PCA.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from sklearn.datasets import load_iris\n",
    "from matplotlib import pyplot as plt\n",
    "%matplotlib inline\n",
    "import pandas as pd\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(800, 2)\n"
     ]
    }
   ],
   "source": [
    "# create some data\n",
    "mean_01 = np.array([0., 0.])\n",
    "cov_01 = np.array([[1.0, 1.2], [1.2, 1.5]])\n",
    "\n",
    "data = np.random.multivariate_normal(mean_01, cov_01, 800)\n",
    "print(data.shape)\n",
    "# print(np.cov(data.T))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def pca(X, k=None):\n",
    "    # set number of output dims\n",
    "    if k is None:\n",
    "        k = X.shape[1]\n",
    "    \n",
    "    # compute the covariance\n",
    "    A = np.cov(X.T)\n",
    "    \n",
    "    # Compute the eigenvectors and eigenvalues\n",
    "    eig_val, eig_vec = np.linalg.eig(A)\n",
    "    #Z = X.dot(W)\n",
    "    return eig_val, eig_vec"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(2,) (2, 2)\n"
     ]
    }
   ],
   "source": [
    "lam, W = pca(data)\n",
    "print(lam.shape, W.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.02545654 2.3902987 ]\n",
      "[[-0.776258   -0.63041535]\n",
      " [ 0.63041535 -0.776258  ]]\n"
     ]
    }
   ],
   "source": [
    "print(lam)\n",
    "print(W)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "plt.figure(0)\n",
    "plt.scatter(data[:, 0], data[:, 1])\n",
    "plt.plot([0, 10*W[0, 0]], [0, 10*W[1, 0]], 'ro--')\n",
    "plt.plot([0, 10*W[0, 1]], [0, 10*W[1, 1]], 'ro--')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x110b8a198>]"
      ]
     },
     "execution_count": 12,
     "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": [
    "plt.plot([0, W[1, 0]], [0, W[0, 0]], '*-')\n",
    "plt.plot([0, W[1, 1]], [0, W[0, 1]], '*--')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(800, 2)\n",
      "[[-0.04618047 -2.41504956]\n",
      " [-0.04167997  0.33568056]\n",
      " [-0.12033041 -1.13818892]\n",
      " [ 0.04589857 -2.03433465]\n",
      " [ 0.30420384  1.96323347]\n",
      " [-0.04002885  0.22719741]\n",
      " [-0.09998056  0.93413337]\n",
      " [ 0.27592333 -0.38710617]\n",
      " [-0.27729602  0.85370779]\n",
      " [ 0.07137632 -0.53388364]]\n"
     ]
    }
   ],
   "source": [
    "Z = data.dot(W[:])\n",
    "print(Z.shape)\n",
    "print(Z[:10])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, 2)"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "W.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "plt.figure(0)\n",
