mec-16.4.1a-feature-selection-and-dimensionality-reduction.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CRIM</th>\n",
       "      <th>ZN</th>\n",
       "      <th>INDUS</th>\n",
       "      <th>CHAS</th>\n",
       "      <th>NOX</th>\n",
       "      <th>RM</th>\n",
       "      <th>AGE</th>\n",
       "      <th>DIS</th>\n",
       "      <th>RAD</th>\n",
       "      <th>TAX</th>\n",
       "      <th>PTRATIO</th>\n",
       "      <th>B</th>\n",
       "      <th>LSTAT</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.00632</td>\n",
       "      <td>18.0</td>\n",
       "      <td>2.31</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.538</td>\n",
       "      <td>6.575</td>\n",
       "      <td>65.2</td>\n",
       "      <td>4.0900</td>\n",
       "      <td>1.0</td>\n",
       "      <td>296.0</td>\n",
       "      <td>15.3</td>\n",
       "      <td>396.90</td>\n",
       "      <td>4.98</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.02731</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>6.421</td>\n",
       "      <td>78.9</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>396.90</td>\n",
       "      <td>9.14</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.02729</td>\n",
       "      <td>0.0</td>\n",
       "      <td>7.07</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.469</td>\n",
       "      <td>7.185</td>\n",
       "      <td>61.1</td>\n",
       "      <td>4.9671</td>\n",
       "      <td>2.0</td>\n",
       "      <td>242.0</td>\n",
       "      <td>17.8</td>\n",
       "      <td>392.83</td>\n",
       "      <td>4.03</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.03237</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>6.998</td>\n",
       "      <td>45.8</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3.0</td>\n",
       "      <td>222.0</td>\n",
       "      <td>18.7</td>\n",
       "      <td>394.63</td>\n",
       "      <td>2.94</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.06905</td>\n",
       "      <td>0.0</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.458</td>\n",
       "      <td>7.147</td>\n",
       "      <td>54.2</td>\n",
       "      <td>6.0622</td>\n",
       "      <td>3.0</td>\n",
       "      <td>222.0</td>\n",
       "      <td>18.7</td>\n",
       "      <td>396.90</td>\n",
       "      <td>5.33</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      CRIM    ZN  INDUS  CHAS    NOX     RM   AGE     DIS  RAD    TAX  \\\n",
       "0  0.00632  18.0   2.31   0.0  0.538  6.575  65.2  4.0900  1.0  296.0   \n",
       "1  0.02731   0.0   7.07   0.0  0.469  6.421  78.9  4.9671  2.0  242.0   \n",
       "2  0.02729   0.0   7.07   0.0  0.469  7.185  61.1  4.9671  2.0  242.0   \n",
       "3  0.03237   0.0   2.18   0.0  0.458  6.998  45.8  6.0622  3.0  222.0   \n",
       "4  0.06905   0.0   2.18   0.0  0.458  7.147  54.2  6.0622  3.0  222.0   \n",
       "\n",
       "   PTRATIO       B  LSTAT  \n",
       "0     15.3  396.90   4.98  \n",
       "1     17.8  396.90   9.14  \n",
       "2     17.8  392.83   4.03  \n",
       "3     18.7  394.63   2.94  \n",
       "4     18.7  396.90   5.33  "
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#feature selection\n",
    "\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import matplotlib\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "\n",
    "from sklearn.datasets import load_boston\n",
    "import pandas as pd\n",
