PCA_notebook.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c19c6e6d",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "from sklearn.datasets import load_digits\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.decomposition import PCA\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "2838b053",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x14aa6e6b0>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 480x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dataset = load_digits()\n",
    "\n",
    "\n",
    "firstDigit = dataset.data[0].reshape(8,8)\n",
    "\n",
    "plt.gray()\n",
    "\n",
    "plt.matshow(firstDigit)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "7c74c516",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797, 64)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame(dataset.data, columns=dataset.feature_names)\n",
    "\n",
    "X= df\n",
    "Y = dataset.target\n",
    "\n",
    "X.shape\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "337ac78a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797,)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "6dc87d90",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "accuracy without PCA 0.9722222222222222\n"
     ]
    }
   ],
   "source": [
    "scaler = StandardScaler()\n",
    "\n",
    "X_scaled = scaler.fit_transform(X)\n",
    "\n",
    "\n",
    "X_train, X_test, Y_train, Y_test = train_test_split(X_scaled, Y,  test_size=0.2, random_state=30)\n",
    "\n",
    "\n",
    "model = LogisticRegression()\n",
    "\n",
    "model.fit(X_train, Y_train)\n",
    "\n",
    "accuracy  = model.score(X_test,Y_test)\n",
    "\n",
    "\n",
    "print(\"accuracy without PCA\", accuracy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "61062718",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "accuracy with PCA 0.9694444444444444\n"
     ]
    }
   ],
   "source": [
    "# use 95% of useful features\n",
    "pca = PCA(0.95)\n",
    "\n",
    "\n",
    "# use use only two components\n",
    "# pca = PCA(n_components=2)\n",
    "\n",
    "X_pca = pca.fit_transform(X)\n",
    "\n",
    "\n",
    "firstComponent = X_pca[2][:25].reshape(5,5)\n",
    "\n",
    "\n",
    "\n",
    "varianceRatio = pca.explained_variance_ratio_\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "X_train_pca, X_test_pca, Y_train, Y_test = train_test_split(X_pca, Y,  test_size=0.2, random_state=30)\n",
    "\n",
    "\n",
    "model = LogisticRegression(max_iter=1000)\n",
    "\n",
    "model.fit(X_train_pca, Y_train)\n",
    "\n",
    "accuracy  = model.score(X_test_pca,Y_test)\n",
    "\n",
    "print(\"accuracy with PCA\", accuracy)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "efdcc175",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.14890594, 0.13618771, 0.11794594, 0.08409979, 0.05782415,\n",
       "       0.0491691 , 0.04315987, 0.03661373, 0.03353248, 0.03078806,\n",
       "       0.02372341, 0.02272697, 0.01821863, 0.01773855, 0.01467101,\n",
       "       0.01409716, 0.01318589, 0.01248138, 0.01017718, 0.00905617,\n",
       "       0.00889538, 0.00797123, 0.00767493, 0.00722904, 0.00695889,\n",
       "       0.00596081, 0.00575615, 0.00515158, 0.0048954 ])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "varianceRatio\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "27b29136",
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