exercise8.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Programming Exercise 8: Anomaly Detection and Recommender Systems"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import warnings,os\n",
    "warnings.simplefilter('ignore')\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "\n",
    "from scipy.io import loadmat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1&nbsp;&nbsp;&nbsp;&nbsp;Anomaly detection\n",
    "\n",
    "#### Problem Statement\n",
    "In this part of the exercise, we will implement an anomaly detection algorithm to detect the anomalous behavior in server computers. The features measure the throughput (mb/s) and latency (ms) of response of each server. While our servers were operating, we collected m=307 examples of how they were behaving, and thus have an unlabeled dataset. We suspect that the vast majority of these examples are \"Normal\" (Non-anomalous) examples of servers operating normally, but there might also be some examples of servers acting anomalously within the dataset.\n",
    "\n",
    "**We will use a gaussian model to detect the anomalies in our dataset. On this dataset, we will fit a gaussian distribution and then find the values that have very low probability and hence can be considered anomalies.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "__header__\n",
      "__version__\n",
      "__globals__\n",
      "X\n",
      "Xval\n",
      "yval\n"
     ]
    }
   ],
   "source": [
    "# Loading dataset\n",
    "mat=loadmat('ex8data1.mat')\n",
    "X=mat['X']\n",
    "print(*mat.keys(),sep='\\n')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": false
   },
   "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": [
    "fig=sns.scatterplot(X[:,0],X[:,1],marker='x')\n",
    "fig.set(xlabel='Latency (ms)',ylabel='Throughput (mb/s)',title='Original Dataset');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.1&nbsp;&nbsp;&nbsp;&nbsp;Gaussian Distribution\n",
    "To perform anomaly detection, we will first need to fit a model to the data's distribution.  \n",
    "Given a training set, we want to estimate the gaussian distribution for each of the features. For each feature, we need to find the parameters $\\mu_{i}$ and $\\sigma_{i}^{2}$ that fit the data. The gaussian distribution is given by:\n",
    "\n",
    "$$\\boxed{p(x_{j};\\mu_{j},\\sigma_{j}^{2})=\\frac{1}{\\sqrt{2\\pi\\sigma_{j}^{2}}}e^{-\\frac{(X_{j}-\\mu_{j})^{2}}{2\\sigma_{j}^{2}}}}$$\n",
    "\n",
    "$$p(x)=\\Pi_{j=1}^{n}p(x_{j};\\mu_{j},\\sigma_{j}^{2})$$\n",
    "\n",
    "$$\\text{Anomaly, if }p(x)< \\varepsilon$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def mutlivariateGaussian(X,mu,sigma):\n",
    "    p=(1/(np.sqrt(2*np.pi*np.power(sigma,2))))*np.exp(-np.power(X-mu,2)/(2*np.power(sigma,2)))\n",
    "    p=np.product(p,axis=1).reshape((-1,1))\n",
    "    return p"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.2&nbsp;&nbsp;&nbsp;&nbsp;Estimating parameters for a Gaussian\n",
    "We can estimate the parameters ($\\mu_{i},\\sigma_{i}^{2}$) of the i-th feature by using the following equations. To estimate the mean, we will use\n",
    "$$\\mu_{i}=\\frac{1}{m}\\sum_{j=1}^{m}x_{i}^{(j)}$$\n",
    "\n",
    "And for the variance, we will use:\n",
    "$$\\sigma_{i}^{2}=\\frac{1}{m}\\sum_{j=1}^{m}(x_{i}^{(j)}-\\mu_{i})^2$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def estimateGaussian(X):\n",
    "    mu=np.mean(X,axis=0)\n",
    "    sigma=np.std(X,axis=0)\n",
    "    return (mu,sigma)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at the Gaussian distribution contours of the distribution fit to the dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plotGaussianContour(X,mu,sigma,title=None):\n",
    "    # Constructing grid around the min and max range of original data\n",
    "    temp=np.linspace(np.min(X)-5,np.max(X)+5)\n",
    "    [x1,x2]=np.meshgrid(temp,temp)\n",
    "    # Computing the Gaussian Density Probability for the grid\n",
    "    temp=np.array([x1.reshape(-1),x2.reshape(-1)]).T\n",
    "    z=mutlivariateGaussian(temp,mu,sigma).reshape(x1.shape)\n",
    "    # Plotting\n",
    "    levels=np.power(10,list(map(lambda x:float(x),list(range(-20,0,3)))))\n",
    "    plt.contour(x1,x2,z,levels=levels);\n",
    "    fig=sns.scatterplot(X[:,0],X[:,1],marker='x')\n",
    "    title='Gaussian Distribution Contours' if title==None else title\n",
    "    fig.set(xlabel='Latency (ms)',ylabel='Throughput (mb/s)',title=title);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "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": [
    "# Estimating Gaussian parameters\n",
    "mu,sigma=estimateGaussian(X)\n",
    "# Computing Density Probability\n",
    "p=mutlivariateGaussian(X,mu,sigma)\n",
    "# Plotting\n",
    "plotGaussianContour(X,mu,sigma);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.3&nbsp;&nbsp;&nbsp;&nbsp;Selecting the threshold, $\\varepsilon$\n",
    "Now that we have estimated the gaussian parameters, we can investigate which examples have a very high probability given this distribution and which examples have a very low probability. The low probability examples are more likely to be the anomalies in our dataset. One way to determine which examples are the anomalies is to select the threshold based on a cross validation set. In this part of the exericse, we will implement an algorithm to select the threshold using F1 score on a cross validation set.  \n",
    "\n",
    "**$y=1$ corresponds to an anomalous examples and $y=0$ corresponds to a normal examples.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "Xval=mat['Xval']\n",
    "yval=mat['yval']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For many different values of $\\varepsilon$, we will compute the resulting $F_1$ score by computing how many examples the current threshold classifies correctly and incorrectly. The $F_1$ score is computed using **Precision** (prec) and **Recall** (rec):\n",
    "\n",
    "$$\\boxed{F1=\\frac{2.prec.rec}{prec+rec}}$$\n",
    "\n",
    "We can compute Precision (prec) and Recall (rec) using:\n",
    "\n",
    "$$\\boxed{prec=\\frac{tp}{tp+fp}}$$\n",
    "\n",
    "$$\\boxed{rec=\\frac{tp}{tp+fn}}$$\n",
    "\n",
    "where,\n",
    "- $tp$ is the number of true positives: the ground truth label says it's an anomaly and our algorithm classified it as an anomaly.\n",
    "- $fp$ is the number of false positives: the ground truth label says it's not an anomaly and our algorithm classified it as  an anomaly.\n",