    "\n",
    "boston = load_boston()\n",
    "bos = pd.DataFrame(boston.data)\n",
    "bos.head()\n",
    "bos.columns = boston.feature_names\n",
    "bos.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\n",
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       "        vertical-align: top;\n",
       "    }\n",
       "\n",
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       "        text-align: right;\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>PRICE</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>24.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>21.6</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>34.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>33.4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>36.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   PRICE\n",
       "0   24.0\n",
       "1   21.6\n",
       "2   34.7\n",
       "3   33.4\n",
       "4   36.2"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "target_df =pd.DataFrame(boston.target)\n",
    "target_df.columns=['PRICE']\n",
    "target_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "RandomForestRegressor(bootstrap=True, ccp_alpha=0.0, criterion='mse',\n",
       "                      max_depth=10, max_features='auto', max_leaf_nodes=None,\n",
       "                      max_samples=None, min_impurity_decrease=0.0,\n",
       "                      min_impurity_split=None, min_samples_leaf=1,\n",
       "                      min_samples_split=2, min_weight_fraction_leaf=0.0,\n",
       "                      n_estimators=100, n_jobs=None, oob_score=False,\n",
       "                      random_state=1, verbose=0, warm_start=False)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.ensemble import RandomForestRegressor\n",
    "model = RandomForestRegressor(random_state=1, max_depth=10)\n",
    "model.fit(bos,target_df)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "importances [0.03471508 0.00077918 0.00528333 0.00071711 0.02325583 0.42525205\n",
      " 0.01204471 0.06823625 0.00260498 0.01342757 0.01841127 0.01183494\n",
      " 0.38343769]\n",
      "[ 3  1  8  2 11  6  9 10  4  0  7 12  5]\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 864x576 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "features = bos.columns\n",
    "importances = model.feature_importances_\n",
    "\n",
    "plt.figure(figsize=(12, 8))\n",
    "print ('importances',importances)\n",
    "index_for_importance_features = np.argsort(importances) \n",
    "print(index_for_importance_features)\n",
    "plt.title('Feature Importance')\n",
    "plt.bar(range(len(index_for_importance_features)), importances[index_for_importance_features], color='g')\n",
    "plt.xticks(range(len(index_for_importance_features)), [features[i] for i in index_for_importance_features])\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "download csv data from here https://www.kaggle.com/c/cuny-csi-fashion-mnist/data?select=train.csv\n",
    "\n",
    "    \n",
    "Each image is 28 pixels in height and 28 pixels in width, for a total of 784 pixels in total. \n",
    "Each pixel has a single pixel-value associated with it, indicating the lightness or darkness of that pixel, with higher numbers meaning darker. This pixel-value is an integer between 0 and 255. The training and test data sets have 785 columns. The first column consists of the class labels (see above), and represents the article of clothing. The rest of the columns contain the pixel-values of the associated image.\n",
