    "test_img = scaler.transform(test_img)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now that the data is standardized next step is to apply the PCA tranformation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "PCA(copy=True, iterated_power='auto', n_components=0.95, random_state=None,\n",
       "  svd_solver='auto', tol=0.0, whiten=False)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "\n",
    "pca = PCA(0.95)\n",
    "\n",
    "# fit the PCA transformation on the training set\n",
    "\n",
    "pca.fit(train_img)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# transforming the train and test dataset with the PCA transformation\n",
    "\n",
    "train_img = pca.transform(train_img)\n",
    "test_img = pca.transform(test_img)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(60000, 330)\n"
     ]
    }
   ],
   "source": [
    "print(train_img.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(10000, 330)\n"
     ]
    }
   ],
   "source": [
    "print(test_img.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Apply Logistic Regression on The Transformed Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "logist_regr = LogisticRegression(solver='lbfgs')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
       "          intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,\n",
       "          penalty='l2', random_state=None, solver='lbfgs', tol=0.0001,\n",
       "          verbose=0, warm_start=False)"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logist_regr.fit(train_img,train_lbl)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([4.])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Predict For one observation\n",
    "\n",
    "logist_regr.predict(train_img[0].reshape(1,-1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.92"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "logist_regr.score(test_img, test_lbl)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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