    "- $fn$ is the number of false negatives: the ground truth labels says it's an anomaly and our alogrithm classified it as not being anomalous."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def selectThreshold(yval,pval):\n",
    "    '''\n",
    "     Returns the threshold value of epsilon and the corresponding F1 score.\n",
    "    '''\n",
    "    bestEpsilon=bestF1=F1=0\n",
    "    epsilons=np.linspace(np.min(pval),np.max(pval),1000)\n",
    "    for epsilon in epsilons:\n",
    "        cvPrediction=pval<epsilon\n",
    "        tp=np.sum((cvPrediction==1) & (yval==1))\n",
    "        fp=np.sum((cvPrediction==1) & (yval==0))\n",
    "        fn=np.sum((cvPrediction==0) & (yval==1))\n",
    "        prec=rec=0\n",
    "        # Computing Precision\n",
    "        if tp+fp>0:\n",
    "            prec=tp/(tp+fp)\n",
    "        # Computing Recall\n",
    "        if tp+fn>0:\n",
    "            rec=tp/(tp+fn)\n",
    "        # Computing F1 Score\n",
    "        if prec+rec>0:\n",
    "            F1=(2*prec*rec)/(prec+rec)\n",
    "        if F1>bestF1:\n",
    "            bestF1=F1\n",
    "            bestEpsilon=epsilon\n",
    "    return (bestEpsilon,bestF1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": false
   },
   "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": [
    "# Using sample mean and std. to compute density probability for cross validation set\n",
    "pval=mutlivariateGaussian(Xval,mu,sigma)\n",
    "# Calculating the threshold based on the best F1 Score\n",
    "epsilon,f1=selectThreshold(yval,pval)\n",
    "# Getting indices for anomalous examples\n",
    "indices=np.where((p<epsilon)==True)[0]\n",
    "# Plotting anomalies\n",
    "title=f'Threshold : {epsilon:.5f} & F1 Score : {f1:.2f}'\n",
    "plotGaussianContour(X,mu,sigma,title=title)\n",
    "sns.scatterplot(X[indices,0],X[indices,1],marker='o',facecolors='none',edgecolor='r',label='Anomalies');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.4&nbsp;&nbsp;&nbsp;&nbsp;High Dimensional Dataset\n",
    "In this dataset, each example is described by 11 features, caputring many more properties of our compute servers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "__header__\n",
      "__version__\n",
      "__globals__\n",
      "X\n",
      "Xval\n",
      "yval\n"
     ]
    }
   ],
   "source": [
    "# Loading dataset\n",
    "mat=loadmat('ex8data2.mat')\n",
    "X=mat['X']\n",
    "print(*mat.keys(),sep='\\n')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>10</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>556</th>\n",
       "      <td>5.910590</td>\n",
       "      <td>-12.615204</td>\n",
       "      <td>2.676946</td>\n",
       "      <td>-11.324394</td>\n",
       "      <td>-10.272347</td>\n",
       "      <td>13.754559</td>\n",
       "      <td>4.554619</td>\n",
       "      <td>16.681212</td>\n",
       "      <td>-10.842368</td>\n",
       "      <td>1.174451</td>\n",
       "      <td>-1.089831</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>248</th>\n",
       "      <td>-2.285877</td>\n",
       "      <td>6.038106</td>\n",
       "      <td>17.318113</td>\n",
       "      <td>-16.839057</td>\n",
       "      <td>-10.467959</td>\n",
       "      <td>7.506228</td>\n",
       "      <td>-6.796361</td>\n",
       "      <td>10.779354</td>\n",
       "      <td>-3.068714</td>\n",
       "      <td>17.908079</td>\n",
       "      <td>2.206354</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>123</th>\n",
       "      <td>4.563001</td>\n",
       "      <td>-8.496912</td>\n",
       "      <td>15.619104</td>\n",
       "      <td>-14.768893</td>\n",
       "      <td>-11.961261</td>\n",
       "      <td>14.880552</td>\n",
       "      <td>2.513666</td>\n",
       "      <td>10.198711</td>\n",
       "      <td>-9.767350</td>\n",
       "      <td>-18.314827</td>\n",
       "      <td>5.113531</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>422</th>\n",
       "      <td>7.621583</td>\n",
       "      <td>-12.535020</td>\n",
       "      <td>2.151187</td>\n",
       "      <td>-19.608959</td>\n",
       "      <td>-13.361148</td>\n",
       "      <td>22.217723</td>\n",
       "      <td>-10.183170</td>\n",
       "      <td>-9.384710</td>\n",
       "      <td>-12.871305</td>\n",
       "      <td>7.268207</td>\n",
       "      <td>6.562899</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>924</th>\n",
       "      <td>-4.552759</td>\n",
       "      <td>-1.874163</td>\n",
       "      <td>16.899972</td>\n",
       "      <td>-21.780599</td>\n",
       "      <td>-3.100516</td>\n",
       "      <td>12.718703</td>\n",
       "      <td>-0.094860</td>\n",
       "      <td>4.773496</td>\n",
       "      <td>0.160380</td>\n",
       "      <td>-0.360359</td>\n",
       "      <td>7.040524</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           0          1          2          3          4          5   \\\n",
       "556  5.910590 -12.615204   2.676946 -11.324394 -10.272347  13.754559   \n",
       "248 -2.285877   6.038106  17.318113 -16.839057 -10.467959   7.506228   \n",
       "123  4.563001  -8.496912  15.619104 -14.768893 -11.961261  14.880552   \n",
       "422  7.621583 -12.535020   2.151187 -19.608959 -13.361148  22.217723   \n",
       "924 -4.552759  -1.874163  16.899972 -21.780599  -3.100516  12.718703   \n",
       "\n",
       "            6          7          8          9         10  \n",
       "556   4.554619  16.681212 -10.842368   1.174451 -1.089831  \n",
       "248  -6.796361  10.779354  -3.068714  17.908079  2.206354  \n",
       "123   2.513666  10.198711  -9.767350 -18.314827  5.113531  \n",
       "422 -10.183170  -9.384710 -12.871305   7.268207  6.562899  \n",
       "924  -0.094860   4.773496   0.160380  -0.360359  7.040524  "
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(X).sample(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Principal Component Analysis (Optional)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "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": [
    "# Centering and scaling the data matrix\n",
    "xPCA=(X-X.mean(axis=0))/X.std(axis=0)\n",
    "# Computing Covariance\n",
    "C=np.cov(xPCA.T)\n",
    "# Computing eigenvalues and eigenvectors\n",
    "eigenValues,eigenVectors=np.linalg.eig(C)\n",
    "# Sorting eigenvalues in descending order\n",
    "idx=eigenValues.argsort()[::-1]\n",
    "eigenValues=eigenValues[idx]\n",