    "plt.xlim(-6, 6)\n",
    "plt.ylim(-6, 6)\n",
    "plt.scatter(Z[:, 0], Z[:, 1])\n",
    "# plt.plot([0, 10*W[0, 0]], [0, 10*W[1, 0]], 'ro--')\n",
    "# plt.plot([0, 10*W[0, 1]], [0, 10*W[1, 1]], 'ro--')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 2.54565401e-02, -3.55716013e-17],\n",
       "       [-3.55716013e-17,  2.39029870e+00]])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.cov(Z.T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.98946229 1.        ]\n"
     ]
    }
   ],
   "source": [
    "print(np.cumsum(lam[::-1]/lam.sum()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PCA on MNIST"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(10000, 784)\n"
     ]
    }
   ],
   "source": [
    "ds = pd.read_csv('./train.csv')\n",
    "data = ds.values[:10000, 1:]\n",
    "print(data.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(784, 784)\n"
     ]
    }
   ],
   "source": [
    "A = np.cov(data.T)\n",
    "print(A.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(784,)\n"
     ]
    }
   ],
   "source": [
    "eig_vals, eig_vecs = np.linalg.eig(A)\n",
    "print(eig_vals.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "784\n"
     ]
    }
   ],
   "source": [
    "info = []\n",
    "for ix in range(eig_vals.shape[0]):\n",
    "    dx = [eig_vals[ix], eig_vecs[:, ix]]\n",
    "    info.append(dx)\n",
    "print(len(info))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "info = sorted(info, key=lambda z: z[0], reverse=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "sorted_lambda = []\n",
    "sorted_W = []\n",
    "\n",
    "for ix in range(len(info)):\n",
    "    sorted_lambda.append(info[ix][0])\n",
    "    sorted_W.append(info[ix][1])\n",
    "\n",
    "sorted_lambda = np.asarray(sorted_lambda)\n",
    "sorted_W = np.asarray(sorted_W)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.7/site-packages/numpy/core/numeric.py:501: ComplexWarning: Casting complex values to real discards the imaginary part\n",
      "  return array(a, dtype, copy=False, order=order)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x112e81438>]"
      ]
     },
     "execution_count": 29,
     "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": [
