projet 8 - Anomaly Detection and Recommender Systems.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Programming Exercise 8: Anomaly Detection and Recommender Systems\n",
    "> In this exercise, you will implement the anomaly detection algorithm and apply it to detect failing servers on a network. In the second part, you will use collaborative filtering to build a recommender system for movies.\n",
    "\n",
    "## 1. Anomaly Detection\n",
    "> In this exercise, you will implement an anomaly detection algorithm to detect anomalous behavior in server computers. The features measure the throughput (mb/s) and latency (ms) of response of each server."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 368,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.io\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 369,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['__header__', '__version__', '__globals__', 'X', 'Xval', 'yval'])"
      ]
     },
     "execution_count": 369,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mat = scipy.io.loadmat('data/ex8data1.mat')\n",
    "mat.keys()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 370,
   "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": [
    "ax = sns.scatterplot(mat['X'][:,0], mat['X'][:,1], marker='x', color='b', s=20)\n",
    "ax.set(xlabel='Latency (ms)', ylabel='Throughput (mb/s)', title='The first dataset');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.1 Gaussian Distribution\n",
    "\n",
    "> To perform anomaly detection, you will first need to fit a model to the data’s distribution.\n",
    "\n",
    "The Gaussian distribution is given by: \n",
    "\n",
    "$$p(x;\\mu,\\sigma^2) = \\frac{1}{\\sqrt{2\\pi\\sigma^2}}e^{-\\frac{(x-\\mu)^2}{2\\sigma^2}} = \\frac{1}{\\sqrt{(2\\pi^k)det\\Sigma}}e^{-\\frac{1}{2}(x-\\mu)^T \\Sigma^{-1} (x-\\mu)}$$\n",
    "\n",
    "where $\\mu$ is the mean and $\\sigma^2$ controls the variance; $\\Sigma$ is the covariance matrix and $k$ is the dimension of the space where $x$ takes values.\n",
    "\n",
    "### 1.2 Estimating Parameters for a Gaussian\n",
    "\n",
    "Mean: $\\mu_i = \\frac{1}{m}\\sum_{j=1}^m x_i^{(j)}$\n",
    "\n",
    "Variance: $\\sigma_i^2 = \\frac{1}{m}\\sum_{j=1}^m(x_i^{(j)}-\\mu_i)^2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 371,
   "metadata": {},
   "outputs": [],
   "source": [
    "def estimate_gaussian(X):\n",
    "    mean = np.mean(X, axis=0)\n",
    "    var = np.var(X, axis=0)\n",
    "    return mean, var"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 372,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import multivariate_normal\n",
    "def multivariate_gaussian(X, mu, sigma):\n",
    "    p = multivariate_normal.pdf(X, mu, np.diag(sigma))\n",
    "    return p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 373,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([14.11222578, 14.99771051]), array([1.83263141, 1.70974533]))"
      ]
     },
     "execution_count": 373,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mu, sigma2 = estimate_gaussian(mat['X'])\n",
    "mu, sigma2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 374,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = multivariate_gaussian(mat['X'], mu, sigma2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 375,
   "metadata": {},
   "outputs": [],
   "source": [
    "def visualize_fit(X, mu, sigma2):\n",
    "    x, y = np.mgrid[0:35.5:0.5, 0:35.5:0.5]\n",
    "    pos = np.dstack((x, y))\n",
    "    z = multivariate_gaussian(pos, mu, sigma2)\n",
    "    z = z.reshape(x.shape)\n",
    "    ax = sns.scatterplot(X[:,0], X[:,1], marker='x', color='b', s=20)\n",
    "    ax.contour(x, y, z, levels=10.0**(np.arange(-20,0,3)))\n",
    "    ax.set(xlabel='Latency (ms)', ylabel='Throughput (mb/s)', title='Visualizing Gaussian Fit');\n",
    "    ax.set_xlim(0,30)\n",
    "    ax.set_ylim(0,30)\n",
    "    return ax"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 376,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x11fe19470>"
      ]
     },
     "execution_count": 376,
     "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": [
    "visualize_fit(mat['X'], mu, sigma2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.3 Selecting the threshold $\\epsilon$\n",
    "\n",
    "The low probability examples are more likely to be the anomalies in our dataset. One way to determine which examples are anomalies is to select a threshold based on a cross validation set. In this part of the exercise, you will implement an algorithm to select the threshold $\\epsilon$ using the $F1 score$ on a cross validation set.\n",
    "\n",
    "$$F_1 = \\frac{2 \\cdot prec \\cdot rec}{prec + rec}$$\n",
    "\n",
    "$$prec = \\frac{tp}{tp+fp}$$\n",
    "\n",
    "$$rec = \\frac{tp}{tp+fn}$$\n",
    "\n",
    "* tp: true positive; label says it's true and our algorithm too\n",
    "* fp: false positive; label says it's not true and our algorithm says it's true\n",
    "* fn: false negative; label says it's true and our algorithm says it's not true"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 377,
   "metadata": {},
   "outputs": [],
   "source": [
    "def select_threshold(yval, pval):\n",
    "    best_f1 = 0\n",
    "    best_epsilon = 0\n",
    "    step = (np.max(pval) - np.min(pval))/1000\n",
    "    for epsilon in np.arange(np.min(pval), np.max(pval), step):\n",
    "        y_pred = pval < epsilon\n",
    "        tp = np.sum(np.logical_and(yval == 1, y_pred == 1))\n",
    "        fp = np.sum(np.logical_and(yval == 0, y_pred == 1))\n",
    "        fn = np.sum(np.logical_and(yval == 1, y_pred == 0))\n",
    "        \n",
    "        precision = tp / (tp+fp)\n",
    "        recall = tp / (tp+fn)\n",
    "        \n",
    "        f1 = (2*precision*recall)/(precision+recall)\n",
    "        if f1 > best_f1:\n",
    "            best_f1 = f1\n",
    "            best_epsilon = epsilon\n",
    "    return best_epsilon, best_f1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 378,
   "metadata": {},
   "outputs": [],
   "source": [
    "pval = multivariate_gaussian(mat['Xval'], mu, sigma2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 379,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/suellen/workspace/github/machine-learning-andrew-ng/env/lib/python3.7/site-packages/ipykernel_launcher.py:11: RuntimeWarning: invalid value encountered in long_scalars\n",
      "  # This is added back by InteractiveShellApp.init_path()\n"
     ]
    }
   ],
   "source": [