    "eigenVectors=eigenVectors[idx]\n",
    "\n",
    "# Plotting elbow curve\n",
    "chart=sns.lineplot(list(range(len(eigenValues))),np.cumsum(eigenValues));\n",
    "chart.set(xlabel='Eigen Values',ylabel='Cumulative sum');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looking at the graph above, we can conclude that most of the singular values matter for this dataset.\n",
    "\n",
    "#### Finding Anomalies"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Computing Gaussian Parameters\n",
    "mu,sigma=estimateGaussian(X)\n",
    "p=mutlivariateGaussian(X,mu,sigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epsilon : 1.3786074982000233e-18\n",
      "F1 Score : 0.6153846153846154\n"
     ]
    }
   ],
   "source": [
    "# Using Cross Validation set to select a threshold\n",
    "Xval=mat['Xval']\n",
    "yval=mat['yval']\n",
    "# Computing density probability\n",
    "pval=mutlivariateGaussian(Xval,mu,sigma)\n",
    "epsilon,f1=selectThreshold(yval,pval)\n",
    "print(f'Epsilon : {epsilon}')\n",
    "print(f'F1 Score : {f1}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Found 117 Anomalies**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "\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>0</th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>10</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>15.107877</td>\n",
       "      <td>-16.430766</td>\n",
       "      <td>19.707360</td>\n",
       "      <td>-19.811888</td>\n",
       "      <td>-1.644537</td>\n",
       "      <td>-6.444184</td>\n",
       "      <td>-6.121214</td>\n",
       "      <td>7.042283</td>\n",
       "      <td>7.232476</td>\n",
       "      <td>17.223479</td>\n",
       "      <td>-2.956852</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>12.411706</td>\n",
       "      <td>3.150959</td>\n",
       "      <td>14.827734</td>\n",
       "      <td>-10.482672</td>\n",
       "      <td>-8.250082</td>\n",
       "      <td>-7.982698</td>\n",
       "      <td>-20.766918</td>\n",
       "      <td>30.689476</td>\n",
       "      <td>4.622547</td>\n",
       "      <td>12.234751</td>\n",
       "      <td>23.167294</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>20.946754</td>\n",
       "      <td>1.048170</td>\n",
       "      <td>8.296324</td>\n",
       "      <td>-2.595042</td>\n",
       "      <td>-14.061970</td>\n",
       "      <td>8.776611</td>\n",
       "      <td>-21.886068</td>\n",
       "      <td>9.769264</td>\n",
       "      <td>-20.071130</td>\n",
       "      <td>13.871906</td>\n",
       "      <td>4.197881</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>5.127033</td>\n",
       "      <td>-18.517137</td>\n",
       "      <td>11.422480</td>\n",
       "      <td>-28.993408</td>\n",
       "      <td>-5.797960</td>\n",
       "      <td>-15.989215</td>\n",
       "      <td>-12.039753</td>\n",
       "      <td>31.296681</td>\n",
       "      <td>8.203208</td>\n",
       "      <td>8.035668</td>\n",
       "      <td>19.519680</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>11.622006</td>\n",
       "      <td>-0.229723</td>\n",
       "      <td>10.005823</td>\n",
       "      <td>-9.700729</td>\n",
       "      <td>-14.765493</td>\n",
       "      <td>26.933578</td>\n",
       "      <td>-9.299882</td>\n",
       "      <td>13.109171</td>\n",
       "      <td>8.976218</td>\n",
       "      <td>8.157170</td>\n",
       "      <td>18.663064</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>112</th>\n",
       "      <td>-7.514689</td>\n",
       "      <td>-11.633082</td>\n",
       "      <td>12.714199</td>\n",
       "      <td>-9.659930</td>\n",
       "      <td>-20.170026</td>\n",
       "      <td>46.574569</td>\n",
       "      <td>-10.498804</td>\n",
       "      <td>20.522685</td>\n",
       "      <td>-1.223742</td>\n",
       "      <td>4.478910</td>\n",
       "      <td>-0.186369</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>113</th>\n",
       "      <td>8.610956</td>\n",
       "      <td>-2.087595</td>\n",
       "      <td>13.609762</td>\n",
       "      <td>-5.509457</td>\n",
       "      <td>4.565548</td>\n",
       "      <td>-2.150133</td>\n",
       "      <td>6.652794</td>\n",
       "      <td>6.604923</td>\n",
       "      <td>-0.554557</td>\n",
       "      <td>-21.551409</td>\n",
       "      <td>5.522046</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>114</th>\n",
       "      <td>4.712890</td>\n",
       "      <td>-5.468014</td>\n",
       "      <td>7.463785</td>\n",
       "      <td>15.156009</td>\n",
       "      <td>-4.815854</td>\n",
       "      <td>-10.092629</td>\n",
       "      <td>3.830391</td>\n",
       "      <td>-0.360002</td>\n",
       "      <td>-11.221351</td>\n",
       "      <td>-3.262486</td>\n",
       "      <td>1.591322</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>115</th>\n",
       "      <td>-12.120077</td>\n",
       "      <td>-5.845913</td>\n",
       "      <td>28.951978</td>\n",
       "      <td>-10.215184</td>\n",
       "      <td>-18.070297</td>\n",
       "      <td>15.439734</td>\n",
       "      <td>-4.961338</td>\n",
       "      <td>31.429439</td>\n",
       "      <td>-7.406423</td>\n",
       "      <td>5.847000</td>\n",
       "      <td>20.797016</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>116</th>\n",
       "      <td>3.059507</td>\n",
       "      <td>-5.926298</td>\n",
       "      <td>31.837423</td>\n",
       "      <td>0.245340</td>\n",
       "      <td>10.050776</td>\n",
       "      <td>-1.997428</td>\n",
       "      <td>2.059449</td>\n",
       "      <td>12.571624</td>\n",
       "      <td>4.110159</td>\n",
       "      <td>14.815644</td>\n",
       "      <td>9.035330</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>117 rows × 11 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            0          1          2          3          4          5   \\\n",
       "0    15.107877 -16.430766  19.707360 -19.811888  -1.644537  -6.444184   \n",
       "1    12.411706   3.150959  14.827734 -10.482672  -8.250082  -7.982698   \n",
       "2    20.946754   1.048170   8.296324  -2.595042 -14.061970   8.776611   \n",
       "3     5.127033 -18.517137  11.422480 -28.993408  -5.797960 -15.989215   \n",
       "4    11.622006  -0.229723  10.005823  -9.700729 -14.765493  26.933578   \n",
       "..         ...        ...        ...        ...        ...        ...   \n",