    "plt.plot(sorted_lambda)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAD8CAYAAACMwORRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4xLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvDW2N/gAAGptJREFUeJzt3X10XHd95/H3V6PnJ8u2ZMeR5MhO7BgT8uC6iYFC0gAhSUvCnnZ74hNaoBT3gfTAQpeTbLspze7Zs3T3sH1KgdBNaTlLTMhScMGcLCQp6aEk2CZxEj8F2U5s+UkPtp6lGc3Md/+YK3ssS5qxPdLMvfq8jufo3t+9nvuVZ/TxT79772/M3RERkWgpK3YBIiJSeAp3EZEIUriLiESQwl1EJIIU7iIiEaRwFxGJIIW7iEgEKdxFRCIoZ7ib2eNm1m1mr82w3czsr8ys08xeMbMNhS9TREQuRnke+3wV+BvgH2fYfhewJnjcAnwx+Dqr5uZm7+joyKtIERHJ2LVrV6+7t+TaL2e4u/vzZtYxyy73Av/omXkMXjCzJjNb4e4nZnvejo4Odu7cmevwIgtaOu2k3EmlnfTk1zTntaXdcQcHPFgGgrYp24L2YI+sbVn7Zi3P9jycfa7CTWFSyNlQCj2xSiFr61hay7LG6kv6u2b2Zj775dNzz6UVOJq13hW0zRruIsWUTKUZT6YZS6QYn0gRT6YYS6QZT6bOto0n04wnUowng30m0kyk0iRSzkQqTTJrefKRSAbb0mkmkk4ia9tEykmm05lwDkL7vPA+23YuvCWa/usHr+NDm66a02MUItzzZmZbgC0AK1eunM9DS8i5OyOJFANjEwyOTTAcTzIcTzISPIbjqeDr1PYkI1nbxhIpxiZSJC8jOCtjZVTEjIryMipiZefWY2WUx8qoDJYrYmU0VlacXS+PlVFeZpSZESuD2Nnlc19j2dvNKCuzc1+zly34+8H+BpiBYQR/sOz2YJtZ5nuwYCH775mdW+e89QufZ/IYZG0vFCvgkxW2ssLVtrqlrjBPNItChPsxoD1rvS1ou4C7PwY8BrBx40Z1SxagdNoZHJ+gbyRB33CC0yMJBscmGAge/WMJBsaSZ9cHs77mE8hV5WXUV5VTFzzqq2I011dy1dJa6qvKqamMUV0Ro6YiRnVFGTUVMaoqzm+bujz5qCrPhLMVMn1E5kghwn0b8ICZbSVzInUg13i7RMtEKk3PUJxTg+N0D8WD0I7TG4R330imrW8kwZmRxIwhXWawqKbi7KOxpoL2xTXntU0+6qsnwzv4WllObVWMipiu7hWBPMLdzJ4AbgOazawL+FOgAsDdvwRsB+4GOoFR4KNzVazMv8HxCY6dGePk4Djdg+OcHIhzamicUwPjnBrKrPeNxKc92dRQVc7S+kqW1FXSvqSWG9ubWFJXydL6KpbWVbK0vpLFtZU01QaBXVWuXrFIgeRztczmHNsd+ETBKpJ5NRxP0nVmlKOnx+g6M0rXmXNfj54eZXA8ecHfWVpXyfLGapY3VvG21kUsa6jmikWZ9WUN1WcDvao8VoTvSERgnk+oSnHEkymO9I1ysGeEw70jHO4d5lCw3DeSOG/fmooYbYtraF9Syy9ctZi2xTW0NtWeF96V5Rr6ECl1CvcImUilOdw7wv6TQxw4OciBk0O8fmqYrjOjZA9ztzRUsaq5jjveupyrltbRvriWtsU1tC2uYUldpYZGRCJA4R5S4xMp9hwf4OWjA+w5NsC+k0Mc7B4mkUoDmcvkrm6p4/q2RXzwplaubqljVXMdHc11NFZXFLl6EZlrCvcQcHc6u4fZ9eYZdnf1s/voAAdODZ29yWVZQxXrVjTy7jXNXHtFA+uuaOTqZXUa8xZZwBTuJcjdOdgzzE8O9vHCodO8cKjv7Nh4Y3U5N7Q38fvrrub6tkXc0N7E8ku8jVlEokvhXiIGxiZ4/vUent3fzb/+vIfe4UyYr1hUza1rW9i0eim/uGoJHUtrNSYuIjkp3IvoWP8Y2185wQ/3nWLnm2dIpZ3FtRXcuraFd1zdzKbVS2lfUqMwF5GLpnCfZ33Dcba/eoLvvHycnW+eAWDdFQ383q2ruX3dcm5sbyJWpjAXkcujcJ8H6bTz/M97+PqLR3hmfzeptLN2eT1/dMdaPnDDlVy1dO4nERKRhUXhPof6huN8Y+dRnvjpEY6eHmNpXSW/865V/LubWll3RWOxyxORCFO4z4Fj/WN85flDbN1xhPGJNJtWL+Gz71/HHW9drssTRWReKNwL6OTAOH/xw9d5alcXAB+8qZXfffdq1ixvKHJlIrLQKNwLYDie5Ms/OshX/vUQqbRz/y0r2XLr1bQ21RS7NBFZoBTul8Hd+f5rJ/nTbXvoGYrzgRuu5LPvv5b2JbXFLk1EFjiF+yU6MTDGf/72a/xwXzfXtTby2G/+AjetXFzsskREAIX7JfnB3lP80Td3k0im+ZNfeQsfeUcH5foEIBEpIQr3i5BIpvnv39/P4z8+zHWtjfzN5g10NOsadREpPQr3PPUMxdnytZ28dKSfj76zgwfvWqfLGkWkZCnc8/D6qSE++vc76BuJ88X7N3DX21YUuyQRkVkp3HPYc3yA+//uRSpjZXzzd9/B29oWFbskEZGcFO6zeO1YJtjrq8