Principal Component Analysis.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "4e98a961",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "from sklearn.datasets import load_digits "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "fc40cd68",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['data', 'target', 'frame', 'feature_names', 'target_names', 'images', 'DESCR'])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ds = load_digits()\n",
    "ds.keys()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "0fefaca1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['pixel_0_0',\n",
       " 'pixel_0_1',\n",
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       " 'pixel_0_3',\n",
       " 'pixel_0_4',\n",
       " 'pixel_0_5',\n",
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       " 'pixel_1_5',\n",
       " 'pixel_1_6',\n",
       " 'pixel_1_7',\n",
       " 'pixel_2_0',\n",
       " 'pixel_2_1',\n",
       " 'pixel_2_2',\n",
       " 'pixel_2_3',\n",
       " 'pixel_2_4',\n",
       " 'pixel_2_5',\n",
       " 'pixel_2_6',\n",
       " 'pixel_2_7',\n",
       " 'pixel_3_0',\n",
       " 'pixel_3_1',\n",
       " 'pixel_3_2',\n",
       " 'pixel_3_3',\n",
       " 'pixel_3_4',\n",
       " 'pixel_3_5',\n",
       " 'pixel_3_6',\n",
       " 'pixel_3_7',\n",
       " 'pixel_4_0',\n",
       " 'pixel_4_1',\n",
       " 'pixel_4_2',\n",
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       " 'pixel_6_1',\n",
       " 'pixel_6_2',\n",
       " 'pixel_6_3',\n",
       " 'pixel_6_4',\n",
       " 'pixel_6_5',\n",
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       " 'pixel_7_3',\n",
       " 'pixel_7_4',\n",
       " 'pixel_7_5',\n",
       " 'pixel_7_6',\n",
       " 'pixel_7_7']"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ds.feature_names"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "55a442e3",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797, 64)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ds.data.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "b49533ae",
   "metadata": {},
   "outputs": [
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       "(1797,)"
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     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "ds.target.shape"
   ]
  },
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   "cell_type": "code",
   "execution_count": 8,
   "id": "e7842a71",
   "metadata": {},
   "outputs": [
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       "array([ 0.,  0.,  5., 13.,  9.,  1.,  0.,  0.,  0.,  0., 13., 15., 10.,\n",
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      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ds.data[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "89e96e03",
   "metadata": {},
   "outputs": [
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       "array([[ 0.,  0.,  5., 13.,  9.,  1.,  0.,  0.],\n",
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     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ds.data[0].reshape(8,8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "38c7a15a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x22ef14de0b0>"
      ]
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     "execution_count": 10,
     "metadata": {},
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      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "plt.gray()\n",
    "plt.matshow(ds.data[15].reshape(8,8))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "69b27794",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, ..., 8, 9, 8])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ds.target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "9e17f471",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "np.unique(ds.target)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "e5cd4f37",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ds.target[19]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "30cd6cd0",
   "metadata": {},
   "outputs": [
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     "execution_count": 14,
     "metadata": {},
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   ],
   "source": [
    "pd.DataFrame(ds.target)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "ddde3217",
   "metadata": {},
   "outputs": [
    {
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       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>1.0</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>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>6.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>12.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>5.0</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>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>11.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>10.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>12.0</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>5.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>3.0</td>\n",
       "      <td>11.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>15.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>...</td>\n",
       "      <td>9.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>13.0</td>\n",
       "      <td>9.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>11.0</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>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>2.0</td>\n",
       "      <td>16.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 64 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   pixel_0_0  pixel_0_1  pixel_0_2  pixel_0_3  pixel_0_4  pixel_0_5  \\\n",