       "112  -7.514689 -11.633082  12.714199  -9.659930 -20.170026  46.574569   \n",
       "113   8.610956  -2.087595  13.609762  -5.509457   4.565548  -2.150133   \n",
       "114   4.712890  -5.468014   7.463785  15.156009  -4.815854 -10.092629   \n",
       "115 -12.120077  -5.845913  28.951978 -10.215184 -18.070297  15.439734   \n",
       "116   3.059507  -5.926298  31.837423   0.245340  10.050776  -1.997428   \n",
       "\n",
       "            6          7          8          9          10  \n",
       "0    -6.121214   7.042283   7.232476  17.223479  -2.956852  \n",
       "1   -20.766918  30.689476   4.622547  12.234751  23.167294  \n",
       "2   -21.886068   9.769264 -20.071130  13.871906   4.197881  \n",
       "3   -12.039753  31.296681   8.203208   8.035668  19.519680  \n",
       "4    -9.299882  13.109171   8.976218   8.157170  18.663064  \n",
       "..         ...        ...        ...        ...        ...  \n",
       "112 -10.498804  20.522685  -1.223742   4.478910  -0.186369  \n",
       "113   6.652794   6.604923  -0.554557 -21.551409   5.522046  \n",
       "114   3.830391  -0.360002 -11.221351  -3.262486   1.591322  \n",
       "115  -4.961338  31.429439  -7.406423   5.847000  20.797016  \n",
       "116   2.059449  12.571624   4.110159  14.815644   9.035330  \n",
       "\n",
       "[117 rows x 11 columns]"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "indices=np.where((p<epsilon)==True)[0]\n",
    "pd.DataFrame(X[indices])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2&nbsp;&nbsp;&nbsp;&nbsp;Recommender Systems\n",
    "\n",
    "#### Problem Statement\n",
    "In this part of the exercise ,we will implement the Collaborative Filtering learnign algorithm and apply it to a dataset of movie ratings. This dataset consists of ratings on a scale of 1 to 5. This dataset has $n_u=943$ users, amd $n_m=1682$ movies. We will first write a cost function that computes the collaborative filtering objective function and gradient. After implmenting that, we will use gradient descent to learn the parameters for collaborative filtering.  \n",
    "**The objective of collaborative filtering is to predict movie ratings for that movies that users have not yet rated.**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.1&nbsp;&nbsp;&nbsp;&nbsp;Movie ratings dataset\n",
    "The matrix $Y$ (num_movies X num_users) stores the ratings $y^{(i,j)}$ from 1 to 5. The matrix $R$ is an binary valued indicator matrix where $R(i,j)=1$ if user j gave a rating to movie i, and $R(i,j)=0$ otherwise."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.2&nbsp;&nbsp;&nbsp;&nbsp;Collaborative filtering learning algorithm\n",
    "The collaborative filtering algorithm in the setting of movie recommendation 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 $y^{(i,j)}=(\\theta^{(j)})^Tx^{(i)}$. Given a dataset that consists of a set of ratings produced by some users on some movies, we wish to learn the parameter vectors that produce the best fit."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 2.2.1/2.2.3&nbsp;&nbsp;&nbsp;&nbsp;Collaborative filtering cost function/Regularized cost function\n",
    "Given $x^{(1)},...,x^{(n_m)}$, estimate $\\theta^{(1)},...,\\theta^{(n_u)}$ : \n",
    "$$\\min_{\\theta^{(1)},...,\\theta^{(n_u)}} \\frac{1}{2}\\sum_{j=1}^{n_u}\\sum_{i:r(i,j)=1}((\\theta^{(j)})^Tx^{(i)}-y^{(i,j)})^2+\\frac{\\lambda}{2}\\sum_{j=1}^{n_u}\\sum_{k=1}^n(\\theta_k^{(j)})^2$$\n",
    "\n",
    "\n",
    "Given $\\theta^{(1)},...,\\theta^{(n_u)}$, estimate $x^{(1)},...,x^{(n_m)}$ : \n",
    "$$\\min_{x^{(1)},...,x^{(n_m)}}  \\frac{1}{2}\\sum_{i=1}^{n_m}\\sum_{j:r(i,j)=1}((\\theta^{(j)})^Tx^{(i)}-y^{(i,j)})^2+\\frac{\\lambda}{2}\\sum_{i=1}^{n_m}\\sum_{k=1}^n(x_k^{(i)})^2$$\n",
    "\n",
    "\n",
    "Minimizing $x^{(1)},...,x^{(n_m)}$ and $\\theta^{(1)},...,\\theta^{(n_u)}$ simultaneously:\n",
    "\n",
    "$$\\boxed{J(x^{(1)},...,x^{(n_m)},\\theta^{(1)},...,\\theta^{(n_u)})=\\frac{1}{2}\\sum_{(i,j):r(i,j)=1}((\\theta^{(j)})^Tx^{(i)}-y^{(i,j)})^2+\\frac{\\lambda}{2}\\sum_{i=1}^{n_m}\\sum_{k=1}^n(x_k^{(i)})^2+\\frac{\\lambda}{2}\\sum_{j=1}^{n_u}\\sum_{k=1}^n(\\theta_k^{(j)})^2}$$\n",
    "\n",
    "$$\\min J(x^{(1)},...,x^{(n_m)},\\theta^{(1)},...,\\theta^{(n_u)})$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### 2.2.2/2.2.4&nbsp;&nbsp;&nbsp;&nbsp;Collaborative filtering gradient/Regularized Gradient\n",
    "$\\frac{\\partial{J}}{\\partial{x_k^{(i)}}}=\\sum_{j:r(i,j)=1}((\\theta^{(j)})^Tx^{(i)}-y^{(i,j)})\\theta_k^{(j)}+\\lambda x_k^{(j)}$\n",
    "\n",
    "$x_k^{(i)}:x_k^{(i)}-\\alpha\\frac{\\partial{J}}{\\partial{x_k^{(i)}}}$\n",
    "\n",
    "$$\\boxed{x_k^{(i)}:x_k^{(i)}-\\alpha[\\sum_{j:r(i,j)=1}((\\theta^{(j)})^Tx^{(i)}-y^{(i,j)})\\theta_k^{(j)}+\\lambda x_k^{(i)}]}$$\n",
    "\n",
    "$\\frac{\\partial{J}}{\\partial{\\theta_k^{(j)}}}=\\sum_{i:r(i,j)=1}((\\theta^{(j)})^Tx^{(i)}-y^{(i,j)})x_k^{(i)}+\\lambda \\theta_k^{(j)}$\n",
    "\n",
    "$\\theta_k^{(i)}:\\theta_k^{(i)}-\\alpha\\frac{\\partial{J}}{\\partial{\\theta_k^{(j)}}}$\n",
    "\n",
    "$$\\boxed{\\theta_k^{(i)}:\\theta_k^{(i)}-\\alpha[\\sum_{i:r(i,j)=1}((\\theta^{(j)})^Tx^{(i)}-y^{(i,j)})x_k^{(i)}+\\lambda \\theta_k^{(j)}]}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def costFunction(params,Y,R,numUsers,numMovies,numFeatures,lmbda):\n",
    "    # Unrolling Parameters\n",
    "    Y=Y[:numMovies,:numUsers]\n",
    "    R=R[:numMovies,:numUsers]\n",
    "    params=params.reshape(-1)\n",
    "    X=params[:numMovies*numFeatures].reshape((numMovies,numFeatures))\n",
    "    theta=params[numMovies*numFeatures:].reshape((numUsers,numFeatures))\n",
    "    # Computing Cost\n",
    "    H=np.dot(X,theta.T)\n",
    "    J=(1/2)*np.power(np.multiply(R,H-Y),2).sum()\n",
    "    Jreg=(lmbda/2)*(np.power(X,2).sum()+np.power(theta,2).sum())\n",
    "    J=J+Jreg\n",
    "    # Computing Gradient\n",
    "    xGrad=np.dot(np.multiply(R,H-Y),theta)+lmbda*X\n",
    "    thetaGrad=np.dot(np.multiply(R,H-Y).T,X)+lmbda*theta\n",
    "    # Rolling into one variable\n",
    "    params=np.row_stack((xGrad.reshape((-1,1)),thetaGrad.reshape((-1,1))))\n",
    "    return (J,params)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "def regularizedGradientDescent(initialParams,Y,R,numUsers,numMovies,numFeatures,lmbda,alpha,iterations):\n",
    "    jHistory=[]\n",
    "    params=initialParams\n",
    "    print('Training Collaborative Filtering...')\n",
    "    for i in range(iterations):\n",
    "        # Computing cost\n",