    "\n",
    "To locate a pixel on the image, suppose that we have decomposed x as x = i * 28 + j, \n",
    "where i and j are integers between 0 and 27. The pixel is located on row i and column j of a 28 x 28 matrix.\n",
    "For example, pixel31 indicates the pixel that is in the fourth column from the left, \n",
    "and the second row from the top, as in the ascii-diagram below.\n",
    "\n",
    "\n",
    "use only 2000 rows \n",
    "head -2001 train.csv > train_2000_rows.csv\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\n",
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       "        vertical-align: top;\n",
       "    }\n",
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>label</th>\n",
       "      <th>pixel1</th>\n",
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       "      <th>pixel782</th>\n",
       "      <th>pixel783</th>\n",
       "      <th>pixel784</th>\n",
       "    </tr>\n",
       "  </thead>\n",
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       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>6</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>30</td>\n",
       "      <td>43</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>...</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 785 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   label  pixel1  pixel2  pixel3  pixel4  pixel5  pixel6  pixel7  pixel8  \\\n",
       "0      2       0       0       0       0       0       0       0       0   \n",
       "1      9       0       0       0       0       0       0       0       0   \n",
       "2      6       0       0       0       0       0       0       0       5   \n",
       "3      0       0       0       0       1       2       0       0       0   \n",
       "4      3       0       0       0       0       0       0       0       0   \n",
       "\n",
       "   pixel9    ...     pixel775  pixel776  pixel777  pixel778  pixel779  \\\n",
       "0       0    ...            0         0         0         0         0   \n",
       "1       0    ...            0         0         0         0         0   \n",
       "2       0    ...            0         0         0        30        43   \n",
       "3       0    ...            3         0         0         0         0   \n",
       "4       0    ...            0         0         0         0         0   \n",
       "\n",
       "   pixel780  pixel781  pixel782  pixel783  pixel784  \n",
       "0         0         0         0         0         0  \n",
       "1         0         0         0         0         0  \n",
       "2         0         0         0         0         0  \n",
       "3         1         0         0         0         0  \n",
       "4         0         0         0         0         0  \n",
       "\n",
       "[5 rows x 785 columns]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "mnist_data = pd.read_csv('train_2000_rows.csv')\n",
    "mnist_data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "X =  mnist_data.iloc[:, 1:].values\n",
    "y =  mnist_data.iloc[:, 0].values\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "labels = ['T-shirt/top', 'Trouser', 'Pullover', 'Dress', 'Coat','Sandal', 'Shirt', 'Sneaker', 'Bag', 'Ankle boot']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 72x72 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#look at few images \n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.figure(figsize=(1,1))\n",