       "0        0.0        0.0        5.0       13.0        9.0        1.0   \n",
       "1        0.0        0.0        0.0       12.0       13.0        5.0   \n",
       "2        0.0        0.0        0.0        4.0       15.0       12.0   \n",
       "3        0.0        0.0        7.0       15.0       13.0        1.0   \n",
       "4        0.0        0.0        0.0        1.0       11.0        0.0   \n",
       "\n",
       "   pixel_0_6  pixel_0_7  pixel_1_0  pixel_1_1  ...  pixel_6_6  pixel_6_7  \\\n",
       "0        0.0        0.0        0.0        0.0  ...        0.0        0.0   \n",
       "1        0.0        0.0        0.0        0.0  ...        0.0        0.0   \n",
       "2        0.0        0.0        0.0        0.0  ...        5.0        0.0   \n",
       "3        0.0        0.0        0.0        8.0  ...        9.0        0.0   \n",
       "4        0.0        0.0        0.0        0.0  ...        0.0        0.0   \n",
       "\n",
       "   pixel_7_0  pixel_7_1  pixel_7_2  pixel_7_3  pixel_7_4  pixel_7_5  \\\n",
       "0        0.0        0.0        6.0       13.0       10.0        0.0   \n",
       "1        0.0        0.0        0.0       11.0       16.0       10.0   \n",
       "2        0.0        0.0        0.0        3.0       11.0       16.0   \n",
       "3        0.0        0.0        7.0       13.0       13.0        9.0   \n",
       "4        0.0        0.0        0.0        2.0       16.0        4.0   \n",
       "\n",
       "   pixel_7_6  pixel_7_7  \n",
       "0        0.0        0.0  \n",
       "1        0.0        0.0  \n",
       "2        9.0        0.0  \n",
       "3        0.0        0.0  \n",
       "4        0.0        0.0  \n",
       "\n",
       "[5 rows x 64 columns]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame(ds.data, columns=ds.feature_names)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "2226b17b",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>pixel_0_0</th>\n",
       "      <th>pixel_0_1</th>\n",
       "      <th>pixel_0_2</th>\n",
       "      <th>pixel_0_3</th>\n",
       "      <th>pixel_0_4</th>\n",
       "      <th>pixel_0_5</th>\n",
       "      <th>pixel_0_6</th>\n",
       "      <th>pixel_0_7</th>\n",
       "      <th>pixel_1_0</th>\n",
       "      <th>pixel_1_1</th>\n",
       "      <th>...</th>\n",
       "      <th>pixel_6_6</th>\n",
       "      <th>pixel_6_7</th>\n",
       "      <th>pixel_7_0</th>\n",
       "      <th>pixel_7_1</th>\n",
       "      <th>pixel_7_2</th>\n",
       "      <th>pixel_7_3</th>\n",
       "      <th>pixel_7_4</th>\n",
       "      <th>pixel_7_5</th>\n",
       "      <th>pixel_7_6</th>\n",
       "      <th>pixel_7_7</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>count</th>\n",
       "      <td>1797.0</td>\n",
       "      <td>1797.000000</td>\n",
       "      <td>1797.000000</td>\n",
       "      <td>1797.000000</td>\n",
       "      <td>1797.000000</td>\n",
       "      <td>1797.000000</td>\n",
       "      <td>1797.000000</td>\n",
       "      <td>1797.000000</td>\n",
       "      <td>1797.000000</td>\n",
       "      <td>1797.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>1797.000000</td>\n",
       "      <td>1797.000000</td>\n",
       "      <td>1797.000000</td>\n",
       "      <td>1797.000000</td>\n",
       "      <td>1797.000000</td>\n",
       "      <td>1797.000000</td>\n",
       "      <td>1797.000000</td>\n",
       "      <td>1797.000000</td>\n",
       "      <td>1797.000000</td>\n",
       "      <td>1797.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>mean</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.303840</td>\n",
       "      <td>5.204786</td>\n",
       "      <td>11.835838</td>\n",
       "      <td>11.848080</td>\n",
       "      <td>5.781859</td>\n",
       "      <td>1.362270</td>\n",
       "      <td>0.129661</td>\n",
       "      <td>0.005565</td>\n",
       "      <td>1.993879</td>\n",
       "      <td>...</td>\n",
       "      <td>3.725097</td>\n",
       "      <td>0.206455</td>\n",
       "      <td>0.000556</td>\n",
       "      <td>0.279354</td>\n",
       "      <td>5.557596</td>\n",
       "      <td>12.089037</td>\n",
       "      <td>11.809126</td>\n",
       "      <td>6.764051</td>\n",
       "      <td>2.067891</td>\n",
       "      <td>0.364496</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>std</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.907192</td>\n",
       "      <td>4.754826</td>\n",
       "      <td>4.248842</td>\n",
       "      <td>4.287388</td>\n",
       "      <td>5.666418</td>\n",
       "      <td>3.325775</td>\n",
       "      <td>1.037383</td>\n",
       "      <td>0.094222</td>\n",
       "      <td>3.196160</td>\n",
       "      <td>...</td>\n",
       "      <td>4.919406</td>\n",
       "      <td>0.984401</td>\n",
       "      <td>0.023590</td>\n",
       "      <td>0.934302</td>\n",
       "      <td>5.103019</td>\n",
       "      <td>4.374694</td>\n",
       "      <td>4.933947</td>\n",
       "      <td>5.900623</td>\n",
       "      <td>4.090548</td>\n",
       "      <td>1.860122</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>min</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25%</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>11.000000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>50%</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>13.000000</td>\n",
       "      <td>13.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>4.000000</td>\n",
       "      <td>13.000000</td>\n",
       "      <td>14.000000</td>\n",
