Scikit - 08 Clustering.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "\n",
    "\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.datasets import make_blobs\n",
    "from sklearn.cluster import KMeans\n",
    "from sklearn.cluster import DBSCAN\n",
    "from sklearn.metrics import homogeneity_score\n",
    "\n",
    "from scipy.cluster.hierarchy import linkage, dendrogram\n",
    "\n",
    "np.set_printoptions(suppress=True, precision=5)\n",
    "\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, y = make_blobs(n_samples = 150, n_features=2, \n",
    "                  centers=3, cluster_std=0.5, shuffle=True, random_state=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x11fe4c358>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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tAEqj5FIK586f7EI2X7C9r9f1Il5SQGYlj1aC2l6x2lYTUW0XypQOUUKZtQMw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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11caae7b8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:, 0], X[:, 1], c = \"steelblue\", marker = \"o\", s = 50)\n",
    "plt.xlabel(\"X1\")\n",
    "plt.ylabel(\"X2\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "km = KMeans(n_clusters=3, init=\"random\", n_init = 10, \n",
    "            max_iter = 300, tol = 1e-04, random_state=0)\n",
    "y_km = km.fit_predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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": [
    "def show_cluster(X, y, estimator = None, ignore_noise = True):\n",
    "    levels = set(y)\n",
    "    \n",
    "    if ignore_noise and -1 in levels:\n",
    "        levels.remove(-1)\n",
    "    \n",
    "    colors = sns.color_palette(\"husl\", len(levels))\n",
    "    centroids = None \n",
    "    if estimator is not None and hasattr(estimator, \"cluster_centers_\"):\n",
    "        centroids = estimator.cluster_centers_  \n",
    "\n",
    "    for k in levels:\n",
    "        data = X[y == k, :]\n",
    "        plt.scatter(data[:, 0], data[:, 1], color = colors[k], s = 50, label = \"Cluster %s\" % k)\n",
    "\n",
    "    if not centroids is None:\n",
    "        plt.scatter(centroids[:, 0], centroids[:, 1], color = \"black\", marker = \"*\", s = 150)\n",
    "\n",
    "    plt.xlabel(\"X1\")\n",
    "    plt.ylabel(\"X2\")\n",
    "    plt.legend(loc = \"lower left\")\n",
    "    \n",
    "show_cluster(X, y_km, km)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.91564,  4.44603],\n",
       "       [-1.73388,  3.00577],\n",
       "       [ 2.07418,  1.04097]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "km.cluster_centers_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Distortion (Within Cluster SSE): 262.72\n"
     ]
    }
   ],
   "source": [
    "#Sum of distances of samples to their closest cluster center.\n",
    "print(\"Distortion (Within Cluster SSE): %.2f\" % km.inertia_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6812190697089529"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Sum of distances of samples to their closest cluster center.\n",
    "homogeneity_score(y, y_km)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Homogeneity score:  0.6812190697089529 Inertia:  262.72046565264066\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Estimated clusters')"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "X, y = make_blobs(n_samples = 150, n_features=2, centers=3, \n",
    "                  cluster_std=1.0, shuffle=True, random_state=0)\n",
    "km = KMeans(n_clusters=3, init=\"random\", n_init = 10, \n",
    "            max_iter = 300, tol = 1e-04, random_state=0)\n",
    "y_km = km.fit_predict(X)\n",
    "print(\"Homogeneity score: \", homogeneity_score(y, y_km), \"Inertia: \", km.inertia_)\n",
    "plt.figure(figsize=(10, 5))\n",
    "plt.subplot(1, 2, 1)\n",
    "show_cluster(X, y, km)\n",
    "plt.title(\"True Clusters\")\n",
    "plt.subplot(1, 2, 2)\n",
    "show_cluster(X, y_km, km)\n",
    "plt.title(\"Estimated clusters\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Find optimal number of clusters using elbow method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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": [
    "def find_elbow(X, n = 10):\n",
    "    distortions = []\n",
    "    for i in range(1, n):\n",
    "        km = KMeans(n_clusters=i, max_iter=300, n_init=10, random_state=0, init=\"k-means++\")\n",
    "        km.fit(X)\n",
    "        distortions.append(km.inertia_)\n",
    "    plt.plot(range(1, n), distortions)\n",
    "    plt.xlabel(\"Number of clusters (K)\")\n",
    "    plt.ylabel(\"Distortion\")\n",
    "\n",
    "find_elbow(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Find number of clusters from Dendogram"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x720 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (15, 10))\n",
    "row_clusters = linkage(X, method=\"complete\", metric=\"euclidean\")\n",
