94-775, 95-865 Hierarchical clustering.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 94-775/95-865 Hierarchical Clustering\n",
    "Author: George H. Chen (georgechen [at symbol] cmu.edu)\n",
    "\n",
    "Part of this demo uses the [random color map code created by Felipe Delestro Matos](https://github.com/delestro/rand_cmap)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "plt.style.use('seaborn')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1138373d0>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# manually create 4 clusters\n",
    "# (note that this is actually a 4-cluster Gaussian mixture model!)\n",
    "\n",
    "np.random.seed(0)\n",
    "\n",
    "points_cluster1 = .5*np.random.randn(10, 2) + np.array([-1.5, 0])[np.newaxis, :]\n",
    "points_cluster2 = .5*np.random.randn(10, 2) + np.array([1, 0.5])[np.newaxis, :]\n",
    "points_cluster3 = .5*np.random.randn(10, 2) + np.array([-2, -2])[np.newaxis, :]\n",
    "points_cluster4 = .5*np.random.randn(10, 2) + np.array([-0.5, -2.5])[np.newaxis, :]\n",
    "\n",
    "points = np.vstack([points_cluster1,\n",
    "                    points_cluster2,\n",
    "                    points_cluster3,\n",
    "                    points_cluster4])\n",
    "\n",
    "plt.scatter(points[:, 0], points[:, 1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Divisive clustering\n",
    "\n",
    "The code below uses highest cluster RSS to decide which cluster to split next, and uses k-means (with k=2) to do the actual split. We stop the algorithm after 3 splits."
   ]
  },
  {
   "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"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.cluster import KMeans\n",
    "\n",
    "cluster_assignment = np.zeros(len(points)).astype(np.int)  # everything starts off being in cluster 0\n",
    "\n",
    "num_splits = 3  # really simple stopping rule: stop after doing 3 splits (so we end up with 4 clusters)\n",
    "\n",
    "for split_idx in range(num_splits):\n",
    "    # select which cluster to split by looking at which one has the highest residual sum of squares (RSS)\n",
    "    num_clusters = cluster_assignment.max() + 1\n",
    "    max_cluster_RSS = -np.inf\n",
    "    arg_max = None\n",
    "    for cluster_idx in range(num_clusters):\n",
    "        # compute cluster's Residual Sum of Squares (RSS)\n",
    "        cluster_mask = (cluster_assignment == cluster_idx)\n",
    "        cluster_size = cluster_mask.sum()\n",
    "        if cluster_size == 1:\n",
    "            cluster_RSS = 0.\n",