       "      <td>6.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>75%</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>9.000000</td>\n",
       "      <td>15.000000</td>\n",
       "      <td>15.000000</td>\n",
       "      <td>11.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>3.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>7.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>10.000000</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>12.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>max</th>\n",
       "      <td>0.0</td>\n",
       "      <td>8.000000</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>15.000000</td>\n",
       "      <td>2.000000</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>13.000000</td>\n",
       "      <td>1.000000</td>\n",
       "      <td>9.000000</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>16.000000</td>\n",
       "      <td>16.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>8 rows × 64 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "       pixel_0_0    pixel_0_1    pixel_0_2    pixel_0_3    pixel_0_4  \\\n",
       "count     1797.0  1797.000000  1797.000000  1797.000000  1797.000000   \n",
       "mean         0.0     0.303840     5.204786    11.835838    11.848080   \n",
       "std          0.0     0.907192     4.754826     4.248842     4.287388   \n",
       "min          0.0     0.000000     0.000000     0.000000     0.000000   \n",
       "25%          0.0     0.000000     1.000000    10.000000    10.000000   \n",
       "50%          0.0     0.000000     4.000000    13.000000    13.000000   \n",
       "75%          0.0     0.000000     9.000000    15.000000    15.000000   \n",
       "max          0.0     8.000000    16.000000    16.000000    16.000000   \n",
       "\n",
       "         pixel_0_5    pixel_0_6    pixel_0_7    pixel_1_0    pixel_1_1  ...  \\\n",
       "count  1797.000000  1797.000000  1797.000000  1797.000000  1797.000000  ...   \n",
       "mean      5.781859     1.362270     0.129661     0.005565     1.993879  ...   \n",
       "std       5.666418     3.325775     1.037383     0.094222     3.196160  ...   \n",
       "min       0.000000     0.000000     0.000000     0.000000     0.000000  ...   \n",
       "25%       0.000000     0.000000     0.000000     0.000000     0.000000  ...   \n",
       "50%       4.000000     0.000000     0.000000     0.000000     0.000000  ...   \n",
       "75%      11.000000     0.000000     0.000000     0.000000     3.000000  ...   \n",
       "max      16.000000    16.000000    15.000000     2.000000    16.000000  ...   \n",
       "\n",
       "         pixel_6_6    pixel_6_7    pixel_7_0    pixel_7_1    pixel_7_2  \\\n",
       "count  1797.000000  1797.000000  1797.000000  1797.000000  1797.000000   \n",
       "mean      3.725097     0.206455     0.000556     0.279354     5.557596   \n",
       "std       4.919406     0.984401     0.023590     0.934302     5.103019   \n",
       "min       0.000000     0.000000     0.000000     0.000000     0.000000   \n",
       "25%       0.000000     0.000000     0.000000     0.000000     1.000000   \n",
       "50%       1.000000     0.000000     0.000000     0.000000     4.000000   \n",
       "75%       7.000000     0.000000     0.000000     0.000000    10.000000   \n",
       "max      16.000000    13.000000     1.000000     9.000000    16.000000   \n",
       "\n",
       "         pixel_7_3    pixel_7_4    pixel_7_5    pixel_7_6    pixel_7_7  \n",
       "count  1797.000000  1797.000000  1797.000000  1797.000000  1797.000000  \n",
       "mean     12.089037    11.809126     6.764051     2.067891     0.364496  \n",
       "std       4.374694     4.933947     5.900623     4.090548     1.860122  \n",
       "min       0.000000     0.000000     0.000000     0.000000     0.000000  \n",
       "25%      11.000000    10.000000     0.000000     0.000000     0.000000  \n",
       "50%      13.000000    14.000000     6.000000     0.000000     0.000000  \n",
       "75%      16.000000    16.000000    12.000000     2.000000     0.000000  \n",
       "max      16.000000    16.000000    16.000000    16.000000    16.000000  \n",
       "\n",
       "[8 rows x 64 columns]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "818d6bd8",
   "metadata": {},
   "outputs": [],
   "source": [
    "x=df\n",
    "y=ds.target"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "5707eae8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, ..., 8, 9, 8])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "192bd8cf",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.        , -0.33501649, -0.04308102, ..., -1.14664746,\n",
       "        -0.5056698 , -0.19600752],\n",
       "       [ 0.        , -0.33501649, -1.09493684, ...,  0.54856067,\n",
       "        -0.5056698 , -0.19600752],\n",
       "       [ 0.        , -0.33501649, -1.09493684, ...,  1.56568555,\n",
       "         1.6951369 , -0.19600752],\n",
       "       ...,\n",
       "       [ 0.        , -0.33501649, -0.88456568, ..., -0.12952258,\n",
       "        -0.5056698 , -0.19600752],\n",
       "       [ 0.        , -0.33501649, -0.67419451, ...,  0.8876023 ,\n",
       "        -0.5056698 , -0.19600752],\n",
       "       [ 0.        , -0.33501649,  1.00877481, ...,  0.8876023 ,\n",
       "        -0.26113572, -0.19600752]])"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "\n",
    "scaler = StandardScaler()\n",
    "X_scaled = scaler.fit_transform(x)\n",