    "f = dendrogram(row_clusters)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Half Moon Dataset and DBSCAN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.datasets import make_moons"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X, y = make_moons(n_samples=200, noise=0.09, random_state=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x1206b18d0>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Lq94rsEJECsDdqlq7egFARG4AbgCYMiXczR3ERjLvjCmHXODxY0ehKKs2vs32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\nAsUwDMOIhP8PY/ueej3udXUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x120f62e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:, 0], X[:, 1], c = \"steelblue\", marker = \"o\", s = 50)\n",
    "plt.xlabel(\"X1\")\n",
    "plt.ylabel(\"X2\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x121699128>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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o2lXmBcGiLA2Lsn4VqJaO+Xab2LQF+fmLEq1fQPU7ZQjRoJHZrNsBjLH9PNp6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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x11fedf8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "km = KMeans(n_clusters=2, init=\"random\", n_init = 10, max_iter = 300, tol = 1e-04, random_state=0)\n",
    "y_km = km.fit_predict(X)\n",
    "#show_cluster(km, X, y_km)\n",
    "\n",
    "plt.figure(figsize=(10, 5))\n",
    "plt.subplot(1, 2, 1)\n",
    "show_cluster(X, y)\n",
    "plt.title(\"True Clusters\")\n",
    "plt.subplot(1, 2, 2)\n",
    "show_cluster(X, y_km, km)\n",
    "plt.title(\"Estimated clusters\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.18109823201826031"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "homogeneity_score(y, y_km)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x120df4358>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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v7i0sX0Nh0xYLRlNKJ525KcDmst+3AKcGnSgi44HzgSvKblbgHhFxgetVdUGr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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1215a92e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "dbscan = DBSCAN(eps=0.2, min_samples=5, metric=\"euclidean\")\n",
    "y_db = dbscan.fit_predict(X)\n",
    "\n",
    "plt.figure(figsize=(10, 5))\n",
    "plt.subplot(1, 2, 1)\n",
    "show_cluster(X, y, dbscan)\n",
    "plt.title(\"True Clusters\")\n",
    "plt.subplot(1, 2, 2)\n",
    "show_cluster(X, y_db, dbscan)\n",
    "plt.title(\"Estimated clusters\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "No of clusters:  2\n"
     ]
    }
   ],
   "source": [
    "labels = set(y_db)\n",
    "if -1 in labels: #Noise\n",
    "    labels.remove(-1)\n",
    "print(\"No of clusters: \", len(labels))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.98377443751081795"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "homogeneity_score(y, y_db)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Applying clustering to grouplens movies dataset based on genre"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>title</th>\n",
       "      <th>genres</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>movieId</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Toy Story (1995)</td>\n",
       "      <td>Adventure|Animation|Children|Comedy|Fantasy</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Jumanji (1995)</td>\n",
       "      <td>Adventure|Children|Fantasy</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>Grumpier Old Men (1995)</td>\n",
       "      <td>Comedy|Romance</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>Waiting to Exhale (1995)</td>\n",
       "      <td>Comedy|Drama|Romance</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>Father of the Bride Part II (1995)</td>\n",
       "      <td>Comedy</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                      title  \\\n",
       "movieId                                       \n",
       "1                          Toy Story (1995)   \n",
       "2                            Jumanji (1995)   \n",
       "3                   Grumpier Old Men (1995)   \n",
       "4                  Waiting to Exhale (1995)   \n",
       "5        Father of the Bride Part II (1995)   \n",
       "\n",
       "                                              genres  \n",
       "movieId                                               \n",
       "1        Adventure|Animation|Children|Comedy|Fantasy  \n",
       "2                         Adventure|Children|Fantasy  \n",
       "3                                     Comedy|Romance  \n",
       "4                               Comedy|Drama|Romance  \n",
       "5                                             Comedy  "
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "movies = pd.read_csv(\"data/ml-latest-small/movies.csv\", index_col=\"movieId\")\n",
    "movies.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>title</th>\n",
       "      <th>genres</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>movieId</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>90376</th>\n",
       "      <td>We Need to Talk About Kevin (2011)</td>\n",
       "      <td>Drama|Thriller</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1756</th>\n",
       "      <td>Prophecy II, The (1998)</td>\n",
       "      <td>Horror</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27646</th>\n",
       "      <td>Soldier's Girl (2003)</td>\n",