    "\n",
    "plt.imshow(X_train[0].reshape(28, 28), cmap=\"binary\")\n",
    "plt.xlabel(labels[y_train[0]])\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 72x72 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#look at few images \n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.figure(figsize=(1,1))\n",
    "\n",
    "plt.imshow(X_train[2].reshape(28, 28), cmap=\"binary\")\n",
    "plt.xlabel(labels[y_train[2]])\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 72x72 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#look at few images \n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.figure(figsize=(1,1))\n",
    "\n",
    "plt.imshow(X_train[1000].reshape(28, 28), cmap=\"binary\")\n",
    "plt.xlabel(labels[y_train[1000]])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "\n",
    "pca = PCA(n_components = 0.90)\n",
    "#to explain 90% of variance\n",
    "#pca = PCA(n_components = 75)\n",
    "#upon using 90 percent and finding length of pca.explained_variance_ratio_, \n",
    "# found that number of components needed is 75\n",
    "X_dimension_reduced = pca.fit_transform(X_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.28787606, 0.17719219, 0.0622009 , 0.04842095, 0.03993166,\n",
       "       0.03681644, 0.02273841, 0.01923902, 0.01499581, 0.01302894,\n",
       "       0.00996471, 0.00933554, 0.00810615, 0.00680433, 0.00644035,\n",
       "       0.00632705, 0.00579732, 0.00526105, 0.00485383, 0.00456198,\n",
       "       0.00438141, 0.00411063, 0.00383126, 0.00379413, 0.00362296,\n",
       "       0.00355332, 0.00346992, 0.00322975, 0.00311404, 0.00297462,\n",
       "       0.00283853, 0.00278181, 0.00273354, 0.0026167 , 0.00259676,\n",
       "       0.0024565 , 0.00232193, 0.0023079 , 0.00223395, 0.00213201,\n",
       "       0.00205689, 0.00205384, 0.00192429, 0.00189916, 0.00184062,\n",
       "       0.00179127, 0.00175991, 0.00169763, 0.00164575, 0.00162972,\n",
       "       0.00156209, 0.0015592 , 0.00154336, 0.00148462, 0.00147099,\n",
       "       0.00143963, 0.00138205, 0.00137455, 0.00134067, 0.00132457,\n",
       "       0.00126844, 0.00125317, 0.00122363, 0.00121259, 0.0011943 ,\n",
       "       0.00118402, 0.00115244, 0.00114176, 0.00110183, 0.0010982 ,\n",
       "       0.00106539, 0.00104123, 0.0010062 , 0.00099981, 0.00098577])"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.explained_variance_ratio_\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "75"
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(pca.explained_variance_ratio_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9007039551719133"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(pca.explained_variance_ratio_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [],
   "source": [
    "#rebuild data again\n",
    "\n",
    "pca = PCA(n_components = 75)\n",
    "X_dimension_reduced = pca.fit_transform(X_train)\n",
    "X_recovered = pca.inverse_transform(X_dimension_reduced)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9007251562703898"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(pca.explained_variance_ratio_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dimenstion reduced image\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "print('dimenstion reduced image')\n",
    "\n",
    "plt.figure(figsize=(5,5))\n",
