28-Clustering.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Clustering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "from scipy.spatial.distance import pdist, squareform\n",
    "from scipy.cluster.hierarchy import linkage\n",
    "from scipy.cluster.hierarchy import dendrogram\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib import cm\n",
    "\n",
    "from sklearn.datasets import make_blobs\n",
    "from sklearn.datasets import make_moons\n",
    "\n",
    "from sklearn.cluster import KMeans\n",
    "from sklearn.metrics import silhouette_samples\n",
    "from sklearn.cluster import AgglomerativeClustering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X, y = make_blobs(n_samples=150, \n",
    "                  n_features=2, \n",
    "                  centers=3, \n",
    "                  cluster_std=0.5, \n",
    "                  shuffle=True, \n",
    "                  random_state=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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v1yM7OxtGoxHFxcXIzs7GsGHDUFlZCbPZjF/96lew2WxYtGiR6DknT57s6lvi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\n/H8Ji0az49Px5wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10ac2cb38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[:, 0], X[:, 1], \n",
    "            c='white', marker='o', edgecolor='black', s=50)\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "km = KMeans(n_clusters=3, \n",
    "            init='random', \n",
    "            n_init=10, \n",
    "            max_iter=300,\n",
    "            tol=1e-04,\n",
    "            random_state=0)\n",
    "\n",
    "y_km = km.fit_predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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PjSbrwh/ENm3NCVPxg6awoIDd+/fzA9B1+3bqxsVbYtgzZ0y3LEbaCzeU58Hl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\nYL+fhRkAAAANSURBVIhwC4IgBBj/DykvZmD5JUnxAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e94fb00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(X[y_km == 0, 0],\n",
    "            X[y_km == 0, 1],\n",
    "            s=50, c='lightgreen',\n",
    "            marker='s', edgecolor='black',\n",
    "            label='cluster 1')\n",
    "plt.scatter(X[y_km == 1, 0],\n",
    "            X[y_km == 1, 1],\n",
    "            s=50, c='orange',\n",
    "            marker='o', edgecolor='black',\n",
    "            label='cluster 2')\n",
    "plt.scatter(X[y_km == 2, 0],\n",
    "            X[y_km == 2, 1],\n",
    "            s=50, c='lightblue',\n",
    "            marker='v', edgecolor='black',\n",
    "            label='cluster 3')\n",
    "plt.scatter(km.cluster_centers_[:, 0],\n",
    "            km.cluster_centers_[:, 1],\n",
    "            s=250, marker='*',\n",
    "            c='red', edgecolor='black',\n",
    "            label='centroids')\n",
    "plt.legend(scatterpoints=1)\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using the elbow method to find the optimal number of clusters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Distortion: 72.48\n"
     ]
    }
   ],
   "source": [
    "print('Distortion: %.2f' % km.inertia_)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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lhyOJUbXVjKqtZuLY/s8daY7M/7rsrCO+bm9vZPZ0OrvZfzA4Dp2X2T/gcWYs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\nNEN9UEjAxu8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x100ec8d30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "distortions = []\n",
    "for i in range(1, 11):\n",
    "    km = KMeans(n_clusters=i, \n",
    "                init='k-means++', \n",
    "                n_init=10, \n",
    "                max_iter=300, \n",
    "                random_state=0)\n",
    "    km.fit(X)\n",
    "    distortions.append(km.inertia_)\n",
    "plt.plot(range(1, 11), distortions, marker='o')\n",
    "plt.xlabel('Number of clusters')\n",
    "plt.ylabel('Distortion')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quantifying the quality of clustering via silhouette plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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BkJkjuwCbAT8GHglsAVwN7D5pmwOBC4EAngx8u0XZHgQ8AXg/8LaWvW/7Ag8obz+3Ze/b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\nC74k9YQFX5J64v8Bf9igwVSe2msAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10edf2198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "km = KMeans(n_clusters=3, \n",
    "            init='k-means++', \n",
    "            n_init=10, \n",
    "            max_iter=300,\n",
    "            tol=1e-04,\n",
    "            random_state=0)\n",
    "y_km = km.fit_predict(X)\n",
    "\n",
    "cluster_labels = np.unique(y_km)\n",
    "n_clusters = cluster_labels.shape[0]\n",
    "silhouette_vals = silhouette_samples(X, y_km, metric='euclidean')\n",
    "y_ax_lower, y_ax_upper = 0, 0\n",
    "yticks = []\n",
    "for i, c in enumerate(cluster_labels):\n",
    "    c_silhouette_vals = silhouette_vals[y_km == c]\n",