p54uObWLlUlziKSDgo3GfQ2T10Nti3btmka9dFJFR0/d40Tg2O8+HHd1ARK1Owi0goKdynGI4n+e2v7uDMaIKvfvQXFewiEkoK9yzuzkPfepV9JwZ59P4NXNeqk6ciEk4K9yxbdxzln3cf59PvW8svX7us2OWIiFwyhXtg/8lBPrdtD+9a08wf3HZNscsREbksCncy0wp8auvLNFRX8IXfuJEyfYapiIScLoUEvvyjg+w/OcRXfmsjLQ1VxS5HROSyLfiee2f3EH/9bCe/cv0K3rd+ebHLEREpiAUd7u7Ow9/ZQ01ljM994K3FLkdEpGAWdLg/s6+bfzvYx2fuWKvhGBGJlAUb7hOpNP9t+z6ubqlj880ri12OiEhBLdhw/6efHeNQ7wj/6e63UKFPURKRiMkr1czsTjM7YGadZvbgNNtXmtlzZvaSmb1iZncXvtTCSaWdL/7oINe1NnL7Ot2sJCLRkzPczSwGPArcBawHNpvZ+im7/QnwpLvfBNwH/G2hCy2k7716gsO9I3zitmsw0zXtIhI9+fTcbwY63f2QuyeArcC9U/ZxoDFYXgQcL1yJhZVOO3/7XCfXLKvn/W+9otjliIjMiXzCvRU4mrXeFbRl+xzwITPrArYDf1iQ6ubATw71sf/kEL9369W6E1VEIqtQZxI3A1919zbgbuBrZnbBc5vZFjPbaWY7e3p6CnToi/P1F4+wuLaCX71en4MqItGVT7gfA9qz1tuCtmwfA54EcPefANVA89QncvfH3H2ju29saWm5tIovQ89QnKf3nOTXNrRRXRGb9+OLiMyXfMJ9B7DGzFaZWSWZE6bbpuxzBHgPgJm9hUy4F6drPoundnWRTDv36bp2EYm4nOHu7kngAeBpYB+Zq2L2mNkjZnZPsNtngI+b2W7gCeAj7u5zVfSlSKedrTuOcPOqJVyzrL7Y5YiIzKm8ZoV09+1kTpRmtz2ctbwXeGdhSyusXUfO8GbfKJ98z5pilyIiMucWzK2Z/7z7OFXlZdyhyx9FZAFYEOGeTKXZ/uoJ3vuW5dRXaQp7EYm+BRHuPznUR+9wgg/coMsfRWRhWBDh/r1XTlBfVc5t+tBrEVkgIh/u7s6z+7u5dW2Lrm0XkQUj8uG+98Qg3UNxbrt2/m+aEhEplsiH+78cyNxLdavCXUQWkAUQ7t1c19rIsobqYpciIjJvIh3uA6MT7HrzDL+sE6kissBEOtxfONxH2uFdazQkIyILS6TD/cVDp6kqL+OG9kXFLkVEZF5FO9wP93HTyiaqynUJpIgsLJEN94GxCfaeGOSWVUuLXYqIyLyLbLjvevM07nDL6iXFLkVEZN5FNtxfPtJPmcGN7U3FLkVEZN5FNtx3dw2wdnkDtZWaBVJEFp5Ihru7s7urn+vbdJWMiCxMkQz3o6fH6B+d4AYNyYjIAhXJcN/d1Q/ADW0KdxFZmCIZ7q909VNZXsa1VzQUuxQRkaKIZLjv7hpg/YpGKmKR/PZERHKKXPql087e44M6mSoiC1rkwv1Y/xjD8STrrmgsdikiIkUTuXA/cHIIQOPtIrKgRS/cT2XCfe3y+iJXIiJSPNEL95NDtDbV0FBdUexSRESKJpLhvk5DMiKywEUq3BPJNAd7hjXeLiILXqTC/cjpUZJp55plGm8XkYUtUuH+Ru8IAKua64pciYhIcUUr3PsU7iIiELFwP9Q7QlNtBU21lcUuRUSkqCIV7m/0jtCxVL12EZHIhbuGZERE8gx3M7vTzA6YWaeZPTjDPr9hZnvNbI+Zfb2wZeY2PpHi+MC4eu4iIkDODxg1sxjwKPA+oAvYYWbb3H1v1j5rgIeAd7r7GTNbNlcFz+TNvlEAVrUo3EVE8um53wx0uvshd08AW4F7p+zzceBRdz8D4O7dhS0zt8O9wwCsUs9dRCSvcG8FjmatdwVt2dYCa83sx2b2gpndWagC83W4N9Nz72iune9Di4iUnJzDMhfxPGuA24A24Hkze5u792fvZGZbgC0AK1euLNChM97sG6G5vlIThomIkF/P/RjQnrXeFrRl6wK2ufuEux8GXicT9udx98fcfaO7b2xpabnUmqcvsn+M1sXqtYuIQH7hvgNYY2arzKwSuA/YNmWfb5PptWNmzWSGaQ4VsM6cjvePceWi6vk8pIhIycoZ7u6eBB4Angb2AU+6+x4ze8TM7gl2exroM7O9wHPAf3T3vrkqepoaOTEwzopFNfN1SBGRkpbXmLu7bwe2T2l7OGvZgU8Hj3k3OJZkNJHiyib13EVEICJ3qB7rHwNQz11EJBCJcD8xEIS7eu4iIkBEwv34wDgArU3quYuIQETC/UT/GOVlRnN9VbFLEREpCdEI94FxljdWEyuzYpciIlISIhHux/vHdKWMiEiWSIR791CcZY0KdxGRSZEI996hOC0abxcROSv04T4+kWIonqSlQeEuIjIp9OHeMxQHUM9dRCRL+MN9OAh39dxFRM4Kf7gHPXdd4y4ick7ow71XPXcRkQuEPtwne+5L6yuLXImISOkIfbj3DsdZXFtBRSz034qISMGEPhF7huIakhERmSIS4a6TqSIi5wt9uPcOJ9RzFxGZIgLhrp67iMhUoQ73eDLFaCLF4tqKYpciIlJSQh3uA2MTACyqUbiLiGQLdbgPBuHeqHAXETlPqMNdPXcRkekp3EVEIijU4d4/mgn3plpNPSAiki3U4a6eu4jI9CIR7o3V5UWuRESktIQ+3OuryinXpGEiIucJdSoOjE5oSEZEZBrhDvcxhbuIyHQU7iIiEaRwFxGJoFCHe7/CXURkWqEO94GxCZo0I6SIyAXyCnczu9PMDphZp5k9OMt+v2ZmbmYbC1fi9MYnUiSSaU0aJiIyjZzhbmYx4FHgLmA9sNnM1k+zXwPwSeDFQhc5Hd2dKiIys3x67jcDne5+yN0TwFbg3mn2+y/A54HxAtY3o6HxJAANujtVROQC+YR7K3A0a70raDvLzDYA7e7+vQLWNquReCbc6yoV7iIiU132CVUzKwO+AHwmj323mNlOM9vZ09NzWccdSQThXqVwFxGZKp9wPwa0Z623BW2TGoDrgH8xszeATcC26U6quvtj7r7R3Te2tLRcetXAaDwFQF1V7LKeR0QkivIJ9x3AGjNbZWaVwH3AtsmN7j7g7s3u3uHuHcALwD3uvnNOKg5M9txrNSwjInKBnOHu7kngAeBpYB/wpLvvMbNHzOyeuS5wJiNBz71ewzIiIhfIKxndfTuwfUrbwzPse9vll5Xb6GTPXcMyIiIXCO0dqsPB1TK1FQp3EZGpQhvuo4kU1RVl+qAOEZFphDYZR+JJXeMuIjKDUIe7xttFRKYX3nBPpNRzFxGZQWjDfTSR1N2pIiIzCG24D8dTCncRkRmENtxH40nqKjXmLiIynfCGeyKlqQdERGYQ4nBPUqueu4jItEIb7uMTaaorQlu+iMicCmU6ujvjyRTVmnpARGRaoQz3RCqNOwp3EZEZhDLcxyfSAFSVh7J8EZE5F8p0HJ/IzOWunruIyPQU7iIiERTScM8My+hqGRGR6YUyHc/23MvVcxcRmU64w13DMiIi0wpnuCc1LCMiMptQpqN67iIiswt5uIeyfBGRORfKdIyfvYlJPXcRkemEMtzHkxqWERGZTTjDXcMyIiKzCmU6nruJST13EZHphDTcU8TKjIpYKMsXEZlzoUzH8Yk01ZoRUkRkRqFMSH1Qh4jI7MIZ7hMKdxGR2YQy3OMTaap0pYyIyIxCmZDxZEozQoqIzCKk4Z6mUidURURmFMqETCjcRURmlVdCmtmdZnbAzDrN7MFptn/azPaa2Stm9oyZXVX4Us9JpNJU6hp3EZEZ5UxIM4sBjwJ3AeuBzWa2fspuLwEb3f164CngzwtdaLaJlHruIiKzySchbwY63f2QuyeArcC92Tu4+3PuPhqsvgC0FbbM8yWS6rmLiMwmn4RsBY5mrXcFbTP5GPD9yykqF425i4jMrryQT2ZmHwI2ArfOsH0LsAVg5cqVl3wchbuIyOzySchjQHvWelvQdh4zey/wx8A97h6f7onc/TF33+juG1taWi6lXiA4oapwFxGZUT4JuQNYY2arzKwSuA/Ylr2Dmd0EfJlMsHcXvszzxTXmLiIyq5wJ6e5J4AHgaWAf8KS77zGzR8zsnmC3/wHUA980s5fNbNsMT1cQiWSaKvXcRURmlNeYu7tvB7ZPaXs4a/m9Ba5rtlo0LCMikkPoEjKZdtzRB3WIiMwidAk5kcp8xJ567iIiMwtdQiaSQbir5y4iMqPQJeTZcFfPXURkRqFLyLjCXUQkp9AlZCIYc9elkCIiMwtdQmrMXUQkt9AlpMbcRURyC11CJnQppIhITqFLyMmeu25iEhGZWegSUsMyIiK5hS4hzw7LqOcuIjKj0CXkZM9dl0KKiMwsdAmpYRkRkdxCl5C6WkZEJLfQJaRuYhIRyS10CalhGRGR3EKXkO1Larh93TKqymPFLkVEpGTl9TF7peTO61Zw53Uril2GiEhJC13PXUREclO4i4hEkMJdRCSCFO4iIhGkcBcRiSCFu4hIBCncRUQiSOEuIhJBCncRkQhSuIuIRJDCXUQkghTuIiIRpHAXEYkghbuISAQp3EVEIiivcDezO83sgJl1mtmD02yvMrNvBNtfNLOOQhcqIiL5yxnuZhYDHgXuAtYDm81s/ZTdPgaccfdrgP8FfL7QhYqISP7y6bnfDHS6+yF3TwBbgXun7HMv8A/B8lPAe8zMClemiIhcjHzCvRU4mrXeFbRNu4+7J4EBYGkhChQRkYs3r5+hamZbgC3B6rCZHbjEp2oGegtTVcGptkuj2i6Nart4pVoX5FfbVfk8UT7hfgxoz1pvC9qm26fLzMqBRUDf1Cdy98eAx/IpbDZmttPdN17u88wF1XZpVNulUW0Xr1TrgsLWls+wzA5gjZmtMrNK4D5g25R9tgEfDpZ/HXjW3b0QBYqIyMXL2XN396SZPQA8DcSAx919j5k9Aux0923A/wa+ZmadwGky/wGIiEiR5DXm7u7bge1T2h7OWh4H/n1hS5vVZQ/tzCHVdmlU26VRbRevVOuCAtZmGj0REYkeTT8gIhJBoQv3XFMhzMPxHzezbjN7LattiZn9wMx+HnxdHLSbmf1VUOsrZrZhDutqN7PnzGyvme0xs0+WUG3VZvZTM9sd1PZnQfuqYLqKzmD6isqgfd6nszCzmJm9ZGbfLaXazOwNM3vVzF42s51BW9Ff0+B4TWb2lJntN7N9Zvb2UqjNzK4N/r0mH4Nm9qlSqC043n8Ifg5eM7Mngp+Pwr/f3D00DzIndA8Cq4FKYDewfp5reDewAXgtq+3PgQeD5QeBzwfLdwPfBwzYBLw4h3WtADYEyw3A62SmiyiF2gyoD5YrgBeDYz4J3Be0fwn4/WD5D4AvBcv3Ad+Yh9f108DXge8G6yVRG/AG0DylreivaXC8fwB+J1iuBJpKpbasGmPASTLXhhe9NjI3fB4GarLeZx+Zi/fbnP/jFvgf5u3A01nrDwEPFaGODs4P9wPAimB5BXAgWP4ysHm6/eahxu8A7yu12oBa4GfALWRu1iif+tqSuTLr7cFyebCfzWFNbcAzwO3Ad4Mf8lKp7Q0uDPeiv6Zk7mU5PPV7L4XaptRzB/DjUqmNc3fzLwneP98F3j8X77ewDcvkMxVCMSx39xPB8klgebBclHqDX91uItNDLonagmGPl4Fu4AdkfgPr98x0FVOPP9/TWfwF8FkgHawvLaHaHPh/ZrbLMnd4Q2m8pquAHuDvg+GsvzOzuhKpLdt9wBPBctFrc/djwP8EjgAnyLx/djEH77ewhXvJ88x/sUW7BMnM6oH/C3zK3QeztxWzNndPufuNZHrJNwPrilHHVGb2q0C3u+8qdi0z+CV330BmVtZPmNm7szcW8TUtJzM8+UV3vwkYITPUUQq1ARCMW98DfHPqtmLVFozz30vmP8crgTrgzrk4VtjCPZ+pEIrhlJmtAAi+dgft81qvmVWQCfb/4+7fKqXaJrl7P/AcmV89mywzXcXU45+tzWaZzqJA3gncY2ZvkJnx9HbgL0uktsmeHu7eDfwTmf8YS+E17QK63P3FYP0pMmFfCrVNugv4mbufCtZLobb3AofdvcfdJ4BvkXkPFvz9FrZwz2cqhGLInn7hw2TGuyfbfys4G78JGMj6tbCgzMzI3Cm8z92/UGK1tZhZU7BcQ+ZcwD4yIf/rM9Q2L9NZuPtD7t7m7h1k3k/Puvv9pVCbmdWZWcPkMpnx49cogdfU3U8CR83s2qDpPcDeUqgty2bODclM1lDs2o4Am8ysNviZnfx3K/z7ba5PaMzBCYm7yVwJchD44yIc/wkyY2UTZHovHyMzBvYM8HPgh8CSYF8j80EnB4FXgY1zWNcvkfk18xXg5eBxd4nUdj3wUlDba8DDQftq4KdAJ5lfnauC9upgvTPYvnqeXtvbOHe1TNFrC2rYHTz2TL7fS+E1DY53I7AzeF2/DSwuodrqyPRwF2W1lUptfwbsD34WvgZUzcX7TXeoiohEUNiGZUREJA8KdxGRCFK4i4hEkMJdRCSCFO4iIhGkcBcRiSCFu4hIBCncRUQi6P8D7WsDtylYaeIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(0)\n",
    "plt.ylim(0, 1.01)\n",
    "plt.plot(np.cumsum(sorted_lambda/sorted_lambda.sum()))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "explained_variances_ratio = np.cumsum(sorted_lambda/sorted_lambda.sum())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "326\n"
     ]
    }
   ],
   "source": [
    "for ix in range(explained_variances_ratio.shape[0]):\n",
    "    if explained_variances_ratio[ix] <= 0.99:\n",
    "        pass\n",
    "    else:\n",
    "        print(ix)\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(10000, 148)\n"
     ]
    }
   ],
   "source": [
    "k = 148\n",
    "W = sorted_W[:, :k]\n",
    "Z = data.dot(W)\n",
    "print(Z.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(10000, 784)\n",
      "[255 254 251 252   0 254   0   1   2 255   0   2   0   0   1 255 248 254\n",