    "epsilon, f1 = select_threshold(mat['yval'].ravel(), pval)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 380,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best epsilon found using cross-validation: 8.990852779269493e-05\n",
      "Best F1 on Cross Validation Set: 0.8750000000000001\n",
      "   (you should see a value epsilon of about 8.99e-05)\n",
      "   (you should see a Best F1 value of  0.875000)\n"
     ]
    }
   ],
   "source": [
    "print('Best epsilon found using cross-validation:', epsilon)\n",
    "print('Best F1 on Cross Validation Set:', f1)\n",
    "print('   (you should see a value epsilon of about 8.99e-05)')\n",
    "print('   (you should see a Best F1 value of  0.875000)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 381,
   "metadata": {},
   "outputs": [],
   "source": [
    "outliers = np.argwhere(p < epsilon)\n",
    "outliers = outliers.T[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 382,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "ax = visualize_fit(mat['X'], mu, sigma2)\n",
    "ax.scatter(x=mat['X'][outliers,0], y=mat['X'][outliers,1], color='r', facecolors='none', s=200)\n",
    "ax.set(title='The classified anomalies');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1.4 High Dimensional Dataset"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 363,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dict_keys(['__header__', '__version__', '__globals__', 'X', 'Xval', 'yval'])"
      ]
     },
     "execution_count": 363,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mat = scipy.io.loadmat('data/ex8data2.mat')\n",
    "mat.keys()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 366,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/suellen/workspace/github/machine-learning-andrew-ng/env/lib/python3.7/site-packages/ipykernel_launcher.py:11: RuntimeWarning: invalid value encountered in long_scalars\n",
      "  # This is added back by InteractiveShellApp.init_path()\n"
     ]
    }
   ],
   "source": [
    "mu, sigma2 = estimate_gaussian(mat['X'])\n",
    "p = multivariate_gaussian(mat['X'], mu, sigma2)\n",
    "pval = multivariate_gaussian(mat['Xval'], mu, sigma2)\n",
    "epsilon, f1 = select_threshold(mat['yval'].ravel(), pval)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 367,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Best epsilon found using cross-validation: 1.3772288907613604e-18\n",
      "Best F1 on Cross Validation Set: 0.6153846153846154\n",
      "   (you should see a value epsilon of about 1.38e-18)\n",
      "   (you should see a Best F1 value of 0.615385)\n",
      "# Outliers found:  117\n"
     ]
    }
   ],
   "source": [
    "print('Best epsilon found using cross-validation:', epsilon)\n",
    "print('Best F1 on Cross Validation Set:', f1)\n",
    "print('   (you should see a value epsilon of about 1.38e-18)')\n",
    "print('   (you should see a Best F1 value of 0.615385)')\n",
    "print('# Outliers found: ', sum(p < epsilon))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Recommender Systems\n",
    "\n",
    "> In this part of the exercise, you will implement the collaborative filtering learning algorithm and apply it to a dataset of movie ratings. This dataset consists of ratings on a scale of $1$ to $5$. The dataset has $n_u = 943$ users, and $n_m = 1682$ movies. \n",
    "\n",
    "### 2.1 Movie Ratings Dataset\n",
    "\n",
    "* Matrix $Y$ (num_movies x num_users): ratings $y^{(i,j)}$ (from 1 to 5)\n",
    "* Matrix $R$: binary where $R(i,j)=1$ if user $j$ gave a rating to movie $i$, and $R(i,j)=0$ otherwise.\n",
    "* Matrix $X$: each row corresponds to the feature vector $x^{(i)}$ for the i-th movie.\n",
    "* Matrix $Theta$: each row corresponds to one parameter vector $\\theta^{(j)}$ for the j-th user."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 412,
   "metadata": {},
   "outputs": [],
   "source": [
    "mat = scipy.io.loadmat('data/ex8_movies.mat')\n",
    "Y = mat['Y']\n",
    "R = mat['R']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 413,
   "metadata": {},
   "outputs": [],
   "source": [
    "mat2 = scipy.io.loadmat('data/ex8_movieParams.mat')\n",
    "X = mat2['X']\n",
    "Theta = mat2['Theta']\n",
    "num_users = mat2['num_users']\n",
    "num_movies = mat2['num_movies']\n",
    "num_features = mat2['num_features']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 426,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'Average rating for movie 1 (Toy Story): 3.8783185840707963 / 5'"
      ]
     },
     "execution_count": 426,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f'Average rating for movie 1 (Toy Story): {np.mean(Y[0, R[0,:]==1])} / 5'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 444,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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2x663TVczKv+MH6g2kK0qcF35hUYIW3bN9mr2AhMsYPxK23f62sousav+FsZddq+bVaWm67In3FnYEFOsVXz8fRKxRhnux0jBN4/Ni899ju0vuXT3cUvS7L+Ivql5OHorssRxaSrKS8zlShl5HWtefL65bF7duHZR5MI+j6+88aQl12LmuT5FHZL/bGxvEAyEbBhGmYucME2xNFTZo1bUzi97wp25Xi58i8kqxPY0zW2aSbYGC48PKduCUIVw9hKG27UKc2IFjE+eDX8Z4Uasa7avXdSxuf/zG9cv6jhSRsNuL0bKjMqF7Z8nETby1TddUDhSD/E7KzflDv1NbZ1ZxrWbT13Ssec10q0zy6KqgnWzgxMg5zeuX5ReWGx6eu3mUxe9pGE8Z59788LhSC79ft3kCQl/prFudv8itzJun8uxV7w22i78MnTlkLdBLzzvp8hE1w/T72BvuPojlc9TcWly55y47/tOX7tkD0jY3vwOKSYQY/hhXLN97ZJ9HGVt2jcZjnXWrr04ipxLOlPuvDLbcMTMkvTMb1y/yPQ8bHN+O41xzpptpX1IbE+K797HPx3VfS8SoOGm1ZS1uthvoal322tHZkUW0IQpYZ51SR2rk2EsVVxemrZ2GTZ//n155V12T5tuY/z4iqyU/JMAi8KoQxcm4U08G8tnm2a0bVC1jFz6/XyEYQybx5T3oug01KrhOsxMOYFQwBR1BEZ/GKaeijqJvtZ/WbqKfm9LcHRheus6ua7qpW8CrYi65d9UvZmZciL+LnVft1+0EBfq9fP8QoU61Ly4Y9f9cIueD8Pyw0xdHynyo+Xy6ocb7ugP3eSUWVxt2TW7sN4VxumXYUzNGEtfmCb/WlkZ+s84dYWv0gzJW2MIyyi8Hl5zcfpqTP+3FDNlp6aJpcXhe5aO5SEsK/+zv3u+SC0WK/uw7v02Eh5TkLKu5Z7Pa1MxLxNVjR3CdSKXxrJ3KO/IBb8t5/UJRWttftv130MoXmcL25cfTuipwKW/bA2uimFCHSZ6BhMW2LCjY/+/78Ildv+1m09NUnGUjTz8UZ77XHXkF4tjbtMMO067aqHzDX+vqqJxZR36vsojdRTrOoazz7059xiEqsTi9OvULy/3Oe+ZMtf/YThFaXDXL919HNduPpW9x+9hx2lXJdd1TK3oxxNLb1EeUtpALI9lMwa/rF1+u5x9zm9cz9nn3lyaVme0UvR7Xv1WmTVVzaO73xcufhqGKbOxV5GJyFHAx4HDAAWuVNUrRORQ4BrgaOD7wEtU9X4REeAK4ExgD3CBqn69KA4nYELBkEIVtUTevWHFD4v/Qow7RR1K2ZpGmVPErlVkVQRMnXSFv5fdn9LOUwZHVdpZHdVMnXWbusTKrAvVXNmAxP9cJz2hMC8asFRpM5OgItsHvElV1wDPAl4nImuAS4AbVHU1cEP2HeD5wOrs7yLgA6kR+dPG1Olfirmrm9LmVWiVFy4lXSsvvyXX3DIvnLJww6l5SpgpKqmU/LgXIyRW9s6yLex8UlSE7j5nYZeqWixTFfr5iOGeKWsHq2+6IBpunrpoWMeEvhVTHlWFhbOsLEtTkapp3Wz+xtIUFU5KO4ADbclZDg678z3vCAoXR4gvUPxyjpnn5xHG48otr04v3X1cYfn4VmUTqSITkc8C78v+TlPVe0XkcOAmVX2qiHww+7w5u/877r68MP1F/i27Zjn2itc2oq6qwqgXFkOT2ZCyWVbZjKEo3ipqHZ+8UV+Yzrr15MIvU/3UtZ4aljDestlGSEwdFlOx+jSZj9SReBhnUVsrS38ZMSvANiwQy9RpPmH+m5pRheVY1gfEmIQZzAIicjTwTOBrwGGe0PghAxUawErgbu+xe7JrSfgu5MsoGpGm4jrE2Ih7GFIWTH2cK/I8nCv1vLz5RxRXIUW45M0IitIJxUKxqI7CkXtZe4h5FwjTW+SdOXV2FaY5zFeRcIktePszHBeW/7wvfPLaacrMNw8nvGP45Rd6QCgayMTSH1KU5huu/siS350rp7oj9thhX3nCJfbehvcV7Vfz8eMLy9nNAv1yLOsDwjDbYGQzGBF5JPA/gXeq6mdE5AFVPcT7/X5VfayIXA+8S1W/nF2/AdioqrcF4V3EQIXGw1mx9g/kzFbTP7dphid+eOlBXTBaD69t4EZcXRxZXDR7iI182xgJpqYn5fcUmpxFNLm+0ZY5cZtHUNSli3WZKnShAfHjcPmfiBmMiDwU+HvgE6r6mezyjzLVGNn/3dn1eeAo7/Ejs2uLUNUrVfVEVT3xoSxftL4QmmoWETP7jD2bJ1xgsEs/Fk9qGnx8k0RH0/6GYrMJP45UJ3pFsyy/LH0zXP++mF8r39zXd6mxZdfS0VnRwnUevh4+NjKtIlxiZr0hsbWyUEgWmUwXEXYY7n+KI8ZYG/D1+ymj/dCUOW+W6jxHxGYWKeGHDOuodG7T0t3+ReHmeR+ImVTn4ZdV7N4i1XbeLDlWPkX3uE3Y0J6PxlFYkQnwMeA+Vf1T7/pfAj9V1XeJyCXAoar6ZhF5AfB6BlZkJwPvVdWlTpc82j4PpkuLpSqzoSbXkLqiSpqHtbxxpI6UuyrPpkaro1z3qxJ3eO84tlvoV7qHSYv/Lk3CDOb3gVcAp4vIbPZ3JvAu4LkisgN4TvYd4HPAHLAT+BDw2kiYlRnGB09RRdYZRReR6ketaQOFIprU21ZJs+/Hy1kC1aFMuBT5viqjqbKpk7cmhUtdD7917q3iWbgNS6cYKbODvgiXYal6ZHMVOhcwqvplVRVVfYaqzmR/n1PVn6rqs1V1tao+R1Xvy+5XVX2dqj5JVY8L115iPOUZe0rT0fVIL6Uxprw8eQIsxeoplbJNcnUtuPLCq5suX/WTUnbunjIVY56b+ZSw87xJFxFTYY3atUmb8Re1xbJ429rPFBKa0tep17pxp1BmINIXJtJVzHfvWMG+09eWni7YtAXFsOHFrHDKBENRZ+mvL6w6b7aR8rhm+9olLuVT1jjyOoZhXtwUCyM48DL6VmR5aQ9f3GOvODBhLrKQcmE7Ywh3r+9pOy+OIusrn7xydvVRVr95bSlmkZQXRx1C6ydfiKS03xhNnuya1zn76Xzihw9YMsbe0TILr9j1MO6w3Ivy2KSgTTnOoi4j3wfTBo+WQ/X1t5/WW6lujH6fkGEYS5mENZjW2XvMIxbtnaiiHqojxcMRTMzCIyUNRbu68yzQUtJb5JwytifFD7PqSDHv/nD0VrSPJExDiKvTonTnhRsLK2wjRTu0i9h3+trKFn6x8P28xSzT8tpJbLbkW8dVwU9D0+seft7KLLXKSLHcK7selnVZ3FXKpYpqOK8NxtKYEkeMvLbT1trWRAqYQx9xYA1m68yyBVv+FFIdNfqkmIG68yPggNl0ntuHWNhuShweIBUeIBQj7xAwd9CR+911tn4Z3HD1R0rD98mzeHNqqTJTVpcWpwOPmQ+7Og0pqru6i9Bl5evX4ynvvnXBBNelPQ/fkMC/z5ktu82Ifp7cZ/8MEseO065i5eW3LFo7WDe7f8lhYKksv31FJfNmpzoKB1s+4cAr3HHuU+aBIgzDeT0oujeMKyxP990/UCyWtnPWbGPd7P7Cw/EcVdZM/TyH+73898K1l7yyjgnuvE2eMKjrVFP0qkykimz5qpX6h99ffAJcE+atIVU2BQ6LM1duylqsjgNNP09V8+ff7+ehSn7qlmnoQsXfdT3MxsQ8c9sqGwabaifrZtM9eNehbZWmX2Z1NyqPUu3axHtZFEbZ5tTU99mPIxamqchq4Be639HEqLLYmue0EcpHzKmjBadyCl+4lE1VRew9fs8ioVsUpvs9b4SVghuRuwZeZeNeXpyxMGLX/AFFOKMN3ZaE8RSNgmPPwmC25pdbUVvzZ7Z++Kl16bfFsLMYZtE2VaXp4nFx5Tm19PMUU0X5aS9q620sRMfCLfruZq1+XkPNQhlhnRc5R53bNJN7tPXZ594MLH6fi/Dvcc+GeWmSqZvBpNA3txFluJHIll3FZ2uMMzGnpXVnQl3Mmhwps5kmZzF+vurOBOqMxvOeKXNbXxRO7L4m3806rmm6miU5IdLUuVKp2AwmgeMe9dPo9XBUFrqTcaOs2PkR7p4UYu49whFeeI9baAuvl5m4btk1uzASyTs+IDZyDEdkeZ/DZ4vuj8Vdh9joccMRMwv5DOPYsmt20VEKRaNpWHyMQ6x8/RFd0TqEH0beiNel2a93vx26WUzMKCQs57z85F2/4eqPVBpVu3bo1jLyRrZ++bp78taqys4iCevB7ySv3XxqaXhhfcc0CkVlkDoLduXvt4fYO+1/9uN175y7p6g+HZc94U4O27o3mqY8d0Jh2vw1zPC+cGY5zObzPCZyBuO7inG66b3H74l6OI5J/bLRQOoIbG7TUoeYqW4ywuspI5R1s/v5yhtP4qAbt9Ue6c1vXB8tK58w7GFGda5RDzsq9Eej8xvXc9fF709KY1Hay/LlFl9j5ezKEQaqtKKRaF4ZVB1hu/TG2kpK+3HP1xnZ150Vhutjfjn5v6W2sbJ1sLptNfZexNY9Yu9d3ZnSOWu2la4X5lG3PmwGU5GtM8tyO8yY3rRoqu8/F2N+4/qFdRlnDXTKu29ddE+otw/XI/yRnD/C8zck5llgwQH9tf9ixnT8eWtNZ597c+lOdude3I2Oqi72h59DgRuOqMpGWOtm9y95gf2XPG9tad3sfnacdtWiOMO4YqM+3yLHP6vEZ+Xltyy4S79m+9ro7Mux/PYVS9qF07uvm92/aGNr0Shz+e0rgANtx7WfVOHicKPmWL7ynoHF5Ryaevt16dIJS48Y8OvRbXLdsuuAVV1o3RXG4/KZV96hBV5ePYfhOms8vw7uuvj9C+9v0Zqon6fUWcKq8wazQj+9TvjH3ocw/nADs7/5N3zWF2BNM9EzmGFGZEazdLmuNW71nZrecTwGouk1izC8cavrKozCGtFmMBXow07xFB34sJYxbYw8mmYY4ZJSPv4ItKpaqQuKZgKp6f3Bq6u1kybdqdQl9g4W1WfeLCgvvK6ESxXLviphFv129rk3J2/czbNoLKItizyfiZ7BVKGvlmNNWIeM48h3WIbN8yj3VNSlq3ruU3vqOs9dzphGUc42g2mJPgoXaMZLatuNtCsX6nnERmLD5jlPuLSV1ybC7aozGjaeJmeNVdJSZG2VGo8z3OiCqjPWPjKxAib0d+S+1/EXVdVMeVj/Sl1Q5PcoD6dyCcthwxEHTtjLCyt8uWMnWsa+Fy3sx0xbY6QuRseIeT7OezalHPPaUmiUEFvEThVCXag+HDHDg6ZPXG2KvP04eeUVy4dvUu7XxzDvdl78Re5y8gwLyui6D5pYFdnvbH7T2Kk4+kZTm7eKqKty6EpV0bSaoq+q2C6Z5IX5LhimTZaVvanIEvE3RIXnlzRB6kJlF/E18XxsdFxFuFQJ3//sqxyq5HHv8XtyN39WTRvkz+iKXuSyRdoYKcIltrk1JJbfIvP11GfL0tTEbKVLNVMRZXnuarRfJZ65TTMcdOO2hWeqln+RuXwbTOwM5oF7Hzf1I8U+kTfq6mIxfRwX7A1jFNgMJpGUkwjbpA8mon0ibybgTgpsEydcYnXS5XrFqGlrRN7XNZdUmiqXuuFU7Sv6tJZbxsgEjIgsE5FviMj12fdjRORrIrJTRK4RkYdl15dn33dmvx+dEr6/G9n/3AXzG9eX6khTG0mfG1MTQjQsp6r5rSIgYnUSnsdShT7XTYxhnXbmMe7rKXVdx/gMM0t2x3CkUnZYXxFdD6hGOYO5GPiW9/1y4D2q+mTgfuDC7PqFwP3Z9fdk95XShYlf3ktX5nMK+rEJdFh+tG558r15jT/PLXxq5120TpQqAN15GlXxXZ40RZ7DxqoUWfTVwR0YZwwI3/E6Gx19mjCmSelTuva0PhIBIyJHAi8APpx9F+B04NPZLR8Dzs4+n5V9J/v92dn9hfiql7AjbGovQ54gSTE7TE1DF4KobnlUGbn69eGXT96iY+yFLRp9xQSEm7GEz4XejCE/L03swE8ND+DZL78w6l0Zykeffr7cuTdNjVj3nb422hb7IHTq5NF/JsWoooyis6HK4s7zWp333PzG9ZV8xOXF3QWjmsEg1CSqAAAgAElEQVT8NfBm4LfZ98cBD6jqvuz7PcDK7PNK4G6A7PefZfcvQkQuEpHbROS2B9m7aAYTHhtb5kK8zm8+KaOEqgYIbW5mLEpLU2tJrrMPD1YKPdGG1/PyHdZFkWVSWB++UCsTEk0bipSF58qpzkgzVgZNjVjzjs6uOwBKtQDMe8anTh5jbbDOGTj+59SyCOO+dvOpSe3MPbfy8ltyj+Zwxz+kxN0FnQsYEXkhsFtVG912rKpXquqJqnriQ1m+yEzZX/Avo6gCys5nd6SOSFJw4TgPxl1TtJYU27BYNoqLbXbL+w0W59v3EBvWU8ro2n2P1XGep9kYTYx461DWObQ52/W9HjeBv8ExtW033TnW9RMY2+Ab9g1VZnbDmA778Vy6+7haxwK0yShmML8PvEhEvg98koFq7ArgEBE5KLvnSGA++zwPHAWQ/f4YIH6imIcvVJqy/U4dzW6dWdbYyNeF08c1G7/Dr5u+sk7DV5VVjSO8v8iazDcEKYvHpTl0id4Eo7ZoymMYY4iiMGF0bTtFYMUOPYs9FwrgKutzwwhOv+zqhNN22XcuYFT1Lap6pKoeDbwUuFFVXwZ8EXhxdtv5wGezz9dl38l+v1ETNu/4HUYbHUEReS9inRe0DzruKlRtsHll4vI9bN3FZiaxWVmeUUhR+bfxci6/fcVCmodRT7aRtnG3FqtDap7Dzr2PHr1HwUg3WorIacCfqeoLRWQVgxnNocA3gJer6l4ReTjwt8AzgfuAl6rqXFG4dbwp16ELtx+xDYptu9ro0pVHF+5o6jLsBs3UvDVVBmG9rZvdv+hERMMoY6I2WqrqTar6wuzznKqepKpPVtX/U1X3Ztf/Lfv+5Oz3QuES4tZD2lgk78JTQGy03VbnHzuBr22KOtamnAnWZdhjoItIOSG1KuEiv7Mk64rUdyw8W6WqS5y+MKqZR9kaYJ9mRBO7k99n9U0XLPFWW6auivnOCo9rDa+7z3kvhVN51BV4bm9D3rNlYfq/+96MY8cC58Wf94zLU5nVV1hmRZ1LuPhbx/IoxH/5fBVU3v6TOp63l9++IjdfLt1FRzq78p3fuL5QTRYemXvOmm1LjidOscLz22VRmmLX/d/9Y7pTcbO3vON/nafuImLvYSyeMOy8cJwZcJlX9KrCu4nDB/3fL3vCnVEfcees2VapDtoU4hPri8ypyGIvdFXqqMJS1Sup6hE/DanpKbrPb1Rl96TmfcuuWS7dfRyXPeHOJc+4tIRhluXLv7/o3ipqJv9e/7MLs67Kys9jmN5YmouO/42loSxdKel291Rt075re79+8+qs6PcwnVt2zbL6pgtK35e8NJflJYxv3+lrOeXdty5YfhU9W/YO+fn0w8prA1XjKCK0ZpvbNMM5a7YtattlKtKwDTatIpt4AdMEfVgnmAY375OSx7z20uZApSjePlCWtpSyaTp/fSmvOuloK+0TtQbTBe5gnmGmgXUqsg960Co68dizVcvMlXWKSiO1fPx0hCqyVD1+SOo+F/9zE+qNFOESqreqqGG6sJasu/fHf4diKuaUskndhxYSq8OmO+i6B4DVxZ+l+GmoSp0D7aowFTOYUYyMm3YRP4rRVh31Yl3VS/g5ZH7jevYev6dWmYbhxqzk8uqr7VlHk4wi3mHapUtvahn3ZcbRNK4cquTPqaP9+2PPl7WJ8BmbwbRI2cJsFZbfviLpubqL/cOGm2Jdt+GImUrrLzDYcJaSJzdy8kelsRG4u2/v8XuGcijoFr/nNs1EN976L2HZInPqSLVq3YajySKDjlgayspn3ez+qNFAHQebsd3sIfMb10fTGebp0t3HJR213bR6LIVUn19heKnGGT55bpNi15xw8eOpUz7++9fGDGziZzBtjXqKwm06zqaP7YXFi7Z5aQ0XX1MXkWOL/CnERrLzG9dz9rk3L0nrMLPSslHdsDOBOiNSiM8Yq+SzbP9SG/ub/DBTw/fLt6ys/PzXqZc23p0UqtR9UzPPKoYFedgMpiLXbF/bimQOG09bIy0YOBpsy5SwKK0bjljc8FPylSpcUkfMKy+/ZSFef7RV5NMsJNTB54303e/DvuyrzhvMCKquifgzRmdKX8UHXdlRxOEmzBhV1qfCMFOFV+j+Z8uu2dy25ddznXrpSriE5RJbL8or87zZcxGxrQWurKr4jWt7n9HEz2CM5hjG5DJlRFfV3NQYT2Ij9nFbP5pUbAbTEVVmPW0eGRtLR4qlVt24inTHKTOTvHuK1Il5z4Z5bKMzcCP2JvzH+Zscq9Cm9VFXlk1V4glH7Otm013dN8m4C5e89tanI6xNwORQpfHFLJJiHXWdio9NtbfOLGvl5dg6s2wolUJR55r3W8xbLXQ3unReb/OO1a6yZpHimiWmkohZ/jR1Dk9Xjl7r1lVbbblNYu/xMIJ8GNPvWHvrk1NSU5G1xKgWF41qONVMnopmVCbHfYnfGI6U+utTX2EqsgrE/PRUGS2Ei8OpG/vmNs1wyrtvXXK9a8d9ZQvfvqpt3+mLjSGKTGSLwqw6SwvTGG6qzFMDhOlNiSP0JQcHFpz98zv8PBSZ/hblNUxbkf86n32nr100g/EPzivLb+xogjZG1uF74PvwyquvsG0Nmzafupuayw7Jy5tFxtKfsoDv47fvU959ayW1tzMrd3/+9TK63gBuM5gW6NLdvaMPo6A6o+0uF1pj9eKutVV+VdtCqiPFsnKzmc/4UKeNhGbeTWG+yBKICZguO7Jxfrm7FlR14zMLoDTGuS32lVEMILvCVGQtk7KfIlQfhX6IzlmzrTF12DBqhJRdyGH44cmObVshharEWJpjaU3Z8Jnyu69uSNl1nhpnmUVZXbVtHn4+/Dh8FVuVuMLyCMON3Z+q+grDqmqplxdH7FqoSvU/OxVYWFdl6V95+S21LQZTwo8RS59f3jFvE3n1F0tPW+r7qZnBGNOLjeINIw2bwVQk1cPvqKjiVbjPNJG+vDDCBfLYvUXxh8Klr21hWLo6ZGpUbXHYkX/T1G1HsV34k8pIBIyIHCIinxaRb4vIt0TkFBE5VEQ+LyI7sv+Pze4VEXmviOwUkTtE5IQqcbnNe33V16eOrKu4f2iKKlNn5wNpmBc6L4/Okqtoo2cV30t1/INVoQ9HNZQxjHfxNjyTt9XJtjlzLTOyyCMsv7rHEDRB2211VDOYK4B/UtWnAccD3wIuAW5Q1dXADdl3gOcDq7O/i4APVI1sFMKl6Rem6zzMbZph68yySp1JyqmEReTlMXa9rjPNkCKdft14himD+Y3ra+/E7osasE7bT2nfKd4g6tBUJ+uHU6Uumho85q2NFdF2m+lcwIjIY4A/BD4CoKq/UdUHgLOAj2W3fQw4O/t8FvBxHfBV4BAROTw1Puf+pOtpqDuWtinqpL/KYmtIrOGVdcarzpvN7RxD9VbTLlVSwnPCwk+j67RiB2JVpWwhPIUyh5WOPqtMy4RF06PmYQdfTXSy4Tpflfc1lv46ZRTLR4q5e5t0vsgvIjPAlcB2BrOXbcDFwLyqHpLdI8D9qnqIiFwPvEtVv5z9dgOwUVVvC8K9iMEMh4ezYu0fyJkLv42zWeG4LFC3aTZctwzCem+6HbSR5z7X9zSahqfWR5/rrQqTsMh/EHAC8AFVfSbwKw6owwDQgdSrJPlU9UpVPVFVT3woyxf9NmynMsrR4rg12jZGRHUPGnP17uqv6UFGG52tc1vTR5rKb5fmvcOS+v6N23vaFaMQMPcA96jq17Lvn2YgcH7kVF/Z/93Z7/PAUd7zR2bXkqjj8iSPUXgpLXMt0gR1z6DwiamaiuKo0sn4h4zlUZSHcB3FD6fq+Sepvw1DuHclFl+sLabmpW45NoXrjPNOvMyj6TWYYVTIo6DslMs+0rmAUdUfAneLyFOzS89moC67Djg/u3Y+8Nns83XAKzNrsmcBP1PVe1PjW3VetdPdYhXmnk8dAcesr+q+BKmHCNXxG+YIz/XOCzNlMTLPf1N4HGzRGk8efj2GA4cir8FhuLFDrPLWT4osfIo6vLy8lNXT3KbBoWNOgPhp8eNLbYv+819540lAseFC3rG9eZ1tnQ2jLm/uMLkqmz9jtGWFlTcriZnNh1QZmKQKsli9+ddSyjGMayIPHMvWYT4MPAyYA/6IgbD7FPBE4H8BL1HV+7L1mPcBZwB7gD8K119Cwo2WffDTZRiG0XcmYQ0GVZ3N1kueoapnq+r9qvpTVX22qq5W1eeo6n3Zvaqqr1PVJ6nqcWXCJYYJl3TKXEpAsTuXqmHWuS9MT16amqDtEV7ZqLPoXJhQTTaMeit02VJlNlK13lw8w7hbcTSpAh8ldfMQm+n2ialwFePPYPzPTZ8B4h/525TFzbhYp5RZaKUct5waVhlVZqxhPRXVW15dNGGd1oal47hbfcXKe1TaiFHEO4o4zZtyAqGAGeWL1nXc4yKQjP4y7oKpDdx71Vev7E299xOhIuuSWINoYjpZFoaburq4h7XOKXveTbGHbWThZsq2rIqqLILXWbys+nweXapfYoYGVdLeVF3F2qyfttjBZlCsznNs2bV0M27q+1jXcCL2XNU+wL1XeQYxRekrIy8tVd5lJ/zqxtUWEz+DWTe7n6+88SRbhzEMozLTphGwGUxFts4sM+EyBUyaR9qqe0Sgvwu948w0CZc2mHgBA92/eCl7Bpqmqp+uvAO2uqBow2CKmsWRt0ekCi7+Opto26rPuU0zC3tEqsQ9qs6wajuqUsd9xJX9qAT6OA0kKqvIMjf6R6nqHe0kaXiaPnCsigWUUZ9pU0c0TWr5FbXnLupgfuN69h6/p/d1PY3tcSQqMhG5SUQeLSKHAl8HPiQi724qEW1TZYQVG11VES7Oc3NTo4wu3dO0OaNJ2bNS9WVu4tjhWPmmHjVb9NwoSC2/ovbcRYe68vJbetFxN1lfw7zvw/RPfZ/NJM1gROQbqvpMEXk1g9nL20TkDlV9RvtJrE5fjkyephHQOM3yJtUMd5y9hhvVaOt9G9Ui/0GZA8qXANc3FfmkMy3CBdo55TCkaKRXxZy4TeHip2PYEfK4r1Xk0bdR9yic2NbBL7ciB659IlXAvAPYAvyrqm4VkVXAjvaS1Szj/KL2ufG3Wa6xTqhIMGw4YmaojqtOXsJn1s3uX/Tix9JbpSOoYv0Ym73MbapWJl11/OHAa9QCp2jWN+q0+RQNWN2R5X0jScCo6t9lfsNek32fU9X/0G7SmuOUd9/aSDhVOvumOt9UlccohGiVDjD1RR1mw+gwM8YfvDo+2yhKd/hMU66BoPrAItZOVp0X91qdx6hm3H2e6RelLW/DaVWqznTz2kYfVdSpazBPAT4AHKaqx4rIM4AXqeplbSewDuEajOmmDaMdpvHdGoXbmK4Y1RrMh4C3AA8CZCbKL20qEW1z2Na9o06CYUwk0yZcIO42xoiTKmBWqGqoZ9rXdGLa4oarP7LwuStVUp90t+PEqE19Q/q8BmZMJ+PUJlMFzE9E5EmAAojIi4HkUyVHjX8SY1duY/qsV+4zfRsVTuMI3eg3rk2Og/FSqoB5HfBB4GkiMg/8KfCa1lLVMO6oWMOoSt9mVF0yzXlPYdQziXHwsVjJVYyIHAw8RFV/0V6Shidc5B+nTYCGYRijoulF/oOKfhSRl6vq1SLyxuA6AKpay12MiPxH4NUMVG53An8EHA58EngcsA14har+RkSWAx8H1gI/Bc5R1e9XiW/1TRewClNZGYZhdEmZiuzg7P+jcv4qIyIrgTcAJ6rqscAyBhZplwPvUdUnA/cDF2aPXAjcn11/T3ZfJZ744X7p9Q3DMKaBwhmMqn4w+/h+Vf1xw/E+QkQeBFYwMBg4HTgv+/1jwNsZ7L05K/sM8GngfSIiOoknpRmGYUwQqYv8/yIi/ywiF2bu+mujqvPAXwE/YCBYfsZAJfaAqjrT53uAldnnlcDd2bP7svsfF4YrIheJyG0ictuDLN73krdLu4wyU+PY7/Mb1+c+V7ZoWvR73m/uuu8mIjzrZd3s/iXPp5hRu2eqnH8Rs2ypkq8idxd1j9rNi9c/1KtOnYXlHIYxzFHAqQvseUcZV01H0bHCKS5I/DZSlvayHfCxMML7/HZfFF+dhfgmF+/D97IuseO0835PtS6rcyx3VZIX+UXkJAaqrLOB7cAnVfXqyhEOBNTfA+cADwB/x2Bm8vZMDYaIHAX8Y+Y14C7gDFW9J/vtX4GTVfUneXGEi/z7Tl87FhYXhmEYo2RkRyar6q2q+kbgJOA+BmqsOjwH+J6q/lhVHwQ+A/w+cIiIOJXdkcB89nkeOAog+/0xDBb7k6k7gzEMwzDqk3rg2KNF5HwR+UfgFgaqrbqbS34APEtEVsjAHO3ZDGZEXwRenN1zPvDZ7PN12Xey32+cpvWXJqavffYqEKojXH5HuQejTB3RBKPeQzFKJiXvfdgn1Od3G9JnMLcDM8A7VPUpqrpRVWvpnFT1awxUYl9nYKL8EOBKYCPwRhHZyWCNxfl3+QjwuOz6G4FLqsa5/PYVdZLaC6rsbM9rbH31KrBl1+ySnfIuv1tnlnXSEYVlNr9x/aLyaqvswnz3qdOtmpaidccYft6rdpCj6lBjZRJ7N+us21aJExYLtjrtc25Td679U70pi6qqiDwSQFV/2XrKhmDcvClPw0bQacijYYw7o1qDebqIfAP4JrBdRLaJyLFNJaJt9h6/J3q9zSlulXM9/I43HA02ObJty3dRymioqnDpaqQam8GMgrz87jt9bWm9NV1WfVe79J2qVlxN31uXNuJIncHcArxVVb+YfT8N+M+q2p95vYdZkU0m43z+hs3gDtB3jUIR7iyYSWVUM5iDnXABUNWbOLDL3zA6YVyFC/TztMFRMa7CBfq7ntlXUgXMnIj8vyJydPZ3KTDXZsKaxD8Pxhg/Rqmyceq/PlgMTQpFmzp9+mT4YNQjVcC8CvgdBntWPpN9flVbiWqaYUePTVhcjGMHVSfN/jNNWaqMctTo2k4Ts6ey8hi2vKp4Dsi7twvromu2r10Sf6yOU2c6VdM8rmtMRfnM+23U/U6SgFHV+1X1Dap6QvZ3sare33bi2qTK6KiqgMozaazTsMvSWRTmsI2rrFONLWa6Z+Y2zSwxXmiSvIXUqnme2zRTuNBfVL5V63PDEcXmoX55ubBTF4zXze5PFsRbZ5bl3jvsYCylTJbfvqKxQUPYzlII425C4NQ1/a3S1lw+Y+9SXhmMWq1cuMgvItcVPayqL2o8RQ0QLvKPiklfEEwhdUHXLeCPusxCQ4IwPdOwWD9Oi/BdtRcXT934Rt2uU+l6kf8UBm5bbmbgoPK/Bn9jQ+rooqnp87g0qCpUmR24cnQdVWh6HY7CXKe+47SrgHrqgGHud+kLR3xhHQ47K3PPFD07arXGuAgX6E596uIpiq+o78h7blzVdamUzWCWAc8FzgWeAfwPYLOqfrOb5NWjLzOYJikbOdcZWVcVgm2YCTcliOuGM0ye+jaI6Ft68hiXdE4jnc5gVHW/qv6Tqp4PPAvYCdwkIq9vKgGTSBsj0DLhUUdtU/UlT+mIU2YL/j1VBVzs8zDhDCMw+3aQ3bR22l25PekzdfuctmfLpYv8IrJcRP4P4GrgdcB7gX9oNVUjoqywU6ezdRbHi1g3u3/RS9TUjvw6589A8QudtxDpP1NFGMbSsWXX7FCCocyHVF7ew3LP27zr8j6sFd44UPZOxPJTRRA2KTza8mQBS89cqpPuYfKa9z6Uhek/10bbK1ORfRw4Fvgcg/Nf7mo8BS0wahVZyiJpqpqga3XCOC3whtRRE66b3c812wcdT9VyrlNW46Qeaiqt4+yBIYbzDNLlu1KlLobxXNL1Iv/LgdXAxcAtIvLz7O8XIvLzphIxTbgRX2pjaaMzKhrJpbwwVU1oq6YhL7483Cht9U0XVE6HM9mtU86pnYs/m8uLp49qnqbani9cmjyVtEnKDDb8313n7dd/2zPPKnXRJ7dYySdajhOjnsEYhjFZ9Glm3+aMcGQnWk4KfRkxGf2gj+3BXKT0j74IF2BBpTsOTJ2AWXXe7II6oo9qibaoMoXvYqHZxTFMHfjP1tmjA+Wqh1j6mhJKeWnuU2fWBm16n6hC3TYzamJttmr6/HbdZj9oKjKj94zTwrhhjDOmIhsD8lQcdVQfbZlW9mVEllImecLFVEn9Y5gZSFF95v02qoPpRkmsLIZJ3/zG9a3NHFubwYjIR4EXArtV9djs2qHANcDRwPeBl6jq/SIiwBXAmcAe4AJV/Xr2zPnApVmwl6nqx8rithmMYRip9GkBf9SM0wzmKuCM4NolwA2quhq4IfsO8HwG5tCrgYuAD8CCQHobcDJwEvA2EXlsi2nuFX0aNQ3LNK13GeNFqjPWrt/HJk35R0VrAkZVvwTcF1w+C3AzkI8BZ3vXP64DvgocIiKHAxuAz6vqfdnxAJ9nqdDqHU1V9qrzZlubuna9YzxvA2RfX4w6NJGXLbtmk7wKVKFv3gGarvMu2lDsiIO24y3bz5Kyv2rUdL0Gc5iq3pt9/iFwWPZ5JXC3d9892bW860sQkYtE5DYRue1B9jab6oo0WdlfeeNJjYXlU8eOvo0XKiyrNt151KFKnpuo9w1HLDZoSK2nohli33bR13V3n3d9VJ3rqDv1JtV6bQ1CRrbIr4PFn8YWgFT1SlU9UVVPfCjLmwp25PRpV24XL1