    "    c_silhouette_vals.sort()\n",
    "    y_ax_upper += len(c_silhouette_vals)\n",
    "    color = cm.jet(float(i) / n_clusters)\n",
    "    plt.barh(range(y_ax_lower, y_ax_upper), c_silhouette_vals, height=1.0, \n",
    "             edgecolor='none', color=color)\n",
    "\n",
    "    yticks.append((y_ax_lower + y_ax_upper) / 2.)\n",
    "    y_ax_lower += len(c_silhouette_vals)\n",
    "    \n",
    "silhouette_avg = np.mean(silhouette_vals)\n",
    "plt.axvline(silhouette_avg, color=\"red\", linestyle=\"--\") \n",
    "\n",
    "plt.yticks(yticks, cluster_labels + 1)\n",
    "plt.ylabel('Cluster')\n",
    "plt.xlabel('Silhouette coefficient')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Comparison to \"bad\" clustering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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jhg2GiyQ1FW6+GZ591rg/ahRMmwZvvGHkdH/2GQwaZJ0cPvBkQX78lcJmc7Bo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\nIYpbEAQhyhDFLQiCEGX8P8S1uPuGNswiAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e93a9b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "km = KMeans(n_clusters=2,\n",
    "            init='k-means++',\n",
    "            n_init=10,\n",
    "            max_iter=300,\n",
    "            tol=1e-04,\n",
    "            random_state=0)\n",
    "y_km = km.fit_predict(X)\n",
    "\n",
    "plt.scatter(X[y_km == 0, 0],\n",
    "            X[y_km == 0, 1],\n",
    "            s=50,\n",
    "            c='lightgreen',\n",
    "            edgecolor='black',\n",
    "            marker='s',\n",
    "            label='cluster 1')\n",
    "plt.scatter(X[y_km == 1, 0],\n",
    "            X[y_km == 1, 1],\n",
    "            s=50,\n",
    "            c='orange',\n",
    "            edgecolor='black',\n",
    "            marker='o',\n",
    "            label='cluster 2')\n",
    "\n",
    "plt.scatter(km.cluster_centers_[:, 0], km.cluster_centers_[:, 1],\n",
    "            s=250, marker='*', c='red', label='centroids')\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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dmfnjzPwd8A3g9VOe83rgK1m4GtgiIrYZdqEN6jtGmXllZv6yvHk1sN2QaxwFg/xfAngv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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10dff8b38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cluster_labelscluster_  = np.unique(y_km)\n",
    "n_clusters = cluster_labels.shape[0]\n",
    "silhouette_vals = silhouette_samples(X, y_km, metric='euclidean')\n",
    "y_ax_lower, y_ax_upper = 0, 0\n",
    "yticks = []\n",
    "for i, c in enumerate(cluster_labels):\n",
    "    c_silhouette_vals = silhouette_vals[y_km == c]\n",
    "    c_silhouette_vals.sort()\n",
    "    y_ax_upper += len(c_silhouette_vals)\n",
    "    color = cm.jet(float(i) / n_clusters)\n",
    "    plt.barh(range(y_ax_lower, y_ax_upper), c_silhouette_vals, height=1.0, \n",
    "             edgecolor='none', color=color)\n",
    "\n",
    "    yticks.append((y_ax_lower + y_ax_upper) / 2.)\n",
    "    y_ax_lower += len(c_silhouette_vals)\n",
    "    \n",
    "silhouette_avg = np.mean(silhouette_vals)\n",
    "plt.axvline(silhouette_avg, color=\"red\", linestyle=\"--\") \n",
    "\n",
    "plt.yticks(yticks, cluster_labels + 1)\n",
    "plt.ylabel('Cluster')\n",
    "plt.xlabel('Silhouette coefficient')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Organizing clusters as a hierarchical tree"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "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>X</th>\n",
       "      <th>Y</th>\n",
       "      <th>Z</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>ID_0</th>\n",
       "      <td>6.964692</td>\n",
       "      <td>2.861393</td>\n",
       "      <td>2.268515</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ID_1</th>\n",
       "      <td>5.513148</td>\n",
       "      <td>7.194690</td>\n",
       "      <td>4.231065</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ID_2</th>\n",
       "      <td>9.807642</td>\n",
       "      <td>6.848297</td>\n",
       "      <td>4.809319</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ID_3</th>\n",
       "      <td>3.921175</td>\n",
       "      <td>3.431780</td>\n",
       "      <td>7.290497</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ID_4</th>\n",
       "      <td>4.385722</td>\n",
       "      <td>0.596779</td>\n",
       "      <td>3.980443</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             X         Y         Z\n",
       "ID_0  6.964692  2.861393  2.268515\n",
       "ID_1  5.513148  7.194690  4.231065\n",
       "ID_2  9.807642  6.848297  4.809319\n",
       "ID_3  3.921175  3.431780  7.290497\n",
       "ID_4  4.385722  0.596779  3.980443"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.random.seed(123)\n",
    "\n",
    "variables = ['X', 'Y', 'Z']\n",
    "labels = ['ID_0', 'ID_1', 'ID_2', 'ID_3', 'ID_4']\n",
    "\n",
    "X = np.random.random_sample([5, 3])*10\n",