    "        J,grad=costFunction(params,Y,R,numUsers,numMovies,numFeatures,lmbda)\n",
    "        jHistory.append(J)\n",
    "        print(f'ITERATIONS : {i+1}\\t\\tCOST : {J:.3f}',end='\\r')\n",
    "        # Parameters update rule\n",
    "        params=params-alpha*grad\n",
    "    df=pd.DataFrame({'Iterations':range(iterations),'Cost Function':jHistory})\n",
    "    sns.lineplot(data=df,x='Iterations',y='Cost Function');\n",
    "    return jHistory,params"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Let's check our gradient from 'costFunction' function by computing the gradient using two point slope equation.**\n",
    "[(Gradient Checking)](https://nbviewer.jupyter.org/github/rj425/ML-Coursera/blob/master/Exercise-4/ex4.ipynb)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "DIFFERENCE : 3.3793260978461595e-12\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>grad (derivative)</th>\n",
       "      <th>grad (numerical)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.799152</td>\n",
       "      <td>-0.799152</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2.447135</td>\n",
       "      <td>2.447135</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.731511</td>\n",
       "      <td>1.731511</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-1.588831</td>\n",
       "      <td>-1.588831</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1.409539</td>\n",
       "      <td>1.409539</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1.363251</td>\n",
       "      <td>1.363251</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.131661</td>\n",
       "      <td>0.131661</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>-2.493433</td>\n",
       "      <td>-2.493433</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>-0.038054</td>\n",
       "      <td>-0.038054</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>-1.186713</td>\n",
       "      <td>-1.186713</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1.332124</td>\n",
       "      <td>1.332124</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>1.143974</td>\n",
       "      <td>1.143974</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1.463751</td>\n",
       "      <td>1.463751</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0.059482</td>\n",
       "      <td>0.059482</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>1.486766</td>\n",
       "      <td>1.486766</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>1.223998</td>\n",
       "      <td>1.223998</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>-0.008117</td>\n",
       "      <td>-0.008117</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>-1.523675</td>\n",
       "      <td>-1.523675</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>-2.188810</td>\n",
       "      <td>-2.188810</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>-0.475980</td>\n",
       "      <td>-0.475980</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>-0.596166</td>\n",
       "      <td>-0.596166</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>-0.624319</td>\n",
       "      <td>-0.624319</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>1.188126</td>\n",
       "      <td>1.188126</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>1.902472</td>\n",
       "      <td>1.902472</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>0.288833</td>\n",
       "      <td>0.288833</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>-0.112661</td>\n",
       "      <td>-0.112661</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>0.701419</td>\n",
       "      <td>0.701419</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    grad (derivative)  grad (numerical)\n",
       "0           -0.799152         -0.799152\n",
       "1            2.447135          2.447135\n",
       "2            1.731511          1.731511\n",
       "3           -1.588831         -1.588831\n",
       "4            1.409539          1.409539\n",
       "5            1.363251          1.363251\n",
       "6            0.131661          0.131661\n",
       "7           -2.493433         -2.493433\n",
       "8           -0.038054         -0.038054\n",
       "9           -1.186713         -1.186713\n",
       "10           1.332124          1.332124\n",
       "11           1.143974          1.143974\n",
       "12           1.463751          1.463751\n",
       "13           0.059482          0.059482\n",
       "14           1.486766          1.486766\n",
       "15           1.223998          1.223998\n",
       "16          -0.008117         -0.008117\n",
       "17          -1.523675         -1.523675\n",
       "18          -2.188810         -2.188810\n",
       "19          -0.475980         -0.475980\n",
       "20          -0.596166         -0.596166\n",
       "21          -0.624319         -0.624319\n",
       "22           1.188126          1.188126\n",
       "23           1.902472          1.902472\n",
       "24           0.288833          0.288833\n",
       "25          -0.112661         -0.112661\n",
       "26           0.701419          0.701419"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def computeNumericalGradient(J,theta):\n",
    "    '''Computes the numerical gradient using two point slope equation'''\n",
    "    numGrad=np.zeros(theta.shape)\n",
    "    perturb=np.zeros(theta.shape)\n",
    "    epsilon=1e-4\n",
    "    for i in range(theta.size):\n",
    "        perturb[i,:]=epsilon\n",
    "        numGrad[i,:]=(J(theta+perturb)-J(theta-perturb))/(2*epsilon)\n",
    "        perturb[i,:]=0\n",
    "    return numGrad\n",
    "\n",
    "def checkNNGradients(lmbda):\n",
    "    # Create small problem\n",
    "    X=np.random.randn(4,3)\n",
    "    theta=np.random.randn(5,3)   \n",
    "    Y=np.dot(X,theta.T)\n",
    "    Y[np.random.rand(*Y.shape)>0.5]=0\n",
    "    R=np.zeros(Y.shape)\n",
    "    R[Y!=0]=1\n",
    "    numUsers=Y.shape[1]\n",
    "    numMovies=Y.shape[0]\n",
    "    numFeatures=theta.shape[1]\n",
    "    # Gradient from cost function derivative\n",
    "    params=np.row_stack((X.reshape((-1,1)),theta.reshape((-1,1))))\n",
    "    J,grad=costFunction(params,Y,R,numUsers,numMovies,numFeatures,lmbda)\n",
    "    # Computing numerical gradient\n",
    "    def cost(params):\n",
    "        J,grad=costFunction(params,Y,R,numUsers,numMovies,numFeatures,lmbda)\n",
    "        return J\n",
    "    numGrad=computeNumericalGradient(cost,params)\n",