    "X_scaled"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "dd24d30d",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "x_train, x_test, y_train, y_test = train_test_split(X_scaled, y, test_size=0.2, random_state=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "5176789c",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "\n",
    "lr = LogisticRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "63520ab0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-2 {color: black;background-color: white;}#sk-container-id-2 pre{padding: 0;}#sk-container-id-2 div.sk-toggleable {background-color: white;}#sk-container-id-2 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-2 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-2 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-2 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-2 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-2 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-2 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-2 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-2 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-2 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-2 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-2 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-2 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-2 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-2 div.sk-item {position: relative;z-index: 1;}#sk-container-id-2 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-2 div.sk-item::before, #sk-container-id-2 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-2 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-2 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-2 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-2 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-2 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-2 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-2 div.sk-label-container {text-align: center;}#sk-container-id-2 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-2 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-2\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LogisticRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-2\" type=\"checkbox\" checked><label for=\"sk-estimator-id-2\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">LogisticRegression</label><div class=\"sk-toggleable__content\"><pre>LogisticRegression()</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "LogisticRegression()"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.fit(x_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "6264a9f7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9833333333333333"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr.score(x_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "1bd5995f",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "\n",
    "# retain 95% of useful features and then create new dimensions\n",
    "pca = PCA(0.95)\n",
    "\n",
    "X_pca = pca.fit_transform(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "8da84754",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797, 29)"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_pca.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "f4689aed",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ -1.25946645,  21.27488348,  -9.46305462, ...,   3.67072108,\n",
       "         -0.9436689 ,  -1.13250195],\n",
       "       [  7.9576113 , -20.76869896,   4.43950604, ...,   2.18261819,\n",
       "         -0.51022719,   2.31354911],\n",
       "       [  6.99192297,  -9.95598641,   2.95855808, ...,   4.22882114,\n",
       "          2.1576573 ,   0.8379578 ],\n",
       "       ...,\n",
       "       [ 10.8012837 ,  -6.96025223,   5.59955453, ...,  -3.56866194,\n",
       "          1.82444444,   3.53885886],\n",
       "       [ -4.87210009,  12.42395362, -10.17086635, ...,   3.25330054,\n",
       "          0.95484174,  -0.93895602],\n",
       "       [ -0.34438963,   6.36554919,  10.77370849, ...,  -3.01636722,\n",
       "          1.29752723,   2.58810313]])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_pca"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "68b220c2",
   "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": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.explained_variance_ratio_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "c3cb45d5",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train_pca, x_test_pca, y_train, y_test = train_test_split(X_pca, y, test_size=0.2, random_state=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "53c31e62",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-2 {color: black;background-color: white;}#sk-container-id-2 pre{padding: 0;}#sk-container-id-2 div.sk-toggleable {background-color: white;}#sk-container-id-2 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-2 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-2 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-2 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-2 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-2 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-2 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-2 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-2 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-2 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-2 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-2 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-2 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-2 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-2 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-2 div.sk-item {position: relative;z-index: 