    "df = pd.DataFrame(X, columns=variables, index=labels)\n",
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Performing hierarchical clustering on a distance matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4.973534  ,  5.51665266,  5.89988504,  3.83539555,  4.34707339,\n",
       "        5.10431109,  6.69823298,  7.24426159,  8.31659367,  4.382864  ])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pdist(df, metric='euclidean')"
   ]
  },
  {
   "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>ID_0</th>\n",
       "      <th>ID_1</th>\n",
       "      <th>ID_2</th>\n",
       "      <th>ID_3</th>\n",
       "      <th>ID_4</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>ID_0</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>4.973534</td>\n",
       "      <td>5.516653</td>\n",
       "      <td>5.899885</td>\n",
       "      <td>3.835396</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ID_1</th>\n",
       "      <td>4.973534</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>4.347073</td>\n",
       "      <td>5.104311</td>\n",
       "      <td>6.698233</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ID_2</th>\n",
       "      <td>5.516653</td>\n",
       "      <td>4.347073</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>7.244262</td>\n",
       "      <td>8.316594</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ID_3</th>\n",
       "      <td>5.899885</td>\n",
       "      <td>5.104311</td>\n",
       "      <td>7.244262</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>4.382864</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ID_4</th>\n",
       "      <td>3.835396</td>\n",
       "      <td>6.698233</td>\n",
       "      <td>8.316594</td>\n",
       "      <td>4.382864</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          ID_0      ID_1      ID_2      ID_3      ID_4\n",
       "ID_0  0.000000  4.973534  5.516653  5.899885  3.835396\n",
       "ID_1  4.973534  0.000000  4.347073  5.104311  6.698233\n",
       "ID_2  5.516653  4.347073  0.000000  7.244262  8.316594\n",
       "ID_3  5.899885  5.104311  7.244262  0.000000  4.382864\n",
       "ID_4  3.835396  6.698233  8.316594  4.382864  0.000000"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "row_dist = pd.DataFrame(squareform(pdist(df, metric='euclidean')),\n",
    "                        columns=labels,\n",
    "                        index=labels)\n",
    "row_dist"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Using the preceding code, we calculated the Euclidean distance between each pair\n",
    "of sample points in our dataset based on the features X, Y, and Z. \n",
    "\n",
    "We provided the condensed distance matrix—returned by pdist—as input to the squareform\n",
    "function to create a symmetrical matrix of the pair-wise distances as shown here.\n",
    "\n",
    "#### linkage - Performs hierarchical/agglomerative clustering\n",
    "\n",
    "Next, we will apply the complete linkage agglomeration to our clusters using the\n",
    "linkage function from SciPy's cluster.hierarchy submodule, which returns a\n",
    "so-called linkage matrix.\n",
    "\n",
    "1. We can use a condensed distance matrix (upper triangular) from the pdist function as an input attribute.\n",
    "2. Alternatively, we could also provide the initial data array and use the 'euclidean' metric as a function argument in linkage. \n",
    "3. However, we should not use the squareform distance matrix that we defined earlier, since it would yield different distance values than expected.\n",
    "\n",
    "To take a closer look at the clustering results, we can turn clustering results into a pandas DataFrame.\n",
    "\n",
    "The linkage matrix consists of several rows where each row represents one merge. \n",
    "\n",
    "The first and second columns denote the most dissimilar members in each cluster, and the third row reports the distance between those members. \n",
    "\n",
    "The last column returns the count of the members in each cluster"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1. incorrect approach: Squareform distance matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/regis/miniconda3/lib/python3.6/site-packages/ipykernel_launcher.py:1: ClusterWarning: scipy.cluster: The symmetric non-negative hollow observation matrix looks suspiciously like an uncondensed distance matrix\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
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       "        text-align: right;\n",
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       "\n",
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       "    }\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>row label 1</th>\n",
       "      <th>row label 2</th>\n",
       "      <th>distance</th>\n",
       "      <th>no. of items in clust.</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>cluster 1</th>\n",