    "    # Evaluating the norm of the differences between two solution\n",
    "    diff=np.linalg.norm(numGrad-grad)/np.linalg.norm(numGrad+grad)\n",
    "    return grad,numGrad,diff        \n",
    "\n",
    "lmbda=1.5\n",
    "grad,numGrad,diff=checkNNGradients(lmbda)\n",
    "print(f'DIFFERENCE : {diff}')\n",
    "pd.DataFrame(data={'grad (derivative)':grad.reshape(-1),'grad (numerical)':numGrad.reshape(-1)})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.3&nbsp;&nbsp;&nbsp;&nbsp;Learning Movie Recommendations\n",
    "Now that we have finished the collaborative filtering cost function and gradient, we can now start training our learning algorithm to make movie recommendations for ourself. Later, we will also enter our own movie preferences, so that when the algorithm runs, we can get our own movie recommendations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Y : 1682 X 943\n",
      "R : 1682 X 943\n"
     ]
    }
   ],
   "source": [
    "# Loading data\n",
    "mat=loadmat('ex8_movies.mat')\n",
    "Y=mat['Y']\n",
    "R=mat['R']\n",
    "\n",
    "numUsers=Y.shape[1]\n",
    "numMovies=Y.shape[0]\n",
    "numFeatures=10\n",
    "\n",
    "print(\"Y : {0} X {1}\".format(*Y.shape))\n",
    "print(\"R : {0} X {1}\".format(*R.shape))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Movie</th>\n",
       "      <th>Year</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ID</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1033</th>\n",
       "      <td>Homeward Bound II: Lost in San Francisco</td>\n",
       "      <td>1996</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>202</th>\n",
       "      <td>Groundhog Day</td>\n",
       "      <td>1993</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1065</th>\n",
       "      <td>Koyaanisqatsi</td>\n",
       "      <td>1983</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>533</th>\n",
       "      <td>Daytrippers, The</td>\n",
       "      <td>1996</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>503</th>\n",
       "      <td>Candidate, The</td>\n",
       "      <td>1972</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>968</th>\n",
       "      <td>Inspector General, The</td>\n",
       "      <td>1949</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1028</th>\n",
       "      <td>Grumpier Old Men</td>\n",
       "      <td>1995</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>332</th>\n",
       "      <td>Kiss the Girls</td>\n",
       "      <td>1997</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>950</th>\n",
       "      <td>Georgia</td>\n",
       "      <td>1995</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>974</th>\n",
       "      <td>Eye for an Eye</td>\n",
       "      <td>1996</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                         Movie  Year\n",
       "ID                                                  \n",
       "1033  Homeward Bound II: Lost in San Francisco  1996\n",
       "202                              Groundhog Day  1993\n",
       "1065                             Koyaanisqatsi  1983\n",
       "533                           Daytrippers, The  1996\n",
       "503                             Candidate, The  1972\n",
       "968                     Inspector General, The  1949\n",
       "1028                          Grumpier Old Men  1995\n",
       "332                             Kiss the Girls  1997\n",
       "950                                    Georgia  1995\n",
       "974                             Eye for an Eye  1996"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Loading Movies\n",
    "movies={'ID':[],'Movie':[],'Year':[]}\n",
    "with open('movie_ids.txt') as f:\n",
    "    for line in f.readlines():\n",
    "        movies['ID'].append(int(line.split()[0]))\n",
    "        movies['Movie'].append(' '.join(line.split()[1:-1]))\n",
    "        movies['Year'].append(line.split()[-1][1:-1])\n",
    "movies=pd.DataFrame(movies)\n",
    "movies=movies.set_index('ID')\n",
    "movies.sample(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Y is a 1682x943 matrix, containing ratings (1-5) of 1682 movies by 943 users"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
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       "      <th></th>\n",
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       "      <th>3</th>\n",
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       "      <th>934</th>\n",
       "      <th>935</th>\n",
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       "      <th>937</th>\n",
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       "      <th>939</th>\n",
       "      <th>940</th>\n",
       "      <th>941</th>\n",
       "      <th>942</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Movie</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
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       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Toy Story</th>\n",
       "      <td>5</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
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       "      <td>2</td>\n",
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       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GoldenEye</th>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
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       "      <td>...</td>\n",
       "      <td>4</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>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Four Rooms</th>\n",
       "      <td>4</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>4</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>Get Shorty</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>5</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>...</td>\n",
       "      <td>5</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>2</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Copycat</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 × 943 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            0    1    2    3    4    5    6    7    8    9    ...  933  934  \\\n",
       "Movie                                                         ...             \n",
       "Toy Story     5    4    0    0    4    4    0    0    0    4  ...    2    3   \n",
       "GoldenEye     3    0    0    0    3    0    0    0    0    0  ...    4    0   \n",
       "Four Rooms    4    0    0    0    0    0    0    0    0    0  ...    0    0   \n",