      "   0 252   0   1   3   4 255   0   4 253 255   1   3 249   5 251   3   0\n",
      "   2   7 251 248   0   5   2   6 250   0   3   1 250  10 250   2   2 244\n",
      " 243 250   2   1 251 251 253  10  10 251   5 253  16   3   2 253   1  18\n",
      "   6   0   7 251 229 253 240 253 244  15   5   6 246 245 239 250   6  11\n",
      " 248 255   1 223 227 242 255 249  10  23   2  12   6 240 246   9 228 249\n",
      " 249 250   3  13  25   0  12 251 236  11  13  10  14 225  12 217 238 247\n",
      " 253   5  17 245 250 236   0  13  14 247 221   6   1 232 241 233 255 247\n",
      " 253  20  33  41 219 250   0   1 242 237 255 248 234 245 237  20  14  39\n",
      " 225 236  25  11 222 255   7   5  32  11  10 235 245  16 240 254 226   2\n",
      "  26 221   0   3  40 231  10  31  23  12  17 249   4 237   4 236 250   4\n",
      " 238  14 217  11 248 248   1  20   3   1  13 231 240   6   1 242   6  18\n",
      "  25   1 251  12   1  19 248  27 233 255   0  16  54 244  24 239 250  32\n",
      "  21   0   6 240 249 250  16  12  39 222   9  20 251 234  12 250   9 247\n",
      " 241  57   0   6   8 235 248  10 251 247  11 228  37 233 252 235  12  36\n",
      " 249 251 242   7 247  12  10   1   1 210 225  11   2   0 231 235 251 237\n",
      " 222  22   2 255  10 239  10  44 252  26  13  25  25   2   2  18  18 251\n",
      " 254 234  22  16   7  23  40  12 242  24   0 241 228  33   4 222  11   9\n",
      "  47   1 252 226 236  16 203  18 254   2 251  15  17   1 229 237  11 241\n",
      " 212 247  24  12   5 252 224  35  35  28   2 253 230 221 239  23 250 226\n",
      "   5  20  22 255  11 250  19  17   1 212 244 248  16   9 225  26   3  22\n",
      "  65 255  72 235  10 250 241 229  15 254 254  24  25 196 250 195  33   5\n",
      "   0  11  23 219  30 213  86  27   1   8 133 106  12 246 235 251 225 243\n",
      "  48 230  22 217  69   4 231 210  34  16  28  19   3 212 255  33   4 138\n",
      "  14  42   0 238  15   7  23  15  16 214 250 222  34  42  44   3 253 226\n",
      "  13 249 229  19  18   7   0 248 239 254  15  54  30 216  51 243   3   2\n",
      " 238 211   9  23   7 242   0 246 252 254   0   8   2   0  10 248 248 255\n",
      "  26 236  32  31 240 231   2   2   9  67  22 243 194 222 217  47  28   0\n",
      "  48  12 236   6   1 245 252   3 239 244  24   0  12 254 225   9 249 254\n",
      " 251  20 245 232 241 255   4  14  25 249   4   8 254 240 231   0   7  12\n",
      " 252   0  52  66 235 145 236  19  61  27 238 239 249 242 248  11 234  15\n",