       "      <td>0.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>6.521973</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cluster 2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>6.729603</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cluster 3</th>\n",
       "      <td>3.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>8.539247</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cluster 4</th>\n",
       "      <td>6.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>12.444824</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           row label 1  row label 2   distance  no. of items in clust.\n",
       "cluster 1          0.0          4.0   6.521973                     2.0\n",
       "cluster 2          1.0          2.0   6.729603                     2.0\n",
       "cluster 3          3.0          5.0   8.539247                     3.0\n",
       "cluster 4          6.0          7.0  12.444824                     5.0"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "row_clusters = linkage(row_dist, method='complete', metric='euclidean')\n",
    "pd.DataFrame(row_clusters,\n",
    "             columns=['row label 1', 'row label 2',\n",
    "                      'distance', 'no. of items in clust.'],\n",
    "             index=['cluster %d' % (i + 1)\n",
    "                    for i in range(row_clusters.shape[0])])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2. correct approach: Condensed distance matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
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       "\n",
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       "        text-align: left;\n",
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       "\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>row label 1</th>\n",
       "      <th>row label 2</th>\n",
       "      <th>distance</th>\n",
       "      <th>no. of items in clust.</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>cluster 1</th>\n",
       "      <td>0.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>3.835396</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cluster 2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>4.347073</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cluster 3</th>\n",
       "      <td>3.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.899885</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cluster 4</th>\n",
       "      <td>6.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>8.316594</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           row label 1  row label 2  distance  no. of items in clust.\n",
       "cluster 1          0.0          4.0  3.835396                     2.0\n",
       "cluster 2          1.0          2.0  4.347073                     2.0\n",
       "cluster 3          3.0          5.0  5.899885                     3.0\n",
       "cluster 4          6.0          7.0  8.316594                     5.0"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "row_clusters = linkage(pdist(df, metric='euclidean'), method='complete')\n",
    "pd.DataFrame(row_clusters,\n",
    "             columns=['row label 1', 'row label 2',\n",
    "                      'distance', 'no. of items in clust.'],\n",
    "             index=['cluster %d' % (i + 1) \n",
    "                    for i in range(row_clusters.shape[0])])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 3. correct approach: Input sample matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "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>row label 1</th>\n",
       "      <th>row label 2</th>\n",
       "      <th>distance</th>\n",
       "      <th>no. of items in clust.</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>cluster 1</th>\n",
       "      <td>0.0</td>\n",
       "      <td>4.0</td>\n",
       "      <td>3.835396</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cluster 2</th>\n",
       "      <td>1.0</td>\n",
       "      <td>2.0</td>\n",
       "      <td>4.347073</td>\n",
       "      <td>2.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cluster 3</th>\n",
       "      <td>3.0</td>\n",
       "      <td>5.0</td>\n",
       "      <td>5.899885</td>\n",
       "      <td>3.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>cluster 4</th>\n",
       "      <td>6.0</td>\n",
       "      <td>7.0</td>\n",
       "      <td>8.316594</td>\n",
       "      <td>5.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           row label 1  row label 2  distance  no. of items in clust.\n",
       "cluster 1          0.0          4.0  3.835396                     2.0\n",
       "cluster 2          1.0          2.0  4.347073                     2.0\n",
       "cluster 3          3.0          5.0  5.899885                     3.0\n",
       "cluster 4          6.0          7.0  8.316594                     5.0"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "row_clusters = linkage(df.values, method='complete', metric='euclidean')\n",