TV/Lateqvrnr1rmj7crW4YKc/l3VPUyXXZmfdhkOO3rX2nr219FtrWIKRrAfOjTPVF9n93dn0eOMq778jsWt71TjFrpXJGtcZSx4t0Uy/rOWvaE/5laYyVt2unTYxs64aR8txhW+MahjqdXBuCxw1yulItljkEPejGbbll0wdhWESr+2BE5Gjges+K7C+Bn6rqu0TkEuBQVX2ziLwAeD0DK7KTgfeq6knZIv824IQsyK8Da1U1XNtZxCRZkdkekNEyjOPAukyac8hJY5LfybGxIhORzcBXgKeKyD0iciHwLuC5IrIDeE72HQbemucYnDfzIeC1AJkg+Qtga/b3jjLhMml03ZBHPSKqG39b6qpRqCjrCpe+LebnMe4agUkVLm1gO/mNkTKKGYJP2Wh0FKPVSR4hG/1mbGYwk8S4j7j6TKpwaasOyjryUXT0ky5c+mQcYbSLCZgEbJfv6Fl5+S1jowIyDGOACZiO6FvnOMpZWV2Ls2lf+O5bG6pL0zO0cSyXYdMcPj9MeG2Wn63BGIZhGICtwRjG0NgawGgxv3TDE5ZhX2dxJmAqMKwJb5tqqUkxRIh1Pk2bTvsqGids8l7QpoVRm51rrA30seOpszm273Q5aFk3u3+hDN270Vf1sanIDMMwDMBUZEbPGQf106SqaEa9SbYu49BmjHrYDMYwDMMAbAZjGI0yqbMZRx/XYGzGMj2YgDGmmj4uOBepuqoKxD4u/k6ipwITmnFMwBgLDPuSjKMl2zB5HsWaR98E4vzG9VPXucba+bSdV5OKrcEYhrHAll2zrQuxaXXmOQ7HMDS9BmMCxjAMwwBskX8saHJhtctF2rlNM2M1/Z5E+rgo3zTTplJri3EoRxMwPefazad2Fteq82ZHejaL0c9F+aYZR/VYH9cXx6EcTcC0QJOdROyogGkY5RqTyziMvEPsyI56mIBpiTZVTdMwynV01RnViaePo9pxYBxG3uPA3KaZ3gvr1gSMiHxURHaLyF3etb8UkW+LyB0i8g8icoj321tEZKeIfEdENnjXz8iu7RSRS9pKb9OYqmkxeS9CmSBuuzNy6aoTT51R7aRv7DSqU3egsuq8WZ744X4PNluzIhORPwR+CXxcVY/Nrj0PuFFV94nI5QCqulFE1gCbgZOAI4AvAE/Jgvou8FzgHmArcK6qbi+K26zIpoP5jetNdWEYDTI2VmSq+iXgvuDaP6vqvuzrV4Ejs89nAZ9U1b2q+j1gJwNhcxKwU1XnVPU3wCeze42AabT+MuEynusZ48g4lHMfVbajXIN5FfCP2eeVwN3eb/dk1/KuL0FELhKR20TktgfZ20Jy+80NV39k1EmYSPqu0hrH9Yxx6KxD+lrOfln2ccA1EgEjIm8F9gGfaCpMVb1SVU9U1RMfyvKmgh0bRu1CpO7oadQzr7LOrq1yHXW+R0lfO+txwW+zfS/LzgWMiFwAvBB4mR5YAJoHjvJuOzK7lnfd6Bl1R08pxhCpI946s41RvaDjZARiZvH94pw1zbedtmbqnQoYETkDeDPwIlXd4/10HfBSEVkuIscAq4FbGSzqrxaRY0TkYcBLs3uNKSJVCNSZbYyjuqZr+m4WP6o69AVvl+sfTdaHK7u2ZuptWpFtBk4DHg/8CHgb8BZgOfDT7LavquofZ/e/lcG6zD7gT1X1H7PrZwJ/DSwDPqqq7yyL26zIjHGjCyeThlGGObtMwASMYRhGdcbGTNkwDMOYbkzATBh9XVNo09x3UhehUy3NJjX/xvhjAmbC6KvZYpvrC31fhK7D/Mb1yZZm45z/vg6IxoE+bqwMMQEzpdiL3W9GvWmuq1lRXwdE48Co20gKJmCmFHuxjSLGeVZk9AcTMIZRkb67jxmGcVC7GOODCRijEaZpoXmS96uMg9ollWlqk0WM0i2RCRijEUylYvQNa5MDRumWyASMYRidYgYm/aLNmZ4JmCnFXnLDSGeS16banOmZgJlSzIqs30zy+sE4tr2zz7151EkYS0zAGI1TZ7Q36hFi32Z0tn7QL67dfOqokzCWmIAxFhFanFTpeN2ou8wSKWbmW/TMqIVPHuM2y+ibEB0nJsm6rkvMm7Ix1ayb3W+zBaMRJqEtmTdlw2iQce8QjP5gbWkpJmAMwzCMVjABYxiGYbSCCRij99jidH0m2W/apNBXI5YmaE3AiMhHRWS3iNwV+e1NIqIi8vjsu4jIe0Vkp4jcISInePeeLyI7sr/z20qv0V/Gcd9EX5hkv2mTwiRbqLU5g2RrvQcAAAm2SURBVLkKOCO8KCJHAc8DfuBdfj6wOvu7CPhAdu+hwNuAk4GTgLeJyGNbTLNhGD3FZrLjR2sCRlW/BNwX+ek9wJsB3z76LODjOuCrwCEicjiwAfi8qt6nqvcDnycitAzDmHxsJjt+dLoGIyJnAfOqenvw00rgbu/7Pdm1vOuGYRhGz+lMwIjICuD/Af5TS+FfJCK3ichtD7K3jSiMBNo4e2KUqpFJXoBtGlNh1aOqR4hxKucuZzBPAo4BbheR7wNHAl8Xkd8F5oGjvHuPzK7lXV+Cql6pqieq6okPZXkLyTdSaOPsiVGqRiZ5AbZpTIVVj6obNMepnDsTMKp6p6o+QVWPVtWjGai7TlDVHwLXAa/MrMmeBfxMVe8FtgDPE5HHZov7z8uuGYZhGD2nTTPlzcBXgKeKyD0icmHB7Z8D5oCdwIeA1wKo6n3AXwBbs793ZNcMw2iBLhx4jpOKZ1zoq+NVc3ZpjJR9p68d6ZGuhmEcwJxdGhNFKFz6NhKzRX7DqI8JGKNXFC14NiV8qrhPmbZFflNfGU1iAsYYG5pyh27uU/LpwkLJZoXTgwkYwyB/5N43ld2oaFIoTNussIxJnjXaIr9hGIYB2CK/YUw8pkLqBzZ7HR4TMIbRM0yF1A/sCOThMQFjGIZhtIIJGMMwOmWSF7WNxZiAMQyjU8bJWaMxHCZgDKMAO9PeMOpjAsYwCrBNmYZRHxMwhjFibE2i/7RxkN40YALGMEaMrUn0H/P4XQ8TMIZhLMI2GBpNYQLGMIxFtL3B0FSC04MJGMMwDKMVTMAYhtEpy29fMeokGB1hAsYwjE4xX2vTQ2sCRkQ+KiK7ReSu4PqfiMi3ReSbIvL/edffIiI7ReQ7IrLBu35Gdm2niFzSVnoNwzDyMA/X9WhzBnMVcIZ/QUT+PXAWcLyqPh34q+z6GuClwNOzZ94vIstEZBnwN8DzgTXAudm9hmEYneFmXbYfphqtCRhV/RJwX3D5NcC7VHVvds/u7PpZwCdVda+qfg/YCZyU/e1U1TlV/Q3wyexewzCMzulyP8wkWNsd1HF8TwFOFZF3Av8G/JmqbgVWAl/17rsnuwZwd3D95FjAInIRcFH2de8X9NN3xe6bQh4P/GTUiegJVhYHsLI4QD/L4txPM9d9rE9tMrCuBcxBwKHAs4B1wKdEZFUTAavqlcCVACJyW5PHfo4zVhYHsLI4gJXFAawsDiAitzUZXtcC5h7gM6qqwK0i8lsGo4d54CjvviOzaxRcNwzDMHpM12bK1wL/HkBEngI8jMHU9DrgpSKyXESOAVYDtwJbgdUicoyIPIyBIcB1HafZMAzDqEFrMxgR2QycBjxeRO4B3gZ8FPhoZrr8G+D8bDbzTRH5FLAd2Ae8TlX3Z+G8HtgCLAM+qqrfTIj+yqbzM8ZYWRzAyuIAVhYHsLI4QKNlIYP+3TAMwzCaxXbyG4ZhGK1gAsYwDMNohYkTMNPmWkZEjhKRL4rI9sz9zsXZ9UNF5PMisiP7/9jsuojIe7PyuUNEThhtDpol8wDxDRG5Pvt+jIh8LcvvNZmxCJlByTXZ9a+JyNGjTHcbiMghIvLpzDXTt0TklCluF/8xez/uEpHNIvLwaWkbMbddddqBiJyf3b9DRM5PiXuiBMyUupbZB7xJVdcw2F/0uizPlwA3qOpq4IbsOwzKZnX2dxHwge6T3CoXA9/yvl8OvEdVnwzcD1yYXb8QuD+7/p7svknjCuCfVPVpwPEMymXq2oWIrATeAJyoqscyMBh6KdPTNq4icNtFxXYgIocyMNQ6mYGHlbc5oVSIqk7MH3AKsMX7/hbgLaNOV8dl8FngucB3gMOza4cD38k+fxA417t/4b5x/2OwT+oG4HTgekAYmMEfFLYPBpaJp2SfD8ruk1HnocGyeAzwvTBPU9ouVjLwCHJoVtfXAxumqW0ARwN31W0HwLnAB73ri+7L+5uoGQwHGpLDdzkz8WRT+WcCXwMOU9V7s59+CByWfZ7kMvpr4M3Ab7PvjwMeUNV92Xc/rwvlkP3+s+z+SeEY4MfAf89Uhh8WkYOZwnahqvMMHOv+ALiXQV1vY3rbBlRvB7Xax6QJmKlFRB4J/D3wp6r6c/83HQw5JtoeXUReCOxW1e68Efabg4ATgA+o6jOBX3FADQJMR7sAyFQ5ZzEQukcAB7NUZTS1tNkOJk3AFLmcmVhE5KEMhMsnVPUz2eUficjh2e+HA85z9aSW0e8DLxKR7zPwun06gzWIQ0TEbSj287pQDtnvjwF+2mWCW+Ye4B5V/Vr2/dMMBM60tQuA5wDfU9Ufq+qDwGcYtJdpbRtQvR3Uah+TJmCmzrWMiAjwEeBbqvpu76frAGfpcT6DtRl3/ZWZtcizgJ95U+WxRVXfoqpHqurRDOr9RlV9GfBF4MXZbWE5uPJ5cXb/xIzmVfWHwN0i4rzjPpuBp4ypahcZPwCeJSIrsvfFlcVUto2Mqu1gC/A8EXlsNiN8XnatmFEvPrWwmHUm8F3gX4G3jjo9HeT3DxhMb+8AZrO/MxnojG8AdgBfAA7N7hcGlnb/CtzJwLJm5PlouExOA67PPq9i4NduJ/B3wPLs+sOz7zuz31eNOt0tlMMMcFvWNq4FHjut7QL4c+DbwF3A3wLLp6VtAJsZrD09yGBme2GddgC8KiuTncAfpcRtrmIMwzCMVpg0FZlhGIbRE0zAGIZhGK1gAsYwDMNoBRMwhmEYRiuYgDEMwzBawQSMYQyBiBzte6nNrr1dRP5sVGkyjL5gAsYweoa3u9wwxhoTMIbREiLyBhmc03OHiHwyu3Zwdj7HrZkTyrOy6xeIyHUiciNwg4gcLiJfEpHZ7AyTU0eaGcOogY2UDKM9LgGOUdW9InJIdu2tDFyPvCq7dquIfCH77QTgGap6n4i8iYH7+Hdm5xyt6D75hjEcJmAMYzjyXGE49z2fEJFrGbhqgYEPpxd5azQPB56Yff68qt6Xfd4KfDRzZHqtqs42n3TDaBdTkRnGcPyUgY8vn0MZHFL1AgZ+nU4AtmZrKwL8B1Wdyf6eqKruBM5fuQBU9UvAHzLwWHuViLyy5XwYRuOYgDGMIVDVXwL3isjpsHC07BnAl4GjVPWLwEYGLt8fycAD7Z9kXn0RkWfGwhWR3wN+pKofAj7MQEgZxlhhKjLDGJ5XAn8jIu64hD9n4CL+iyLyGAazlveq6gMi8hcMTt68Q0QewuBY4xdGwjwN+L9F5EHgl1kchjFWmDdlwzAMoxVMRWYYhmG0ggkYwzAMoxVMwBiGYRitYALGMAzDaAUTMIZhGEYrmIAxDMMwWsEEjGEYhtEK/z98sxYj/JDQ7QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(Y, extent=[0,1000,1600,0], aspect='auto')\n",
    "plt.title('Ratings Matrix');\n",
    "plt.xlabel('Users');\n",
    "plt.ylabel('Movies');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.2 Collaborative Filtering Learning Algorithm\n",
    "\n",
    "> The collaborative filtering algorithm in the setting of movie recommendations considers a set of n-dimensional parameter vectors $x^{(1)} , ..., x^{(n_m)}$ and $\\theta^{(1)},...,\\theta^{(n_u)}$, where the model predicts the rating for movie $i$ by user $j$ as $y^{(i,j)} = (\\theta^{(j)})^T x^{(i)}$. Given a dataset that consists of a set of ratings produced by some users on some movies, you wish to learn the parameter vectors $x^{(1)},...,x^{(n_m)},\\theta^{(1)},...,\\theta^{(n_u)}$ that produce the best fit (minimizes the squared error).\n",
    "\n",
    "#### 2.2.1 Collaborative filtering cost function (without regularization)\n",
    "\n",