1;}#sk-container-id-2 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-2 div.sk-item::before, #sk-container-id-2 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-2 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-2 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-2 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-2 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-2 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-2 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-2 div.sk-label-container {text-align: center;}#sk-container-id-2 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-2 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-2\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LogisticRegression(max_iter=1000)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-2\" type=\"checkbox\" checked><label for=\"sk-estimator-id-2\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">LogisticRegression</label><div class=\"sk-toggleable__content\"><pre>LogisticRegression(max_iter=1000)</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "LogisticRegression(max_iter=1000)"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr_pca = LogisticRegression(max_iter=1000)\n",
    "lr_pca.fit(x_train_pca, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "896d59c4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9638888888888889"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr_pca.score(x_test_pca, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1924b1e3",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "5f1c3586",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1797, 2)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca = PCA(n_components=2)\n",
    "X_pca = pca.fit_transform(x)\n",
    "X_pca.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "6df52a4f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ -1.25946604,  21.27488229],\n",
       "       [  7.95761087, -20.76869828],\n",
       "       [  6.99192196,  -9.95598393],\n",
       "       ...,\n",
       "       [ 10.80128592,  -6.96025598],\n",
       "       [ -4.87210252,  12.42395669],\n",
       "       [ -0.3443889 ,   6.36554815]])"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_pca"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "2f9b2009",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.14890594, 0.13618771])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.explained_variance_ratio_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "698fe697",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "b46b3141",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train_pca, x_test_pca, y_train, y_test = train_test_split(X_pca, y, test_size=0.2, random_state=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "733b3c75",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-3 {color: black;background-color: white;}#sk-container-id-3 pre{padding: 0;}#sk-container-id-3 div.sk-toggleable {background-color: white;}#sk-container-id-3 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-3 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-3 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-3 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-3 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-3 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-3 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-3 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-3 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-3 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-3 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-3 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-3 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-3 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-3 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-3 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-3 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-3 div.sk-item {position: relative;z-index: 1;}#sk-container-id-3 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-3 div.sk-item::before, #sk-container-id-3 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-3 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-3 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-3 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-3 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-3 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-3 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-3 div.sk-label-container {text-align: center;}#sk-container-id-3 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-3 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-3\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LogisticRegression(max_iter=1000)</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-3\" type=\"checkbox\" checked><label for=\"sk-estimator-id-3\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">LogisticRegression</label><div class=\"sk-toggleable__content\"><pre>LogisticRegression(max_iter=1000)</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "LogisticRegression(max_iter=1000)"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr_pca2 = LogisticRegression(max_iter=1000)\n",
    "lr_pca2.fit(x_train_pca, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "id": "7bb994e4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.625"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lr_pca2.score(x_test_pca, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "6f0a131e",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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