    "        else:\n",
    "            points_in_cluster = points[cluster_mask]\n",
    "            cluster_mean = points_in_cluster.mean(axis=0)\n",
    "            cluster_RSS = 0.\n",
    "            for point in points_in_cluster:\n",
    "                cluster_RSS += np.linalg.norm(point - cluster_mean)**2\n",
    "                \n",
    "        if cluster_RSS > max_cluster_RSS:\n",
    "            max_cluster_RSS = cluster_RSS\n",
    "            arg_max = cluster_idx\n",
    "            \n",
    "    # split cluster with largest cluster RSS (arg_max)\n",
    "    kmeans = KMeans(n_clusters=2, n_init=1000, random_state=0)\n",
    "    split_assignments = kmeans.fit_predict(points[cluster_assignment == arg_max])\n",
    "    # every point assigned to k-mean's output cluster 0 will be set to still have cluster index `arg_max`\n",
    "    # whereas every point assigned to k-mean's output cluster 1 will be set to have cluster index `num_clusters`\n",
    "    cluster_assignment[cluster_assignment == arg_max] \\\n",
    "        = arg_max * (split_assignments == 0) + num_clusters * (split_assignments == 1)  # create new cluster\n",
    "    \n",
    "    plt.figure()\n",
    "    plt.scatter(points[:, 0], points[:, 1], c=cluster_assignment, cmap='Accent')\n",
    "    plt.axis('equal')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Agglomerative clustering"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###  The simple way using sklearn (but the functionality is limited)\n",
    "\n",
    "To see what scikit-learn is capable of, look up the documentation for `AgglomerativeClustering`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(-3.1140351183062567,\n",
       " 2.395777334987554,\n",
       " -3.610738369320056,\n",
       " 1.4822764531043595)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn.cluster import AgglomerativeClustering\n",
    "\n",
    "clustering = AgglomerativeClustering(n_clusters=4, affinity='euclidean', linkage='complete')\n",
    "cluster_assignments = clustering.fit_predict(points)\n",
    "plt.scatter(points[:, 0], points[:, 1], c=cluster_assignments, cmap='Accent')\n",
    "plt.axis('equal')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Agglomerative clustering without scikit-learn\n",
    "\n",
    "For simplicity, the following code keeps merging until there's exactly 1 cluster, and at each merge step, the code plots what the clusters are. Because the number of clusters can be quite large, we use a random coloring for each plot; we specifically use the [random color map created by Felipe Delestro Matos](https://github.com/delestro/rand_cmap).\n",