    "$$ J(x^{(1)},...,x^{(n_m)},\\theta^{(1)},...,\\theta^{(n_u)}) = \\frac{1}{2}\\sum_{(i,j):r(i,j)=1}((\\theta^{(j)})^T x^{(i)}-y^{(i,j)})^2$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 446,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cofi_cost_func(params, Y, R, num_users, num_movies, num_features, lambda_r):\n",
    "    X = np.reshape(params[:num_movies*num_features], newshape=(num_movies, num_features), order='F')\n",
    "    Theta = np.reshape(params[num_movies*num_features:], newshape=(num_users, num_features), order='F')\n",
    "    \n",
    "    C = np.subtract(X.dot(Theta.T), Y) ** 2\n",
    "    J = np.sum(np.sum(R*C)) / 2\n",
    "    return J"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 447,
   "metadata": {},
   "outputs": [],
   "source": [
    "#reduce dataset to test\n",
    "num_users = 4\n",
    "num_movies = 5\n",
    "num_features = 3\n",
    "X = X[:num_movies, :num_features]\n",
    "Theta = Theta[:num_users, :num_features]\n",
    "Y = Y[:num_movies, :num_users]\n",
    "R = R[:num_movies, :num_users]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 450,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost at loaded parameters:  22.224603725685675\n",
      "\t(this value should be about 22.22)\n"
     ]
    }
   ],
   "source": [
    "J = cofi_cost_func(np.hstack((X.ravel(order='F'), Theta.ravel(order='F'))),\n",
    "                   Y, R, num_users, num_movies, num_features, 0)\n",
    "print('Cost at loaded parameters: ', J)\n",
    "print('\\t(this value should be about 22.22)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.2.2 Collaborative filtering gradient (without regularization)\n",
    "\n",
    "$$ \\frac{\\partial J}{\\partial x_k^{(i)}} = \\sum_{j:r(i,j)=1}((\\theta^{(j)})^T x^{(i)}-y^{(i,j)})\\theta_k^{(j)} $$\n",
    "\n",
    "$$ \\frac{\\partial J}{\\partial \\theta_k^{(j)}} = \\sum_{i:r(i,j)=1}((\\theta^{(j)})^T x^{(i)}-y^{(i,j)})x_k^{(i)} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 460,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cofi_cost_func(params, Y, R, num_users, num_movies, num_features, lambda_r):\n",
    "    X = np.reshape(params[:num_movies*num_features], newshape=(num_movies, num_features), order='F')\n",
    "    Theta = np.reshape(params[num_movies*num_features:], newshape=(num_users, num_features), order='F')\n",
    "    \n",
    "    C = np.subtract(X.dot(Theta.T), Y) ** 2\n",
    "    J = np.sum(np.sum(R*C)) / 2\n",
    "    \n",
    "    X_grad = np.zeros(X.shape)\n",
    "    Theta_grad = np.zeros(Theta.shape)\n",
    "    \n",
    "    for i in range(num_movies):\n",
    "        idx = np.argwhere(R[i,:]==1).T[0]\n",
    "        X_grad[i,:] = np.subtract(X[i,:].dot(Theta[idx,:].T), Y[i,idx]).dot(Theta[idx,:])\n",
    "        \n",
    "    for j in range(num_users):\n",
    "        idx = np.argwhere(R[:,j]==1).T[0]\n",
    "        Theta_grad[j,:] = np.subtract(X[idx,:].dot(Theta[j,:].T), Y[idx,j]).T.dot(X[idx,:])\n",
    "        \n",
    "    grad = np.hstack((X_grad.ravel(order='F'), Theta_grad.ravel(order='F')))\n",
    "\n",
    "    return J, grad"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Checking Gradients (without regularization)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 461,
   "metadata": {},
   "outputs": [],
   "source": [
    "def compute_numerical_gradient(theta, Y, R, num_users, num_movies, num_features, lambda_r):\n",
    "    e = 0.0001\n",
    "    num_grad = np.zeros(theta.shape)\n",
    "    perturb = np.zeros(theta.shape)\n",
    "    for p in range(len(theta)):\n",
    "        perturb[p] = e\n",
    "        loss1,_ = cofi_cost_func(theta-perturb, Y, R, num_users, num_movies, num_features, lambda_r)\n",
    "        loss2,_ = cofi_cost_func(theta+perturb, Y, R, num_users, num_movies, num_features, lambda_r)\n",
    "        num_grad[p] = (loss2-loss1)/(2*e)\n",
    "        perturb[p] = 0\n",
    "    return num_grad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 462,
   "metadata": {},
   "outputs": [],
   "source": [
    "def check_cost_function(lambda_r=0):\n",
    "    X_t = np.random.uniform(0,1,(4,3))\n",
    "    Theta_t = np.random.uniform(0,1,(5,3))\n",
    "    \n",
    "    Y = X_t.dot(Theta_t.T)\n",
    "    Y[np.random.uniform(0,1,Y.shape)>0.5] = 0\n",
    "    R = np.zeros(Y.shape)\n",
    "    R[Y!=0] = 1\n",
    "    \n",
    "    X = np.random.normal(size=X_t.shape)\n",
    "    Theta = np.random.normal(size=Theta_t.shape)\n",
    "    num_users = Y.shape[1]\n",
    "    num_movies = Y.shape[0]\n",
    "    num_features = Theta_t.shape[1]\n",
    "    \n",
    "    params = np.hstack((X.ravel(order='F'), Theta.ravel(order='F')))\n",
    "    \n",
    "    cost, grad = cofi_cost_func(params, Y, R, num_users, num_movies, num_features, lambda_r)\n",
    "    num_grad = compute_numerical_gradient(params, Y, R, num_users, num_movies, num_features, lambda_r)\n",
    "    \n",
    "    print('The columns should be very similar...')\n",
    "    for i, j in zip(num_grad, grad):\n",
    "        print(i,j)\n",
    "        \n",
    "    diff = np.linalg.norm(num_grad-grad)/np.linalg.norm(num_grad+grad)\n",
    "    print('''If your cost function implementation is correct, then the relative difference will \n",
    "             be small (less than 1e-9). Relative Difference:''', diff)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 463,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The columns should be very similar...\n",
      "4.534710280985621 4.534710280987838\n",
      "-5.15389514749387 -5.153895147477099\n",
      "2.0676030457877914 2.0676030457883914\n",
      "1.710344108012407 1.7103441080090966\n",
      "-5.463542401216159 -5.463542401214781\n",
      "6.668686071904517 6.668686071916491\n",
      "-4.84571787458421 -4.845717874595353\n",
      "-2.2667239972840036 -2.266723997296472\n",
      "-1.6398196269129528 -1.6398196269149445\n",
      "2.214904425379416 2.2149044253903263\n",
      "-0.7788080677428866 -0.778808067722867\n",
      "-0.4352805963669937 -0.4352805963653944\n",
      "-0.736120681548158 -0.7361206815563007\n",
      "6.822943656654701 6.822943656666209\n",
      "-9.66455117627163 -9.664551176268647\n",
      "1.8165669567338227 1.8165669567259517\n",
      "1.9700208824424692 1.9700208824342398\n",
      "-1.5015643731253192 -1.5015643731360209\n",
      "-1.996882072887729 -1.996882072899521\n",
      "16.464228418620053 16.464228418620817\n",
      "-1.612611128756214 -1.6126111287545721\n",