    "plt.imshow(X_recovered[2].reshape(28, 28), cmap=\"binary\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "original image\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "print('original image')\n",
    "\n",
    "plt.figure(figsize=(5,5))\n",
    "plt.imshow(X_train[2].reshape(28, 28), cmap=\"binary\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "#alternate way to get dataset\n",
    "#download images and use opencv to read image and then flatten\n",
    "\n",
    "#https://github.com/zalandoresearch/fashion-mnist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "download png and copy about 100 images from category=2 to new folder\n",
    "https://github.com/DeepLenin/fashion-mnist_png\n",
    "ls -ltr data/\n",
    "cp data/train/2/10* mnist_data_png/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "105"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import cv2\n",
    "import os\n",
    "image_list = []\n",
    "for f in os.listdir('mnist_data_png/'):\n",
    "    #print (f)\n",
    "    file_name = f\"mnist_data_png/{f}\"\n",
    "    image_list.append(cv2.imread(file_name))\n",
    "    \n",
    "len(image_list)\n",
    "    \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 138,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(105, 28, 28, 3)"
      ]
     },
     "execution_count": 138,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "images_np_array = np.array(image_list)\n",
    "images_np_array.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(105, 2352)"
      ]
     },
     "execution_count": 82,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#flatten_image\n",
    "\n",
    "flatten_image = []\n",
    "for i in range(0,105):\n",
    "    im = images_np_array[i].flatten()\n",
    "    flatten_image.append(im)\n",
    "flatten_image_np_array = np.array(flatten_image)\n",
    "flatten_image_np_array.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['pixel0', 'pixel1', 'pixel2']"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cols = [ 'pixel'+str(i) for i in range(flatten_image_np_array.shape[1]) ]\n",
    "cols[0:3]\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.DataFrame(flatten_image_np_array,columns=cols)\n",
    "df['label'] = 2\n",
    "#pull overs"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7fbcc32709b0>"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXAAAACRCAYAAADaduOsAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAAPqUlEQVR4nO3dW4xd9XXH8e/C9hgzxtcYY3tGmMvgCFmNTS2HKFEFIRTHqsKDUQRFiAckv1AVqogGWqlS3lKpSpsHVAkVSIQi0jah3BQlUGMLtYoccIKJjeMwBjv4OsYmGNtgMF59OHvSYeLL/GbOnrP/499HGs05e5bPWXP2Ocv/Wfu//zsyEzMzK88FnU7AzMxGxwXczKxQLuBmZoVyATczK5QLuJlZoVzAzcwKNaYCHhGrImJ7RPRHxAPtSsrMzM4tRjsPPCImAb8FbgJ2Ay8Dt2fm6+1Lz8zMzmTyGP7tSqA/M98EiIgfArcAZyzgEeGzhszMdO9k5rzhG8dSwBcBbw+5vxv4/Bgez8zOUxEhxZ+HZ5DvOt3GsRTwEYmItcDaup/HzOx8M5YCvgfoHXK/p9r2KZn5MPAwuIViZtZOYyngLwN9EXE5rcJ9G/CXbcnKGmHhwoVS/Jo1a6T4O+64Q4o/deqUFD937twRx06erH0ULr74Yil+8+bNUvzMmTOl+IMHD0rxL774ohT/+OOPS/EDAwNS/HnYEmmLURfwzDwZEX8F/AyYBDyamVvblpmZmZ3VmHrgmfkT4CdtysXMzAQ+E9PMrFCjPpFnVE/mg5htpfR4AR555BEpvq+vT4pX+8LHjh2T4g8fPizFf/zxxyOO7erqkh67u7tbile9++67Urya/9SpU6V4dV+pPfBbb71Vij8PbcrMFcM3egRuZlYoF3Azs0K5gJuZFco98IKpc3OXLVsmxe/du1eKV+dSq6dPX3CBNt5Q+rZ19tdBn8Ou9tjrPhVd/X17enqk+E2bNknx999/vxQ/AbgHbmY2kbiAm5kVygXczKxQta9GaCO3ZMkSKX7x4sVS/J49f7TW2Fk1raf94Ycf1havzotW49Xf9eTJk1L8lClTpPi6e+BvvvmmFH/ttddK8dbiEbiZWaFcwM3MCuUCbmZWKPfAG+SKK66Q4tU+7KFDh6T4jz76SIpX10JR50ar8UrfWX1std