       "      <td>Drama</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3571</th>\n",
       "      <td>Time Code (2000)</td>\n",
       "      <td>Comedy|Drama</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>149354</th>\n",
       "      <td>Sisters (2015)</td>\n",
       "      <td>Children|Comedy</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7369</th>\n",
       "      <td>Scooby-Doo 2: Monsters Unleashed (2004)</td>\n",
       "      <td>Action|Adventure|Children|Comedy|Mystery</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25792</th>\n",
       "      <td>I Was Born, But... (a.k.a. Children of Tokyo) ...</td>\n",
       "      <td>Comedy|Drama</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5041</th>\n",
       "      <td>Fire and Ice (1983)</td>\n",
       "      <td>Animation|Fantasy</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1897</th>\n",
       "      <td>High Art (1998)</td>\n",
       "      <td>Drama|Romance</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>73290</th>\n",
       "      <td>Hachiko: A Dog's Story (a.k.a. Hachi: A Dog's ...</td>\n",
       "      <td>Drama</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                     title  \\\n",
       "movieId                                                      \n",
       "90376                   We Need to Talk About Kevin (2011)   \n",
       "1756                               Prophecy II, The (1998)   \n",
       "27646                                Soldier's Girl (2003)   \n",
       "3571                                      Time Code (2000)   \n",
       "149354                                      Sisters (2015)   \n",
       "7369               Scooby-Doo 2: Monsters Unleashed (2004)   \n",
       "25792    I Was Born, But... (a.k.a. Children of Tokyo) ...   \n",
       "5041                                   Fire and Ice (1983)   \n",
       "1897                                       High Art (1998)   \n",
       "73290    Hachiko: A Dog's Story (a.k.a. Hachi: A Dog's ...   \n",
       "\n",
       "                                           genres  \n",
       "movieId                                            \n",
       "90376                              Drama|Thriller  \n",
       "1756                                       Horror  \n",
       "27646                                       Drama  \n",
       "3571                                 Comedy|Drama  \n",
       "149354                            Children|Comedy  \n",
       "7369     Action|Adventure|Children|Comedy|Mystery  \n",
       "25792                                Comedy|Drama  \n",
       "5041                            Animation|Fantasy  \n",
       "1897                                Drama|Romance  \n",
       "73290                                       Drama  "
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "movies.sample(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>title</th>\n",
       "      <th>genres</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>movieId</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2095</th>\n",
       "      <td>Shaggy D.A., The (1976)</td>\n",
       "      <td>Children|Comedy</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>117123</th>\n",
       "      <td>Dear White People (2014)</td>\n",
       "      <td>Comedy|Drama</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26394</th>\n",
       "      <td>Turning Point, The (1977)</td>\n",
       "      <td>Drama|Romance</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3574</th>\n",
       "      <td>Carnosaur 3: Primal Species (1996)</td>\n",
       "      <td>Horror|Sci-Fi</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1076</th>\n",
       "      <td>Innocents, The (1961)</td>\n",
       "      <td>Drama|Horror|Thriller</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5675</th>\n",
       "      <td>Swept Away (2002)</td>\n",
       "      <td>Comedy|Romance</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3117</th>\n",
       "      <td>Ride with the Devil (1999)</td>\n",
       "      <td>Drama|Romance|War</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>609</th>\n",
       "      <td>Homeward Bound II: Lost in San Francisco (1996)</td>\n",
       "      <td>Adventure|Children</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4752</th>\n",
       "      <td>Maniac (1980)</td>\n",
       "      <td>Horror</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>86781</th>\n",
       "      <td>Incendies (2010)</td>\n",
       "      <td>Drama|Mystery|War</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                   title  \\\n",
       "movieId                                                    \n",
       "2095                             Shaggy D.A., The (1976)   \n",
       "117123                          Dear White People (2014)   \n",
       "26394                          Turning Point, The (1977)   \n",
       "3574                  Carnosaur 3: Primal Species (1996)   \n",
       "1076                               Innocents, The (1961)   \n",
       "5675                                   Swept Away (2002)   \n",
       "3117                          Ride with the Devil (1999)   \n",