      "   6 248  18 190   1   0   6 255 248  16  72 232  13   3   8 233   1 250\n",
      " 248   0 243 245 250   0   3   0   6 253 249  23 245 255  31 230   9 238\n",
      "  40 182  70  64  68 183 218 242  15 225 251   2 251   1   0   6 254 254\n",
      "   6   0   0 244 236   2   7  11 248 223 243 185 144  14 252  10 250   8\n",
      "   5 251   0   0   0   1   2   0   0   0   3   6 255   0   0   0   1   0\n",
      "   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0\n",
      "   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0\n",
      "   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0\n",
      "   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0\n",
      "   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0\n",
      "   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0\n",
      "   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0   0\n",
      "   0   0   0   0   0   0   0   0   0   0]\n"
     ]
    }
   ],
   "source": [
    "X_reconstruct = Z.dot(W.T)\n",
    "print(X_reconstruct.shape)\n",
    "\n",
    "print(np.asarray(X_reconstruct[0], dtype='uint8'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.decomposition import PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "pca = PCA(n_components=2)\n",
    "\n",
    "X_ = pca.fit_transform(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10000, 784)"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X_re = pca.inverse_transform(X_)\n",
    "X_re.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.7/site-packages/matplotlib/cbook/__init__.py:424: MatplotlibDeprecationWarning: \n",
      "Passing one of 'on', 'true', 'off', 'false' as a boolean is deprecated; use an actual boolean (True/False) instead.\n",
      "  warn_deprecated(\"2.2\", \"Passing one of 'on', 'true', 'off', 'false' as a \"\n"
     ]
    },
    {
     "data": {
      "image/png": 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qZb1xhh8QFF/4AUERfiAowg8ERfiBoAg/EBThB4Ii/EBQhB8I6n8B162uNvmor6wAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "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": [
    "N = 1\n",
    "plt.figure(0)\n",
    "plt.grid(\"off\")\n",
    "plt.imshow(data[N].reshape((28, 28)), cmap='gray')\n",
    "\n",
    "plt.figure(1)\n",
    "plt.grid(\"off\")\n",
    "im = (X_re[N]>0)* X_re[N]\n",
    "plt.imshow(np.asarray(im.reshape((28, 28)), dtype='uint8'), cmap='gray')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "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
}