    "pd.DataFrame(row_clusters,\n",
    "             columns=['row label 1', 'row label 2',\n",
    "                      'distance', 'no. of items in clust.'],\n",
    "             index=['cluster %d' % (i + 1)\n",
    "                    for i in range(row_clusters.shape[0])])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.        ,  4.        ,  3.83539555,  2.        ],\n",
       "       [ 1.        ,  2.        ,  4.34707339,  2.        ],\n",
       "       [ 3.        ,  5.        ,  5.89988504,  3.        ],\n",
       "       [ 6.        ,  7.        ,  8.31659367,  5.        ]])"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "row_clusters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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8xOHvJrkxycdbHUOS1F3LM/x3As9tuH9J0jo0C/yq+hBwU6v9S5LWxz58SeqJqQd+kvkk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\npJ4w8CWpJwx8SeoJA1+SesLAl6Se+P+X6WVle+wVcgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fdc4358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "row_dendr = dendrogram(row_clusters, labels=labels)\n",
    "plt.ylabel('Euclidean distance')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The branches in the resulting dendrogram are shown in different\n",
    "colors. \n",
    "\n",
    "The coloring scheme is derived from a list of Matplotlib colors that are\n",
    "cycled for the distance thresholds in the dendrogram.\n",
    "\n",
    "Such a dendrogram summarizes the different clusters that were formed during the\n",
    "agglomerative hierarchical clustering; \n",
    "\n",
    "For example, we can see that the samples ID_0 and ID_4, followed by ID_1 and ID_2, are the most similar ones based on the Euclidean distance metric."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Attaching dendrograms to a heat map\n",
    "\n",
    "In practical applications, hierarchical clustering dendrograms are often used in\n",
    "combination with a heat map, which allows us to represent the individual values in\n",
    "the sample matrix with a color code."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11000a518>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot row dendrogram\n",
    "fig = plt.figure(figsize=(8, 8), facecolor='white')\n",
    "axd = fig.add_axes([0.09, 0.1, 0.2, 0.6])\n",
    "\n",
    "# note: for matplotlib < v1.5.1, please use orientation='right'\n",
    "row_dendr = dendrogram(row_clusters, orientation='left')\n",
    "\n",
    "# reorder data with respect to clustering\n",
    "df_rowclust = df.iloc[row_dendr['leaves'][::-1]]\n",
    "\n",
    "axd.set_xticks([])\n",
    "axd.set_yticks([])\n",
    "\n",
    "# remove axes spines from dendrogram\n",
    "for i in axd.spines.values():\n",
    "    i.set_visible(False)\n",
    "\n",
    "# plot heatmap\n",
    "axm = fig.add_axes([0.23, 0.1, 0.6, 0.6])  # x-pos, y-pos, width, height\n",
    "cax = axm.matshow(df_rowclust, interpolation='nearest', cmap='hot_r')\n",
    "fig.colorbar(cax)\n",
    "axm.set_xticklabels([''] + list(df_rowclust.columns))\n",
    "axm.set_yticklabels([''] + list(df_rowclust.index))\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "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>X</th>\n",
       "      <th>Y</th>\n",
       "      <th>Z</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>ID_0</th>\n",
       "      <td>6.964692</td>\n",
       "      <td>2.861393</td>\n",
       "      <td>2.268515</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ID_1</th>\n",
       "      <td>5.513148</td>\n",
       "      <td>7.194690</td>\n",
       "      <td>4.231065</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ID_2</th>\n",
       "      <td>9.807642</td>\n",
       "      <td>6.848297</td>\n",
       "      <td>4.809319</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ID_3</th>\n",
       "      <td>3.921175</td>\n",
       "      <td>3.431780</td>\n",
       "      <td>7.290497</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>ID_4</th>\n",
       "      <td>4.385722</td>\n",
       "      <td>0.596779</td>\n",
       "      <td>3.980443</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             X         Y         Z\n",
       "ID_0  6.964692  2.861393  2.268515\n",
       "ID_1  5.513148  7.194690  4.231065\n",
       "ID_2  9.807642  6.848297  4.809319\n",
       "ID_3  3.921175  3.431780  7.290497\n",
       "ID_4  4.385722  0.596779  3.980443"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The order of rows in the heat map reflects the clustering of the\n",
    "samples in the dendrogram. \n",
    "\n",
    "In addition to a simple dendrogram, the color-coded values of each sample and feature in the heat map provide us with a nice summary of the dataset."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Applying agglomerative clustering via scikit-learn\n",
    "\n",
    "There is also an AgglomerativeClustering implementation in scikit-learn, which allows us to choose the number of clusters that\n",