       "609      Homeward Bound II: Lost in San Francisco (1996)   \n",
       "4752                                       Maniac (1980)   \n",
       "86781                                   Incendies (2010)   \n",
       "\n",
       "                        genres  \n",
       "movieId                         \n",
       "2095           Children|Comedy  \n",
       "117123            Comedy|Drama  \n",
       "26394            Drama|Romance  \n",
       "3574             Horror|Sci-Fi  \n",
       "1076     Drama|Horror|Thriller  \n",
       "5675            Comedy|Romance  \n",
       "3117         Drama|Romance|War  \n",
       "609         Adventure|Children  \n",
       "4752                    Horror  \n",
       "86781        Drama|Mystery|War  "
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "movies = movies[~movies[\"genres\"].str.contains(\"\\(no genres listed\\)\")]\n",
    "movies.sample(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['Action', 'Adventure', 'Animation', 'Children', 'Comedy', 'Crime', 'Documentary', 'Drama', 'Fantasy', 'Film-Noir', 'Horror', 'IMAX', 'Musical', 'Mystery', 'Romance', 'Sci-Fi', 'Thriller', 'War', 'Western'] 19\n"
     ]
    }
   ],
   "source": [
    "genres = set()\n",
    "movies[\"genres\"].apply(lambda g: genres.update(g.split(r\"|\")))\n",
    "genres = list(genres)\n",
    "genres.sort()\n",
    "print(genres, len(genres))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "movieId\n",
       "1     [0.0, 1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 1.0, ...\n",
       "2     [0.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0, ...\n",
       "3     [0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, ...\n",
       "4     [0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 1.0, 0.0, ...\n",
       "5     [0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, ...\n",
       "6     [1.0, 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, ...\n",
       "7     [0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, ...\n",
       "8     [0.0, 1.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...\n",
       "9     [1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...\n",
       "10    [1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, ...\n",
       "Name: genres, dtype: object"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def to_vector(g):\n",
    "    indices = np.array([genres.index(v) for v in g.split(r\"|\")])\n",
    "    l = np.zeros(len(genres))\n",
    "    l[indices] = 1\n",
    "    return l\n",
    "\n",
    "genres_idx = movies[\"genres\"].apply(to_vector)\n",
    "genres_idx.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X.shape:  (9107, 19)\n"
     ]
    }
   ],
   "source": [
    "X = np.array(genres_idx.tolist())\n",
    "print(\"X.shape: \", X.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Normalize the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "scaler = StandardScaler()\n",
    "X_std = scaler.fit_transform(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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GWpLk0KHFLYfds2cp+/YtT9M0dtmWPXSllNeWUj5WSnnf2GN3KaW8vZTyF8P/Ox/jtY8r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\nOY7jOI7jOI7jdCn/B9Hpq/Z2p7xcAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x120e1ea90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (15, 10))\n",
    "row_clusters = linkage(X_std, method=\"complete\", metric=\"euclidean\")\n",
    "f = dendrogram(row_clusters, p = 5, truncate_mode=\"level\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To visualize the clusters lets apply PCA with 2 components. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn.decomposition import KernelPCA, PCA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x120e1e438>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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G8eyZtn+bpBPTsq+SdRg8U9JJzQ4yspFC/wK8GdgLuC4iLs6tvzoi+nqgTiTr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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x120f62898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pca = PCA(random_state=0)\n",
    "X_pca = pca.fit_transform(X_std)\n",
    "\n",
    "ratios = pca.explained_variance_ratio_\n",
    "plt.bar(range(len(ratios)), ratios)\n",
    "plt.step(range(len(ratios)), np.cumsum(ratios), \n",
    "         label = \"Cumsum of Explained variance ratio\")\n",
    "plt.title(\"Explained variance\")\n",
    "plt.ylabel(\"Explained Variance Ratio\")\n",
    "plt.xlabel(\"Number of PCA components\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With 2 principle components havelow explained variance coverage."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.text.Text at 0x11ff0cf28>"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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S/f4sqcv7n36l7T0T32N5TczMYXh8GptGJzE8Pu3k/ina6YM7Oj536j6wLZpu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\nH92zqmF1vG5ctQCpKpOJDtVnnOo4hSOkfeFEVcXUTSJLtukwuhYKuj1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J+ub3n9G2/feG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\nAAAAAKBjCHoAAAAA0DEEPQAAAADomP8HfwYRztiMWGIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x120ef3fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pca = PCA(random_state=0, n_components=2)\n",