      "3.1563994247107985 3.156399424700015\n",
      "-0.25795459185573577 -0.2579545918661169\n",
      "-2.518921166281274 -2.5189211662717823\n",
      "3.1874141775567466 3.1874141775485088\n",
      "-0.8614888126778908 -0.8614888126751783\n",
      "-1.0384236637683841 -1.038423663767987\n",
      "If your cost function implementation is correct, then the relative difference will \n",
      "             be small (less than 1e-9). Relative Difference: 9.47543254962173e-13\n"
     ]
    }
   ],
   "source": [
    "check_cost_function()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.2.3 Regularized cost function\n",
    "\n",
    "$$ J(x^{(1)},...,x^{(n_m)},\\theta^{(1)},...,\\theta^{(n_u)}) = \\frac{1}{2}\\sum_{(i,j):r(i,j)=1}((\\theta^{(j)})^T x^{(i)}-y^{(i,j)})^2 + \n",
    "\\Big(\\frac{\\lambda}{2}\\sum_{j=1}^{n_u}\\sum_{k=1}^{n}(\\theta_k^{(j)})^2 \\Big) + \\Big(\\frac{\\lambda}{2}\\sum_{i=1}^{n_m}\\sum_{k=1}^{n}(x_k^{(i)})^2 \\Big)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 464,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cofi_cost_func(params, Y, R, num_users, num_movies, num_features, lambda_r):\n",
    "    X = np.reshape(params[:num_movies*num_features], newshape=(num_movies, num_features), order='F')\n",
    "    Theta = np.reshape(params[num_movies*num_features:], newshape=(num_users, num_features), order='F')\n",
    "    \n",
    "    C = np.subtract(X.dot(Theta.T), Y) ** 2\n",
    "    J = np.sum(np.sum(R*C)) / 2 + ((lambda_r/2)*np.sum(np.sum(Theta**2))) + ((lambda_r/2)*np.sum(np.sum(X**2)))\n",
    "    \n",
    "    X_grad = np.zeros(X.shape)\n",
    "    Theta_grad = np.zeros(Theta.shape)\n",
    "    \n",
    "    for i in range(num_movies):\n",
    "        idx = np.argwhere(R[i,:]==1).T[0]\n",
    "        X_grad[i,:] = np.subtract(X[i,:].dot(Theta[idx,:].T), Y[i,idx]).dot(Theta[idx,:])\n",
    "        \n",
    "    for j in range(num_users):\n",
    "        idx = np.argwhere(R[:,j]==1).T[0]\n",
    "        Theta_grad[j,:] = np.subtract(X[idx,:].dot(Theta[j,:].T), Y[idx,j]).T.dot(X[idx,:])\n",
    "        \n",
    "    grad = np.hstack((X_grad.ravel(order='F'), Theta_grad.ravel(order='F')))\n",
    "\n",
    "    return J, grad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 466,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cost at loaded parameters (lambda = 1.5): 31.34405624427422\n",
      "\t(this value should be about 31.34)\n"
     ]
    }
   ],
   "source": [
    "J, _ = cofi_cost_func(np.hstack((X.ravel(order='F'), Theta.ravel(order='F'))),\n",
    "                   Y, R, num_users, num_movies, num_features, 1.5)\n",
    "print('Cost at loaded parameters (lambda = 1.5):', J)\n",
    "print('\\t(this value should be about 31.34)')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.2.4 Regularized gradient\n",
    "\n",
    "$$ \\frac{\\partial J}{\\partial x_k^{(i)}} = \\sum_{j:r(i,j)=1}((\\theta^{(j)})^T x^{(i)}-y^{(i,j)})\\theta_k^{(j)} + \\lambda x_k^{(i)}$$\n",
    "\n",
    "$$ \\frac{\\partial J}{\\partial \\theta_k^{(j)}} = \\sum_{i:r(i,j)=1}((\\theta^{(j)})^T x^{(i)}-y^{(i,j)})x_k^{(i)} + \\lambda \\theta_k^{(j)}$$\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 467,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cofi_cost_func(params, Y, R, num_users, num_movies, num_features, lambda_r):\n",
    "    X = np.reshape(params[:num_movies*num_features], newshape=(num_movies, num_features), order='F')\n",
    "    Theta = np.reshape(params[num_movies*num_features:], newshape=(num_users, num_features), order='F')\n",
    "    \n",
    "    C = np.subtract(X.dot(Theta.T), Y) ** 2\n",
    "    J = np.sum(np.sum(R*C)) / 2 + ((lambda_r/2)*np.sum(np.sum(Theta**2))) + ((lambda_r/2)*np.sum(np.sum(X**2)))\n",
    "    \n",
    "    X_grad = np.zeros(X.shape)\n",
    "    Theta_grad = np.zeros(Theta.shape)\n",
    "    \n",
    "    for i in range(num_movies):\n",
    "        idx = np.argwhere(R[i,:]==1).T[0]\n",
    "        X_grad[i,:] = np.subtract(X[i,:].dot(Theta[idx,:].T), Y[i,idx]).dot(Theta[idx,:]) + (lambda_r * X[i,:])\n",
    "        \n",
    "    for j in range(num_users):\n",
    "        idx = np.argwhere(R[:,j]==1).T[0]\n",
    "        Theta_grad[j,:] = np.subtract(X[idx,:].dot(Theta[j,:].T), Y[idx,j]).T.dot(X[idx,:]) + (lambda_r * Theta[j,:])\n",
    "        \n",
    "    grad = np.hstack((X_grad.ravel(order='F'), Theta_grad.ravel(order='F')))\n",
    "\n",
    "    return J, grad"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 468,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The columns should be very similar...\n",
      "-1.4524081545630452 -1.4524081545243543\n",
      "-3.9894665798811957 -3.989466579935604\n",
      "-3.8493748256485105 -3.8493748256961533\n",
      "5.89234950275852 5.892349502838272\n",
      "24.588504805649336 24.588504805584734\n",
      "-3.411648310773785 -3.4116483107856017\n",
      "17.299202177056827 17.299202177077966\n",
      "-4.048848950901629 -4.048848950914966\n",
      "3.8448012167435763 3.844801216718646\n",
      "-10.625284772700638 -10.625284772687126\n",
      "-0.03590040478229639 -0.035900404744119374\n",
      "-8.403440972699627 -8.403440972745564\n",
      "-7.542464301408813 -7.542464301432494\n",
      "11.234351626256966 11.234351626229781\n",
      "5.043464659522101 5.043464659512603\n",
      "-7.5578869003578575 -7.557886900429807\n",
      "1.61794649038427 1.617946490351315\n",
      "-8.297124341751783 -8.297124341805954\n",
      "-24.996637089458318 -24.99663708937739\n",
      "-15.263339168143375 -15.263339168118492\n",
      "1.4649656390020027 1.4649656390125518\n",
      "-0.5995500631428285 -0.5995500631858357\n",
      "-11.662631582041172 -11.662631582031164\n",
      "3.429218116295374 3.429218116256577\n",
      "-1.092262164874569 -1.0922621648905948\n",
      "13.661286852695298 13.661286852682691\n",
      "1.5379871960163882 1.5379871960267386\n",
      "If your cost function implementation is correct, then the relative difference will \n",
      "             be small (less than 1e-9). Relative Difference: 2.01166620610213e-12\n"
     ]
    }
   ],
   "source": [
    "check_cost_function(1.5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2.3 Learning movie recommendations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 480,
   "metadata": {},
   "outputs": [],
   "source": [
    "with open('data/movie_ids.txt', encoding='latin-1') as f:\n",
    "    content = f.readlines()\n",
    "    \n",