    "we want to return. This is useful if we want to prune the hierarchical cluster tree.\n",
    "\n",
    "By setting the n_cluster parameter to 3, we will now cluster the samples into three\n",
    "groups using the same complete linkage approach based on the Euclidean distance\n",
    "metric, as before."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cluster labels: [1 0 0 2 1]\n"
     ]
    }
   ],
   "source": [
    "ac = AgglomerativeClustering(n_clusters=3, \n",
    "                             affinity='euclidean', \n",
    "                             linkage='complete')\n",
    "labels = ac.fit_predict(X)\n",
    "print('Cluster labels: %s' % labels)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Looking at the predicted cluster labels, we can see that the first and the fifth sample\n",
    "(ID_0 and ID_4) were assigned to one cluster (label 1), and the samples ID_1 and\n",
    "ID_2 were assigned to a second cluster (label 0). \n",
    "\n",
    "The sample ID_3 was put into its own cluster (label 2). \n",
    "\n",
    "Overall, the results are consistent with the results that we observed in the dendrogram. We shall note though that ID_3 is more similar to ID_4 and ID_0 than to ID_1 and ID_2, as shown in the preceding dendrogram\n",
    "figure; this is not clear from scikit-learn's clustering results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Cluster labels: [0 1 1 0 0]\n"
     ]
    }
   ],
   "source": [
    "ac = AgglomerativeClustering(n_clusters=2, \n",
    "                             affinity='euclidean', \n",
    "                             linkage='complete')\n",
    "labels = ac.fit_predict(X)\n",
    "print('Cluster labels: %s' % labels)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In this pruned clustering hierarchy, label ID_3 was not assigned to the\n",
    "same cluster as ID_0 and ID_4, as expected."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Locating regions of high density via DBSCAN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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fvK2E+efOze3igoKBFIKgrof3f/cgVU4FIqqK0bQTPTldxb77PhhLH9OA7qqk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\nf4wZ5gKMhU2PAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x111f06208>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X, y = make_moons(n_samples=200, noise=0.05, random_state=0)\n",
    "plt.scatter(X[:, 0], X[:, 1])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### K-means and hierarchical clustering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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jyPbcnGwCagQya8zgwtGgnhrHdbfdSXBQMN2vv45mrduR/Nkmktd8x0trf+DE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\n3tPrAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10edfdd68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "f, (ax1, ax2) = plt.subplots(1, 2, figsize=(8, 3))\n",
    "\n",
    "km = KMeans(n_clusters=2, random_state=0)\n",
    "y_km = km.fit_predict(X)\n",
    "ax1.scatter(X[y_km == 0, 0], X[y_km == 0, 1],\n",
    "            edgecolor='black',\n",
    "            c='lightblue', marker='o', s=40, label='cluster 1')\n",
    "ax1.scatter(X[y_km == 1, 0], X[y_km == 1, 1],\n",
    "            edgecolor='black',\n",
    "            c='red', marker='s', s=40, label='cluster 2')\n",
    "ax1.set_title('K-means clustering')\n",
    "\n",
    "ac = AgglomerativeClustering(n_clusters=2,\n",
    "                             affinity='euclidean',\n",
    "                             linkage='complete')\n",
    "y_ac = ac.fit_predict(X)\n",
    "ax2.scatter(X[y_ac == 0, 0], X[y_ac == 0, 1], c='lightblue',\n",
    "            edgecolor='black',\n",
    "            marker='o', s=40, label='cluster 1')\n",
    "ax2.scatter(X[y_ac == 1, 0], X[y_ac == 1, 1], c='red',\n",
    "            edgecolor='black',\n",
    "            marker='s', s=40, label='cluster 2')\n",
    "ax2.set_title('Agglomerative clustering')\n",
    "\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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IXRDCBJ+okohoMBEdIaJjROTkc0lE/YjoMhHts05P6V03FFDGIFyzWLB+0VyM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\nsEMEgyAIgmCHCAZBEATBjv8P4gBqFrHtOqkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10fcfa358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.cluster import DBSCAN\n",
    "\n",
    "db = DBSCAN(eps=0.2, min_samples=5, metric='euclidean')\n",
    "y_db = db.fit_predict(X)\n",
    "plt.scatter(X[y_db == 0, 0], X[y_db == 0, 1],\n",
    "            c='lightblue', marker='o', s=40,\n",
    "            edgecolor='black', \n",
    "            label='cluster 1')\n",
    "plt.scatter(X[y_db == 1, 0], X[y_db == 1, 1],\n",
    "            c='red', marker='s', s=40,\n",
    "            edgecolor='black', \n",
    "            label='cluster 2')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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