    "X_pca = pca.fit_transform(X_std)\n",
    "\n",
    "plt.figure(figsize = (15, 8))\n",
    "plt.scatter(X_pca[:, 0], X_pca[:, 1])\n",
    "plt.xlabel(\"PCA1\")\n",
    "plt.ylabel(\"PCA2\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is not visual indication of clusters from 2 PCA components which is consistent with the finding that explained variance with 2 components is only 2%"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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F5VGH45xrwyJJNpJ+AFQC/xfF98fFcYWkIklFmza1zudSRvfrxAWje/OXV1aycrN3FnDO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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x120f46b00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "find_elbow(X_std, 40)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "knn = KMeans(n_clusters=8, max_iter=300, random_state=0)\n",
    "y_pred = knn.fit_predict(X_std)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For each observations, compute distance to the nearest cluster centroid. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>title</th>\n",
       "      <th>genres</th>\n",
       "      <th>distance</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>movieId</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>81132</th>\n",
       "      <td>Rubber (2010)</td>\n",
       "      <td>Action|Adventure|Comedy|Crime|Drama|Film-Noir|...</td>\n",
       "      <td>10.008449</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>81847</th>\n",
       "      <td>Tangled (2010)</td>\n",
       "      <td>Animation|Children|Comedy|Fantasy|Musical|Roma...</td>\n",
       "      <td>8.401892</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>83613</th>\n",
       "      <td>Cowboys &amp; Aliens (2011)</td>\n",
       "      <td>Action|Sci-Fi|Thriller|Western|IMAX</td>\n",
       "      <td>8.313656</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>595</th>\n",
       "      <td>Beauty and the Beast (1991)</td>\n",
       "      <td>Animation|Children|Fantasy|Musical|Romance|IMAX</td>\n",
       "      <td>8.223587</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2142</th>\n",
       "      <td>American Tail: Fievel Goes West, An (1991)</td>\n",
       "      <td>Adventure|Animation|Children|Musical|Western</td>\n",
       "      <td>8.047143</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>103384</th>\n",
       "      <td>Lone Ranger, The (2013)</td>\n",
       "      <td>Action|Adventure|Western|IMAX</td>\n",
       "      <td>7.930896</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7374</th>\n",
       "      <td>Home on the Range (2004)</td>\n",
       "      <td>Animation|Children|Comedy|Musical|Western</td>\n",
       "      <td>7.822317</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>364</th>\n",
       "      <td>Lion King, The (1994)</td>\n",
       "      <td>Adventure|Animation|Children|Drama|Musical|IMAX</td>\n",
       "      <td>7.558606</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3159</th>\n",
       "      <td>Fantasia 2000 (1999)</td>\n",
       "      <td>Animation|Children|Musical|IMAX</td>\n",
       "      <td>7.416244</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26701</th>\n",
       "      <td>Patlabor: The Movie (Kidô keisatsu patorebâ: T...</td>\n",
       "      <td>Action|Animation|Crime|Drama|Film-Noir|Mystery...</td>\n",
       "      <td>7.396372</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                     title  \\\n",
       "movieId                                                      \n",
       "81132                                        Rubber (2010)   \n",
       "81847                                       Tangled (2010)   \n",
       "83613                              Cowboys & Aliens (2011)   \n",
       "595                            Beauty and the Beast (1991)   \n",
       "2142            American Tail: Fievel Goes West, An (1991)   \n",
       "103384                             Lone Ranger, The (2013)   \n",
       "7374                              Home on the Range (2004)   \n",
       "364                                  Lion King, The (1994)   \n",
       "3159                                  Fantasia 2000 (1999)   \n",
       "26701    Patlabor: The Movie (Kidô keisatsu patorebâ: T...   \n",
       "\n",
       "                                                    genres   distance  \n",
       "movieId                                                                \n",
       "81132    Action|Adventure|Comedy|Crime|Drama|Film-Noir|...  10.008449  \n",
       "81847    Animation|Children|Comedy|Fantasy|Musical|Roma...   8.401892  \n",
       "83613                  Action|Sci-Fi|Thriller|Western|IMAX   8.313656  \n",
       "595        Animation|Children|Fantasy|Musical|Romance|IMAX   8.223587  \n",
       "2142          Adventure|Animation|Children|Musical|Western   8.047143  \n",
       "103384                       Action|Adventure|Western|IMAX   7.930896  \n",
       "7374             Animation|Children|Comedy|Musical|Western   7.822317  \n",