+v9rTVnvknn3wixR8/flyKf//996X4adOmSfEXXnihFD979mwpXl1bphQegZuZFcoF3MysUC7gZmaFcg+8QXp7e88dNIQ6l1ft2x49elSKP3HihBSv9szVPrLS1667R63OYVep+ag9bfXx1XMU1NdfXQvfPXAzM2sUF3Azs0K5gJuZFco98AZRe+Bqj1pd20Sl5jNp0iQpXs1fnRutUHNX4z/44AMpXl2rRI1Xj1eox0PU4zMzZ86U4icqj8DNzArlAm5mVigXcDOzQrkH3iCXXXaZFK+uZ6H2MVevXi3FP/vss1K8mo9K6cOq676o87rVdWvUtUHqzufmm2+W4l966SUpXn391WMKE5VH4GZmhXIBNzMrlAu4mVmh3ANvkO7ubilenWur9tgPHDggxe/bt0+KnzdvnhSv9j3V9TXqpO4rdZ0btYe8Y8cOKX7NmjVSvNrDr3stmonKr4KZWaHOWcAj4tGIGIiILUO2zYmIFyLijeq7dnkMMzMbs5GMwL8HrBq27QFgXWb2Aeuq+2ZmNo7O2QPPzJciYvGwzbcA11e3vw9sAL7ZxrzOS+p1/o4dOybFq3N/n3/+eSleXZ9C7duq11lU+qRqT1Vdu0Nde0R9fDX/KVOmSPHqe0Fdr3vv3r1SvNpjn6hG2wOfn5mDR6z2A/PblI+ZmY3QmGehZGZGxBkPmUfEWmDtWJ/HzMw+bbQj8AMRsQCg+j5wpsDMfDgzV2TmilE+l5mZncZoR+DPAHcB366+P922jM5jal9PnSusrte9c+dOKX7p0qVSvErt29Z9HUqF2tNWf1d1/fAZM2ZI8Rs3bpTi77zzTin+yJEjUrz6ek5UI5lG+ATwc2BJROyOiLtpFe6bIuIN4CvVfTMzG0cjmYVy+xl+dGObczEzM4HPxDQzK5TXQmkQdZ6z2uOdM2eOFK/2GdWevDp3WZ1LrVBzUdfuUK/Pqb6W6uOfOnVKiu/q6pLi1XMC1N93+vTpUvxE5RG4mVmhXMDNzArlAm5mVij3wGukXvNR7TOqfcPJk7XdPTBwxvOzTmvlypVSfN3XNVR/3zqpv6u6b9W15NV54+o6Omo+6jEI9fEnKo/AzcwK5QJuZlYoF3Azs0I1p0k4AanXoFSp87Rfe+01KX7Dhg1SfN3rX6hzl5W+ap1zzEdD3bdqj119/K1bt0rxBw8elOLV/NXrqU5UHoGbmRXKBdzMrFAu4GZmhXIPvEa9vb1SvHqNSNXhw4el+EOHDknx6lzeuuexKz1ztb+urtfdtLVW1N/3+PHjUrzaY3/vvfekeF8Ts8UjcDOzQrmAm5kVygXczKxQ7oHXSO3TqXOR1bmze/bskeKXL18uxdfdl1T7yErfts455qOh9sDVnvPChQulePV6quoxgosuukiKV4+fTFQegZuZFcoF3MysUC7gZmaFcg+8QdQeuDrP/LHHHpPie3p6pHj1Gp1q31Z9fIV6PEHtUas927rXQlF71OocfPWcBjWfuteSL4VH4GZmhXIBNzMrlAu4mVmh3AOvkdo3VPuq6tzZnTt3SvFXXnmlFF/3dR/V9T6UeeknTpyQHrvufatSe851X7NSpfb81fiJyiNwM7NCuYCbmRXKBdzMrFDugddo6tSpUry63oTal+zv75fi6+5Lqn1klTJvXH0t1dzrfnz1HAK1J79lyxYpXl0XRz0e4rVQWjwCNzMr1DkLeET0RsT6iHg9IrZGxL3V9jkR8UJEvFF9n11/umZmNmgkI/CTwDcy8xrgOuCeiLgGeABYl5l9wLrqvpmZjZNzNtoycx+wr7r9fkRsAxYBtwDXV2HfBzYA36wly0KpfUC176nOi969e7cUP2vWLCle7fnX3TNX5qWr88DVedd1z6Pu6uqS4tU5+9u3b5fi1eupqp8V9b0/UUnvqohYDCwHNgLzq+IOsB+Y39bMzMzsrEY8pImI6cCPgfsy88jQ0VNmZkSc9rBwRKwF1o41UTMz+7QRjcAjYgqt4v2DzHyy2nwgIhZUP18ADJzu32bmw5m5IjNXtCNhMzNrOecIPFpD7UeAbZn5nSE/ega4C/h29f3pWjIs2LRp06R4tU9a5/rYAH19fVK8cg1KaNZcanU9anUespq7Gq/O67700kuleNW+ffvOHTTEggULaspkYhvJO/yLwJ3AryPi1Wrb39Eq3P8REXcDu4Cv15OimZmdzkhmofwPcKbpAje2Nx0zMxspn4lpZlYor4VSI3XNZXVetNpnVC1atEiKv+GGG6T49evXS/HqPHNlrnPT5hWfOnVKilfnpS9dulSKV+3atUuKV+eBq2u/TFQegZuZFcoF3MysUC7gZmaFcg+8RmpPW52LvGPHDile9dBDD0nxTz31lBSvzmNX50Yrr3/T1pdWe/Jq/uo5Cqp33nlHir/qqquk+KYds+gUj8DNzArlAm5mVigXcDOzQrkHXqOrr75aild75m+99ZYUr1L7qup64zZx7d+/v9bHv+SSS2p9/FJ4BG5mVigXcDOzQrmAm5kVyj3wGqnXHZw7d64U39/fL8Wr1J68Gm+do+4rdd61Og98+vTpUry6ztBE5RG4mVmhXMDNzArlAm5mVij3wGt09OjRWuMPHDggxddNXcPaOkddV0alrk+uXh+17uvBlsIjcDOzQrmAm5kVygXczKxQMZ7rIEdEsxZdbhh13rjXRLbRUueB110nZsyYIcUfOXKkpkwaa1Nmrhi+0SNwM7NCuYCbmRXKBdzMrFDj3QM/COwCPgNoiyWML+c3ek3ODZzfWDm/sRltfpdl5rzhG8e1gP/hSSNeOV1Dvimc3+g1OTdwfmPl/Mam3fm5hWJmVigXcDOzQnWqgD/coecdKec3ek3ODZzfWDm/sWlrfh3pgZuZ2di5hWJmVqhxLeARsSoitkdEf0Q8MJ7PfYZ8Ho2IgYjYMmTbnIh4ISLeqL7P7mB+vRGxPiJej4itEXFvk3KMiAsj4hcRsbnK71vV9ssjYmO1n/89Iro6kV+Vy6SI+FVEPNe03Kp8dkbEryPi1Yh4pdrWlP07KyJ+FBG/iYhtEfGFBuW2pHrNBr+ORMR9TcmvyvFvqs/Floh4ovq8tPX9N24FPCImAQ8BXwWuAW6PiGvG6/nP4HvAqmHbHgDWZWYfsK663ykngW9k5jXAdcA91WvWlBxPAF/OzM8By4BVEXEd8I/AP2fmVcC7wN0dyg/gXmDbkPtNym3QDZm5bMj0sqbs3+8CP83MzwKfo/U6NiK3zNxevWbLgD8FjgP/1ZT8ImIR8NfAisxcCkwCbqPd77/MHJcv4AvAz4bcfxB4cLye/yx5LQa2DLm/HVhQ3V4AbO90jkNyexq4qYk5AhcBvwQ+T+tEhcmn2+/jnFMPrQ/xl4HngGhKbkNy3Al8Zti2ju9fYCbwFtVxsibldppc/xz43yblBywC3gbm0LpwznPAze1+/41nC2XwFxq0u9rWNPMzc191ez8wv5PJDIqIxcByYCMNyrFqUbwKDAAvADuA32fmySqkk/v5X4C/BQYvFTSX5uQ2KIHnI2JTRKyttjVh/14OHAQeq1pQ/xYR3Q3JbbjbgCeq243ILzP3AP8E/A7YB7wHbKLN7z8fxDyLbP032fFpOhExHfgxcF9mfmodzU7nmJmfZOvP2B5gJfDZTuUyVET8BTCQmZs6ncs5fCkzr6XVWrwnIv5s6A87uH8nA9cC/5qZy4FjDGtHdPq9B1D1kL8G/Ofwn3Uyv6r3fgut/wgXAt38cbt2zMazgO8Beofc76m2Nc2BiFgAUH0f6GQyETGFVvH+QWY+WW1uVI4Amfl7YD2tPwtnRcTgRQ47tZ+/CHwtInYCP6TVRvluQ3L7g2qkRmYO0OrhrqQZ+3c3sDszN1b3f0SroDcht6G+CvwyMwcvENuU/L4CvJWZBzPzY+BJWu/Jtr7/xrOAvwz0VUdhu2j92fPMOD7/SD0D3FXdvotW37kjIiKAR4BtmfmdIT9qRI4RMS8iZlW3p9Hqz2+jVchv7WR+mflgZvZk5mJa77UXM/OOJuQ2KCK6I+Liwdu0erlbaMD+zcz9wNsRsaTadCPwehNyG+Z2/r99As3J73fAdRFxUfU5Hnz92vv+G+fG/mrgt7T6pH/fiYMLw/J5glZ/6mNaI467afVJ1wFvAP8NzOlgfl+i9Sfga8Cr1dfqpuQI/Anwqyq/LcA/VNuvAH4B9NP603Zqh/fz9cBzTcutymVz9bV18DPRoP27DHil2r9PAbObkluVXzdwCJg5ZFuT8vsW8Jvqs/E4MLXd7z+fiWlmVigfxDQzK5QLuJlZoVzAzcwK5QJuZlYoF3Azs0K5gJuZFcoF3MysUC7gZmaF+j/4FPlh4XH0kgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "im1 = df.loc[1,feat_cols].values.reshape((28,28*3)).astype(float)\n",
    "plt.imshow(im1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "pca = PCA(n_components=0.9)\n",
    "pca_result = pca.fit_transform(df[cols].values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.39279757, 0.12237024, 0.05866473, 0.03979502, 0.03422344,\n",
       "       0.02458311, 0.02278617, 0.02041936, 0.01985491, 0.01620309,\n",
       "       0.01493185, 0.01291967, 0.01202127, 0.0113323 , 0.01022546,\n",
       "       0.00903932, 0.00880005, 0.00858478, 0.00789595, 0.00750273,\n",
       "       0.00706632, 0.00652784, 0.00600413, 0.00580497, 0.0055478 ,\n",
       "       0.00533766, 0.00499875, 0.00436016])"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.explained_variance_ratio_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "28"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(pca.explained_variance_ratio_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9005986519317273"
      ]
     },
     "execution_count": 128,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sum(pca.explained_variance_ratio_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(105, 2352)"
      ]
     },
     "execution_count": 126,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#rebuild data again\n",
    "\n",
    "pca = PCA(n_components = 0.9)\n",
    "X_dimension_reduced = pca.fit_transform(df[feat_cols].values)\n",
    "X_recovered = pca.inverse_transform(X_dimension_reduced)\n",
    "X_recovered.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "dimenstion reduced image\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7fbcc31d1518>"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "print('dimenstion reduced image')\n",
    "\n",
    "im1 = X_recovered[2].reshape((28,28*3)).astype(float)\n",
    "plt.imshow(im1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6478509938952306"
      ]
     },
     "execution_count": 135,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#testing only 5 components\n",
    "# 5 components itself can explain about 64% of variation\n",
    "from sklearn.decomposition import PCA\n",
    "pca = PCA(n_components=5)\n",
    "pca_result = pca.fit_transform(df[cols].values)\n",
    "sum(pca.explained_variance_ratio_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.39279757, 0.12237024, 0.05866473, 0.03979502, 0.03422344])"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pca.explained_variance_ratio_"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}