       "Get Shorty    3    0    0    0    0    0    5    0    0    4  ...    5    0   \n",
       "Copycat       3    0    0    0    0    0    0    0    0    0  ...    0    0   \n",
       "\n",
       "            935  936  937  938  939  940  941  942  \n",
       "Movie                                               \n",
       "Toy Story     4    0    4    0    0    5    0    0  \n",
       "GoldenEye     0    0    0    0    0    0    0    5  \n",
       "Four Rooms    4    0    0    0    0    0    0    0  \n",
       "Get Shorty    0    0    0    0    2    0    0    0  \n",
       "Copycat       0    0    0    0    0    0    0    0  \n",
       "\n",
       "[5 rows x 943 columns]"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(Y,movies['Movie']).head(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### R is a 1682x943 matrix, where R(i,j) = 1 if and only if user j gave a rating to movie i"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
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       "      <th>Toy Story</th>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
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       "      <td>1</td>\n",
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       "      <td>...</td>\n",
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       "      <td>0</td>\n",
       "      <td>1</td>\n",
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       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>GoldenEye</th>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
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       "      <td>0</td>\n",
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       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\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>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Four Rooms</th>\n",
       "      <td>1</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>1</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>Get Shorty</th>\n",
       "      <td>1</td>\n",
       "      <td>0</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>1</td>\n",
       "      <td>...</td>\n",
       "      <td>1</td>\n",
       "      <td>0</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",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Copycat</th>\n",
       "      <td>1</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 × 943 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            0    1    2    3    4    5    6    7    8    9    ...  933  934  \\\n",
       "Movie                                                         ...             \n",
       "Toy Story     1    1    0    0    1    1    0    0    0    1  ...    1    1   \n",
       "GoldenEye     1    0    0    0    1    0    0    0    0    0  ...    1    0   \n",
       "Four Rooms    1    0    0    0    0    0    0    0    0    0  ...    0    0   \n",
       "Get Shorty    1    0    0    0    0    0    1    0    0    1  ...    1    0   \n",
       "Copycat       1    0    0    0    0    0    0    0    0    0  ...    0    0   \n",
       "\n",
       "            935  936  937  938  939  940  941  942  \n",
       "Movie                                               \n",
       "Toy Story     1    0    1    0    0    1    0    0  \n",
       "GoldenEye     0    0    0    0    0    0    0    1  \n",
       "Four Rooms    1    0    0    0    0    0    0    0  \n",
       "Get Shorty    0    0    0    0    1    0    0    0  \n",
       "Copycat       0    0    0    0    0    0    0    0  \n",
       "\n",
       "[5 rows x 943 columns]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(R,movies['Movie']).head(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Visualizing the movie ratings"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "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.imshow(Y,cmap='gray')\n",
    "plt.xlabel('Users')\n",
    "plt.ylabel('Movies');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Please enter the movie ratings(1-5 or 0 if not seen): \n",
      "\n",
      "Toy Story (1995)                                  5\n",
      "Silence of the Lambs, The (1991)                  2\n",
      "Twelve Monkeys (1995)                             1\n",
      "Usual Suspects, The (1995)                        2\n",
      "Professional, The (1994)                          5\n",
      "Shawshank Redemption, The (1994)                  5\n",
      "While You Were Sleeping (1995)                    5\n",
      "Forrest Gump (1994)                               5\n",
      "Alien (1979)                                      2\n",
      "101 Dalmatians (1996)                             3\n",
      "Sphere (1998)                                     5\n"
     ]
    }
   ],
   "source": [
    "print('Please enter the movie ratings(1-5 or 0 if not seen): \\n')\n",
    "userRatings=np.zeros((numMovies,1))\n",
    "\n",
    "# Ask user ratings for set movies\n",
    "indices=[1,98,7,12,55,64,66,69,183,225,355]\n",
    "for index in indices:\n",
    "    movie=movies.loc[index]\n",
    "    try:\n",
    "        question=f\"{movie['Movie']} ({movie['Year']})\"\n",
    "        question=question.ljust(50)\n",
    "        rating=float(input(question))\n",
    "        if 1<=rating<=5:\n",
    "            userRatings[int(index)-1]=rating\n",
    "    except Exception as e:\n",
    "        break"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Adding new user ratings \n",
    "Y=np.column_stack((userRatings,Y))\n",
    "# Updating R with new user ratings\n",
    "R=np.column_stack((np.zeros(numMovies),R))\n",
    "indices=np.where(Y[:,0]!=0)[0]\n",
    "R[indices,0]=1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "scrolled": false
   },
   "outputs": [],
   "source": [
    "# Normalize Ratings\n",
    "Ymean=np.zeros((numMovies,1))\n",
    "Ynorm=np.zeros(Y.shape)\n",
    "\n",
    "for i in range(numMovies):\n",
    "    idx=np.where(R[i,:]==1)\n",
    "    Ymean[i]=Y[i,idx].mean()\n",
    "    Ynorm[i,idx]=Y[i,idx]-Ymean[i]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training Collaborative Filtering...\n",
      "ITERATIONS : 500\t\tCOST : 38953.011\r"
     ]
    },
    {
     "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": [
    "# Setting Initial Parameters\n",
    "X=np.random.randn(numMovies,numFeatures)\n",
    "theta=np.random.randn(numUsers,numFeatures)\n",
    "initialParams=np.row_stack((X.reshape((-1,1)),theta.reshape((-1,1))))\n",
    "\n",
    "# Setting Gradient descent options\n",
    "lmbda=10\n",
    "alpha=0.003\n",
    "iterations=500\n",
    "\n",
    "# Training Collaborative filtering\n",
    "jHistory,params=regularizedGradientDescent(initialParams,Ynorm,R,numUsers,numMovies,numFeatures,lmbda,alpha,iterations)\n",
    "# Unrolling the learned parameters into X and theta\n",
    "X=params[:numMovies*numFeatures].reshape((numMovies,numFeatures))\n",
    "theta=params[numMovies*numFeatures:].reshape((numUsers,numFeatures))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**After training the model, we can now make the predictions by computing the prediction matrix.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "P=np.dot(X,theta.T)\n",
    "userPrediction=P[:,0]+Ymean.reshape(-1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**For Original Ratings provided by the user :**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Movie</th>\n",
       "      <th>Year</th>\n",
       "      <th>User Ratings</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ID</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Toy Story</td>\n",
       "      <td>1995</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>Twelve Monkeys</td>\n",
       "      <td>1995</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>Usual Suspects, The</td>\n",
       "      <td>1995</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>55</th>\n",
       "      <td>Professional, The</td>\n",
       "      <td>1994</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>64</th>\n",
       "      <td>Shawshank Redemption, The</td>\n",
       "      <td>1994</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>66</th>\n",
       "      <td>While You Were Sleeping</td>\n",
       "      <td>1995</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>69</th>\n",
       "      <td>Forrest Gump</td>\n",
       "      <td>1994</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>98</th>\n",
       "      <td>Silence of the Lambs, The</td>\n",
       "      <td>1991</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>183</th>\n",
       "      <td>Alien</td>\n",
       "      <td>1979</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>225</th>\n",
       "      <td>101 Dalmatians</td>\n",
       "      <td>1996</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>355</th>\n",
       "      <td>Sphere</td>\n",
       "      <td>1998</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                         Movie  Year  User Ratings\n",
       "ID                                                \n",
       "1                    Toy Story  1995           5.0\n",
       "7               Twelve Monkeys  1995           1.0\n",
       "12         Usual Suspects, The  1995           2.0\n",
       "55           Professional, The  1994           5.0\n",
       "64   Shawshank Redemption, The  1994           5.0\n",
       "66     While You Were Sleeping  1995           5.0\n",
       "69                Forrest Gump  1994           5.0\n",
       "98   Silence of the Lambs, The  1991           2.0\n",
       "183                      Alien  1979           2.0\n",
       "225             101 Dalmatians  1996           3.0\n",
       "355                     Sphere  1998           5.0"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df=movies.copy()\n",
    "df['User Ratings']=userRatings\n",
    "df[df['User Ratings']!=0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Top 10 Recommended Movies are :**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Movie</th>\n",
       "      <th>Year</th>\n",
       "      <th>Predicted Ratings</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ID</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>814</th>\n",
       "      <td>Great Day in Harlem, A</td>\n",
       "      <td>1994</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1293</th>\n",
       "      <td>Star Kid</td>\n",
       "      <td>1997</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1536</th>\n",
       "      <td>Aiqing wansui</td>\n",
       "      <td>1994</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1653</th>\n",
       "      <td>Entertaining Angels: The Dorothy Day Story</td>\n",
       "      <td>1996</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1122</th>\n",
       "      <td>They Made Me a Criminal</td>\n",
       "      <td>1939</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1500</th>\n",
       "      <td>Santa with Muscles</td>\n",
       "      <td>1996</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1189</th>\n",
       "      <td>Prefontaine</td>\n",
       "      <td>1997</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1599</th>\n",
       "      <td>Someone Else's America</td>\n",
       "      <td>1995</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1467</th>\n",
       "      <td>Saint of Fort Washington, The</td>\n",
       "      <td>1993</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1201</th>\n",
       "      <td>Marlene Dietrich: Shadow and Light</td>\n",
       "      <td>1996</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                           Movie  Year  Predicted Ratings\n",
       "ID                                                                       \n",
       "814                       Great Day in Harlem, A  1994                5.0\n",
       "1293                                    Star Kid  1997                5.0\n",
       "1536                               Aiqing wansui  1994                5.0\n",
       "1653  Entertaining Angels: The Dorothy Day Story  1996                5.0\n",
       "1122                     They Made Me a Criminal  1939                5.0\n",
       "1500                          Santa with Muscles  1996                5.0\n",
       "1189                                 Prefontaine  1997                5.0\n",
       "1599                      Someone Else's America  1995                5.0\n",
       "1467               Saint of Fort Washington, The  1993                5.0\n",
       "1201          Marlene Dietrich: Shadow and Light  1996                5.0"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "limit=10\n",
    "df=movies.copy()\n",
    "df['Predicted Ratings']=userPrediction\n",
    "df.sort_values(by=['Predicted Ratings'],ascending=False).head(limit)"
   ]
  }
 ],
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