       "364        Adventure|Animation|Children|Drama|Musical|IMAX   7.558606  \n",
       "3159                       Animation|Children|Musical|IMAX   7.416244  \n",
       "26701    Action|Animation|Crime|Drama|Film-Noir|Mystery...   7.396372  "
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def distance(p1, p2):\n",
    "    p1, p2 = p1.flatten(), p2.flatten()\n",
    "    return np.sqrt(np.sum((p1 - p2) ** 2))\n",
    "\n",
    "distances = []\n",
    "for i in range(X_std.shape[0]):\n",
    "    p1 = X_std[i, :]\n",
    "    cluster = knn.labels_[i]\n",
    "    center = knn.cluster_centers_[cluster]\n",
    "    distances.append(distance(p1, center))\n",
    "\n",
    "movies[\"distance\"] = np.array(distances)\n",
    "movies.sort_values(\"distance\", ascending=False)[:10]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "        text-align: right;\n",
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>title</th>\n",
       "      <th>genres</th>\n",
       "      <th>distance</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>movieId</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>101142</th>\n",
       "      <td>Croods, The (2013)</td>\n",
       "      <td>Adventure|Animation|Comedy</td>\n",
       "      <td>4.213158</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>64116</th>\n",
       "      <td>Igor (2008)</td>\n",
       "      <td>Animation|Comedy</td>\n",
       "      <td>4.432396</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>36289</th>\n",
       "      <td>Asterix &amp; Obelix vs. Caesar (Astérix et Obélix...</td>\n",
       "      <td>Adventure|Children|Comedy|Fantasy</td>\n",
       "      <td>4.241107</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>104245</th>\n",
       "      <td>Planes (2013)</td>\n",
       "      <td>Adventure|Animation|Comedy</td>\n",
       "      <td>4.213158</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>52287</th>\n",
       "      <td>Meet the Robinsons (2007)</td>\n",
       "      <td>Action|Adventure|Animation|Children|Comedy|Sci-Fi</td>\n",
       "      <td>5.185785</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2124</th>\n",
       "      <td>Addams Family, The (1991)</td>\n",
       "      <td>Children|Comedy|Fantasy</td>\n",
       "      <td>4.458971</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>392</th>\n",
       "      <td>Secret Adventures of Tom Thumb, The (1993)</td>\n",
       "      <td>Adventure|Animation</td>\n",
       "      <td>4.117683</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>86298</th>\n",
       "      <td>Rio (2011)</td>\n",
       "      <td>Adventure|Animation|Children|Comedy</td>\n",
       "      <td>3.824960</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4911</th>\n",
       "      <td>Jabberwocky (1977)</td>\n",
       "      <td>Adventure|Comedy|Fantasy</td>\n",
       "      <td>4.594276</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1033</th>\n",
       "      <td>Fox and the Hound, The (1981)</td>\n",
       "      <td>Animation|Children|Drama</td>\n",
       "      <td>4.320908</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                                                     title  \\\n",
       "movieId                                                      \n",
       "101142                                  Croods, The (2013)   \n",
       "64116                                          Igor (2008)   \n",
       "36289    Asterix & Obelix vs. Caesar (Astérix et Obélix...   \n",
       "104245                                       Planes (2013)   \n",
       "52287                            Meet the Robinsons (2007)   \n",
       "2124                             Addams Family, The (1991)   \n",
       "392             Secret Adventures of Tom Thumb, The (1993)   \n",
       "86298                                           Rio (2011)   \n",
       "4911                                    Jabberwocky (1977)   \n",
       "1033                         Fox and the Hound, The (1981)   \n",
       "\n",
       "                                                    genres  distance  \n",
       "movieId                                                               \n",
       "101142                          Adventure|Animation|Comedy  4.213158  \n",
       "64116                                     Animation|Comedy  4.432396  \n",
       "36289                    Adventure|Children|Comedy|Fantasy  4.241107  \n",
       "104245                          Adventure|Animation|Comedy  4.213158  \n",
       "52287    Action|Adventure|Animation|Children|Comedy|Sci-Fi  5.185785  \n",
       "2124                               Children|Comedy|Fantasy  4.458971  \n",
       "392                                    Adventure|Animation  4.117683  \n",
       "86298                  Adventure|Animation|Children|Comedy  3.824960  \n",
       "4911                              Adventure|Comedy|Fantasy  4.594276  \n",
       "1033                              Animation|Children|Drama  4.320908  "
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "movies[y_pred == 3].sample(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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