    "movie_list = [' '.join(line.split()[1:]) for line in content]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 482,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1682"
      ]
     },
     "execution_count": 482,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(movie_list)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 483,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['Toy Story (1995)',\n",
       " 'GoldenEye (1995)',\n",
       " 'Four Rooms (1995)',\n",
       " 'Get Shorty (1995)',\n",
       " 'Copycat (1995)']"
      ]
     },
     "execution_count": 483,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "movie_list[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 490,
   "metadata": {},
   "outputs": [],
   "source": [
    "my_ratings = np.zeros((1682, 1))\n",
    "my_ratings[0] = 4\n",
    "my_ratings[10] = 4\n",
    "my_ratings[21] = 5\n",
    "my_ratings[70] = 5\n",
    "my_ratings[97] = 2\n",
    "my_ratings[98] = 5\n",
    "my_ratings[150] = 4\n",
    "my_ratings[154] = 4\n",
    "my_ratings[175] = 3\n",
    "my_ratings[312] = 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 491,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Rated 4 for Toy Story (1995)\n",
      "Rated 4 for Seven (Se7en) (1995)\n",
      "Rated 5 for Braveheart (1995)\n",
      "Rated 5 for Lion King, The (1994)\n",
      "Rated 2 for Silence of the Lambs, The (1991)\n",
      "Rated 5 for Snow White and the Seven Dwarfs (1937)\n",
      "Rated 4 for Willy Wonka and the Chocolate Factory (1971)\n",
      "Rated 4 for Dirty Dancing (1987)\n",
      "Rated 3 for Aliens (1986)\n",
      "Rated 5 for Titanic (1997)\n"
     ]
    }
   ],
   "source": [
    "for i,r in enumerate(my_ratings):\n",
    "    if r>0:\n",
    "        print('Rated {0} for {1}'.format(int(r[0]), movie_list[i]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 493,
   "metadata": {},
   "outputs": [],
   "source": [
    "mat = scipy.io.loadmat('data/ex8_movies.mat')\n",
    "Y = np.hstack((my_ratings,mat['Y']))\n",
    "R = np.hstack((my_ratings!=0,mat['R']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 514,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1682, 944)"
      ]
     },
     "execution_count": 514,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Training Collaborative Filtering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 550,
   "metadata": {},
   "outputs": [],
   "source": [
    "def normalize_ratings(Y, R):\n",
    "    Y_mean = np.zeros((Y.shape[0], 1))\n",
    "    Y_norm = np.zeros(Y.shape)\n",
    "    for i in range(Y.shape[0]):\n",
    "        idx = np.argwhere(R[i,:]==1).T[0]\n",
    "        Y_mean[i] = np.mean(Y[i,idx], axis=0)\n",
    "        Y_norm[i,idx] = np.subtract(Y[i,idx], Y_mean[i])\n",
    "    return Y_norm, Y_mean"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 551,
   "metadata": {},
   "outputs": [],
   "source": [
    "Y_norm, Y_mean = normalize_ratings(Y, R)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 552,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_users = Y.shape[1]\n",
    "num_movies = Y.shape[0]\n",
    "num_features = 10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 553,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.random.normal(size=(num_movies, num_features))\n",
    "Theta = np.random.normal(size=(num_users, num_features))\n",
    "initial_params = np.hstack((X.ravel(order='F'), Theta.ravel(order='F')))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 554,
   "metadata": {},
   "outputs": [],
   "source": [
    "import scipy.optimize as opt\n",
    "lambda_r = 10\n",
    "opt_results = opt.minimize(cofi_cost_func, initial_params, args=(Y, R, num_users, num_movies, num_features, lambda_r),\n",
    "                           method='L-BFGS-B', jac=True, options={'maxiter':100})\n",
    "theta = opt_results['x']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 555,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.reshape(theta[:num_movies*num_features], newshape=(num_movies, num_features), order='F')\n",
    "Theta = np.reshape(theta[num_movies*num_features:], newshape=(num_users, num_features), order='F')    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Recommendation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 556,
   "metadata": {},
   "outputs": [],
   "source": [
    "p = X.dot(Theta.T)\n",
    "my_predictions = p[:,0] + Y_mean.T[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 569,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Top recommendations for you:\n",
      "Predicting rating 8.368993278584279 for movie Titanic (1997)\n",
      "Predicting rating 8.288858532809607 for movie Schindler's List (1993)\n",
      "Predicting rating 8.234374133130322 for movie Shawshank Redemption, The (1994)\n",
      "Predicting rating 8.044420702919398 for movie Star Wars (1977)\n",
      "Predicting rating 7.96560643547238 for movie Good Will Hunting (1997)\n",
      "Predicting rating 7.962937588003024 for movie Raiders of the Lost Ark (1981)\n",
      "Predicting rating 7.941203005532051 for movie Braveheart (1995)\n",
      "Predicting rating 7.804394669167708 for movie Casablanca (1942)\n",
      "Predicting rating 7.771370067735939 for movie Usual Suspects, The (1995)\n",
      "Predicting rating 7.727566323174965 for movie Empire Strikes Back, The (1980)\n"
     ]
    }
   ],
   "source": [
    "sort_idxs = np.argsort(my_predictions)[::-1]\n",
    "print('Top recommendations for you:')\n",
    "for i in range(10):\n",
    "    j = sort_idxs[i]\n",
    "    print('Predicting rating {0} for movie {1}'.format(my_predictions[j], movie_list[j]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 571,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Original ratings provided:\n",
      "Rated 4 for Toy Story (1995)\n",
      "Rated 4 for Seven (Se7en) (1995)\n",
      "Rated 5 for Braveheart (1995)\n",
      "Rated 5 for Lion King, The (1994)\n",
      "Rated 2 for Silence of the Lambs, The (1991)\n",
      "Rated 5 for Snow White and the Seven Dwarfs (1937)\n",
      "Rated 4 for Willy Wonka and the Chocolate Factory (1971)\n",
      "Rated 4 for Dirty Dancing (1987)\n",
      "Rated 3 for Aliens (1986)\n",
      "Rated 5 for Titanic (1997)\n"
     ]
    }
   ],
   "source": [
    "print('Original ratings provided:')\n",
    "for i,r in enumerate(my_ratings):\n",
    "    if r>0:\n",
    "        print('Rated {0} for {1}'.format(int(r[0]), movie_list[i]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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