    "\n",
    "We demonstrate this code using a simple line of points evenly spaced apart; feel free to comment out the next cell if you want to run the algorithm on the random points from earlier in this demo."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1a180ef9d0>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "points = np.vstack([np.arange(10), np.zeros(10)]).T\n",
    "\n",
    "plt.scatter(points[:, 0], points[:, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "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"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAW8AAAEFCAYAAAAsU2YoAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAATE0lEQVR4nO3de5CkVXnH8W/P9Nx2dxbWOPGSwhCMPkSjoJAEVNQiIQpVoEZzsQqqIOAtGhGLMmqJSSUqVkpUiKE0CgZNKCqgJkRBiGtIIt4IKcFLfCyvscpopsxmd5mZndme7fzx9jAzuz2X7ent3jP7/VRRbL/zXp4+ffr3nj5vX2rNZhNJUlkG+l2AJOnwGd6SVCDDW5IKZHhLUoEMb0kqkOEtSQUyvLWqiDgxIpoRcelBy6+MiL/u4nG+HxGnd2t/axxre0TcGxFfj4jfWuc290TESzo83nER8dlOtu1URBwfEQ/2qk3Ve4a31uMAcE1ERL8L6ZJTgUdl5pMz8+M9ON4O4Fd7cBwAIuI84EvAZnm81Ea93wWoCDPANcDNEXFmZs4t/WNrBP61zHzXwbcj4vvAzcDZVCH258AzgdOA/cAFmfmj1q5eHRGnACPANZl5Y2t/5wNvAYaBaeDKzPxCRPwJcCbwWOCBzLzwoLpeCPwx1SBlL/B6YDdwI/BzEfEV4MzMnFmyzaOB9wMnU5203p+Z1y35+4mt+7bt4NutbT8CPLK1+qcy8yrgw8BY63inAU8ErgV+BhgErsvMGyPiua3lU8A24CzgQ8ATWrXcD7wiMw9ExB2t2m5v83i9FrgQuLXN37RJOPLWer0deAh4RwfbjmbmGcBbgb8Crs3MU4AfAhcvWW8mM58OnANcHRFPjogntI55XmY+DXg58PGI2Nra5ueBp7UJ7pOpQvjFrWO9FfgH4L+By4DvZOapS4O75XrgW5l5MtWJ4eUR8YvrvJ8vA77bug9nAU+IiOOAS1r37VSgBtwGvDEzTwOeA1wZEWe09vHLwEsz86nABcB4a7tfaf39JIDMPG+F4CYzn5+Z962zZhXKkbfWpTXauxD4SkTcdZibf6z1/+8AP87MB5bcfsSS9T7QOtaPIuJu4NeBBvAYYOeSWZsDwEKgfjEzG22OeTawMzO/29rnZyPif6hGvqt9J8RvAG9obbObKkxZ54zRp4E7IuJxwGeoAnp3ROxYss4TgccDNy7Z5xjwNOA/gR9m5g9ayz8HvCMi7gH+CXhvZn57PYVo83PkrXXLzB8CrwBuYnFqAKowrC25PXzQprNL/r1/lUPML/n3QGvdQaoQPnXhP+AM4Gut9R5aYV+DHBrSA8DQKseH6mTx8HYRcVJEbF/y9xXva2u0+wtUry5OBL4cEae1qWt3m/vz4YPvT2Z+j+okdTWwHfhMawpJMrx1eDLzNuBO4HVLFk8CpwNExGOppgI6cXFrH4+jGgHvbP33m61pkIWLcQ9SjVZXsxN4XkSc1NrubOAEqgt5q/kM1TQHrSmPnVRzzgv+DxiOiCe1br904Q8R8U7gqsz8e+By4OtUI/cGMBgRNSCBmdarGCLiBKoT0cEhT0S8iirU787MPwLuAp6+Rv06Rhje6sRrgR8suf0XwGMiIqnCptO3xY1GxH8AdwB/mJnfysxvUM1z3xIRDwB/RnWRc6URNwCt7f6Aan78a8A7gfNbUyGreQ3wSxHxIHAvcHVm3r9kv7upplXujIj7qC7mLngvcGrreP8OfA+4hWqe/ctUYT4OvAC4rHWMu6kC/942tXyEaqT+jYi4HzgOuA4gIu6IiAvWuC/axGp+JawklceRtyQVyPCWpAIZ3pJUIMNbkgrUsw/pTE7u7fjK6I4dW9i1a7qb5RTN9lhkWyxneyzaLG0xMTFea7e8iJF3vT7Y7xKOKrbHIttiOdtj0WZviyLCW5K0nOEtSQUyvCWpQB1fsIyIQeCDVF/4Pg9ckpnf6VZhkqSVbWTkfT5AZj6T6ruS392ViiRJa+o4vFvfnPby1s2fB37SlYokSWva8BdTRcRNwIuAl2Tm3Sut12jMNzf7W3ck6Qho+z7vrnyrYOu3+74EPCkzp9qts5EP6UxMjDM5ubfTzTcd22ORbbGc7bFos7RF1z+kExEXRcSbWjenqX6aan6VTSRJXbKRj8d/HPhwRPwr1U9LvS4z93WnLEnSajoO79b0yO90sRZJ0jr5IR1JKpDhLUkFMrwlqUCGtyQVyPCWpAIZ3pJUIMNbkgpkeEtSgQxvSSqQ4S1JBTK8JalAhrckFcjwlqQCGd6SVCDDW5IKZHhLUoEMb0kqkOEtSQUyvCWpQIa3JBXI8JakAhneklQgw1uSCmR4S1KBDG9JKpDhLUkFqneyUUQMATcCJwIjwNsy8/Yu1iVJWkWnI+8LgZ9m5lnAucD7uleSJGktHY28gVuB25bcbnShFknSOtWazWbHG0fEOHA78MHMvHm1dRuN+Wa9PtjxsSTpGFVrt7DTkTcRcQLwCeD6tYIbYNeu6U4PxcTEOJOTezvefrOxPRbZFsvZHos2S1tMTIy3Xd7pBctHAXcDr8nMnRuoS5LUgU5H3m8GdgBXRcRVrWXnZuZMd8qSJK2mo/DOzMuBy7tciyRpnfyQjiQVyPCWpAIZ3pJUIMNbkgpkeEtSgQxvSSqQ4S1JBTK8JalAhrckFcjwlqQCGd6SVCDDW5IKZHhLUoEMb0kqkOEtSQUyvCWpQIa3JBXI8JakAhneklQgw1uSCmR4S1KBDG9JKpDhLUkFMrwlqUCGtyQVyPCWpAJtKLwj4tci4p4u1SJJWqd6pxtGxBuAi4Cp7pUjSVqPWrPZ7GjDiHgx8CDw0cw8Y631G435Zr0+2NGxJOkYVmu3sOORd2Z+LCJOXO/6u3ZNd3ooJibGmZzc2/H2m43tsci2WM72WLRZ2mJiYrztci9YSlKBDG9JKpDhLUkF6njOGyAzvw+sebFSktRdjrwlqUCGtyQVyPCWpAIZ3pJUIMNbkgpkeEtSgQxvSSqQ4S1JBTK8JalAhrckFcjwlqQCGd6SVCDDW5IKZHhLUoEMb0kqkOEtSQUyvCWpQIa3JBXI8JakAhneklQgw1uSCmR4S1KBDG9JKpDhLUkFqve7gNUMDNQYHR0CYGSkzuxsoy911OsDjIxUTTU726DRONCXOkZG6tTrg0DVNgcONHteQ60Go6PDDx9/Zmau5zXA8r4xPFxnbq4/fWNoaJDh4eox6W/fGKJer8ZiR0ffOMDMzP6e1wDHTt+oNZudPcgRMQBcD5wCzAKXZea3V1p/cnLvYR1oZKTO1q0jDA4uvjiYm2uwZ88MHZbcka1bRxgbG6JWqwHQbDaZmdnP1NRs74oAtm8fY3h48OE65ucPMDU129MTWr1eY3x87OETCMD+/fPs3TvD/HzvHpTR0Tpbtiz2jWazydzcPHv2zPSsBoBt20YYHe1v36jVFvrG4jis6hv7mJ2d71kd9foA4+Ojy/pGozHP7t0zPT2RjI4OsXXrMAMDS/tGgz179vWsBji0bywMdKanD3+wMzExXmu3fCPTJi8ERjPzTOCNwDUb2NchtmwZXhbcUJ1Ft2wZ7uZhVjU8PLgsuAFqtRpjY0MPn1F7YcuWYUZG6svqGBwcYOvWYWptH9YjVcfIsicnVKOLrVtHelZDrXZo36jVaoyM9L5vLH1yLtQxNjbE0FBv+8bS4Iaqb2zZ0rvHBKpBzsF9o14fZNu2XvaNGlu2LAb3wrKRkaGe9o2RkfohfWNgoMbY2PDDr466YSN7ehbwaYDM/CJwelcqojp7HtwRFgwN9W6mZ3h4eWAuqNVqhzxhjmwd7dticHCQkZGhntQwMFBbse2HhgbbttORMDo6xODgSn2jd6E5PDy0Yt9YmGLrhZUek3p9sGd1VH2jfdvX64M9G2BUfaN9pPW2b7TPjYGB7vaNjUybfAj4WGbe2br9X8BJmdn2dXyjMd9cKZAlSStqe/rbyGlgDzC+5PbASsENsGvX9Lp3XKvV2LFjS9uz6MzMHA891Js5xZGROuPjo23Ponv27GN2tjcXZLZtG2Fs7NCXffPzB9i1a5pOT8CH67jjxtq+4piba7B7d2/mmwcGahx/fPu+MT09y9RUby6gjo4OMT4+esjyZrPJnj37enaRbPW+MdWz60PHH7+l7eh2dnZ/z+abBwZq7NixlYGBQ5+vvewbY2NDbNu2Ut+YYW7u8K5FTEyMt12+kWmTe4HzACLiDOCrG9jXMgsXfg4Opf375zua8O/U7Gyj7ZNwdnZ/z4IbYGpqjkZj+QO+UhsdSTMzc8zPL79iPj9/oKePyYEDTfbtW6lv9O4x2bevfR9Yqc8cKdPTc+zf365vzPX0wv7MzOwhfaPRONDTx2ThouChfaPR0z46M7P/kDcSNJtN9u1rHHZwr6Yb7zZ5KtWw/pLM/OZK6x/uu02gmusdHh5ibGyIqanZnnfIBaOjixco5+bm2bev92+BqtV4+ILHyMgQu3dPd7UjrNfgYHXhZeHtaNPTc315W9rwcDXfPzpq31i4UNrvvlGvDzA6OsTAQI35+eqtgsdy31i4eN1sVoOLTvvGSu826Ti8D1cn4b1gYmKcycm93SynaLbHIttiOdtj0WZpiyPxVkFJUp8Y3pJUIMNbkgpkeEtSgQxvSSqQ4S1JBTK8JalAhrckFcjwlqQCGd6SVCDDW5IKZHhLUoEMb0kqkOEtSQUyvCWpQIa3JBXI8JakAhneklQgw1uSCmR4S1KBDG9JKpDhLUkFMrwlqUCGtyQVyPCWpAIZ3pJUoA2Fd0S8KCJu7lYxkqT1qXe6YURcCzwP+Er3ypEkrcdGRt6fB17VrUIkSetXazabq64QEZcCVxy0+JLMvC8ingu8MjN/b60DNRrzzXp9sONCJekYVWu3cM1pk8y8Abhho0fftWu6420nJsaZnNy70RI2DdtjkW2xnO2xaLO0xcTEeNvlvttEkgpkeEtSgTp+twlAZt4D3NOVSiRJ6+bIW5IKZHhLUoEMb0kqkOEtSQUyvCWpQIa3JBXI8JakAhneklQgw1uSCmR4S1KBDG9JKpDhLUkFMrwlqUCGtyQVyPCWpAIZ3pJUIMNbkgpkeEtSgQxvSSqQ4S1JBTK8JalAhrckFcjwlqQCGd6SVCDDW5IKZHhLUoHqnWwUEccBfwNsB4aB12fmF7pZmCRpZZ2OvF8P7MzM5wAXA3/ZtYokSWvqaOQNvAeYXbKPfd0pR5K0HrVms7nqChFxKXDFQYsvycz7IuLRwJ3A6zLzX1bbT6Mx36zXBzdUrCQdg2ptF64V3iuJiKcAtwBXZuada60/Obm3swMBExPjTE7u7XTzTcf2WGRbLGd7LNosbTExMd42vDu9YPkk4FbgdzPzgY0UJkk6fJ3OeV8NjALXRgTA7sx8QdeqkiStqqPwNqglqb/8kI4kFcjwlqQCGd6SVCDDW5IKZHhLUoEMb0kqkOEtSQUyvCWpQIa3JBXI8JakAhneklQgw1uSCmR4S1KBDG9JKpDhLUkFMrwlqUCGtyQVyPCWpAIZ3pJUIMNbkgpkeEtSgQxvSSqQ4S1JBTK8JalAhrckFcjwlqQC1TvZKCK2AjcDjwCmgIsyc7KbhUmSVtbpyPtlwP2ZeRZwC/CW7pUkSVpLRyPvzHxvRAy2bj4O+Mla2+zYsYV6fXCt1VY0MTHe8babke2xyLZYzvZYtJnbYs3wjohLgSsOWnxJZt4XEZ8FngKcs9Z+du2a7qxCqgdgcnJvx9tvNrbHIttiOdtj0WZpi5VOQGuGd2beANywwt/OjoiTgU8Bj99IgZKk9etozjsi3hQRF7VuTgHz3StJkrSWjua8gRuBm1pTKoPAJd0rSZK0lk4vWP4EeH6Xa5EkrZMf0pGkAhneklSgWrPZ7HcNkqTD5MhbkgpkeEtSgQxvSSqQ4S1JBTK8JalAhrckFcjwlqQCdfrdJj0REQPA9cApwCxwWWZ+u79V9UdEDFF9p8yJwAjwtsy8va9FHQUi4meB+4FzMvOb/a6nXyLiTcAFwDBwfevbQI9JrefKTVTPlXngZZuxbxztI+8XAqOZeSbwRuCaPtfTTxcCP239etG5wPv6XE/ftZ6kHwBm+l1LP0XEc4FnAM8EngOc0NeC+u88oJ6ZzwD+FHh7n+s5Io728H4W8GmAzPwicHp/y+mrW4Grltxu9KuQo8i7gPcDP+p3IX32POCrwCeAfwQ+2d9y+u5bQL31yn07sL/P9RwRR3t4bwd2L7k9HxFH9VTPkZKZD2Xm3ogYB27jGP/d0Ii4GJjMzLv6XctR4JFUA5vfBl4J/G1E1PpbUl89RDVl8k3gg8B1fa3mCDnaw3sPsPQ3gAYy85gdcUbECcA/Ax/NzJv7XU+f/T5wTkTcA5wKfCQiHt3fkvrmp8BdmTmXmQnsAyb6XFM/XUHVHk+kul52U0SM9rmmrjvaR7H3AucDfxcRZ1C9NDwmRcSjgLuB12Tmzn7X02+Z+eyFf7cC/JWZ+eP+VdRXnwMuj4h3A48BtlIF+rFqF4tTJf8LDFH9aMymcrSH9yeoRlefB2oc27/Y82ZgB3BVRCzMfZ+bmcf0xTpBZn4yIp4NfJnq1fSrM/NY/mnC9wA3RsS/Ub375s2ZOdXnmrrOr4SVpAId7XPekqQ2DG9JKpDhLUkFMrwlqUCGtyQVyPCWpAIZ3pJUoP8HZKKgTWmM/WIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "num_clusters = len(points)\n",
    "\n",
    "cluster_assignment = np.arange(num_clusters).astype(np.int)\n",
    "\n",
    "from scipy.spatial.distance import cdist\n",
    "from rand_cmap import rand_cmap\n",
    "\n",
    "plt.figure()\n",
    "plt.title('Number of clusters: ' + str(num_clusters))\n",
    "plt.scatter(points[:, 0], points[:, 1], c=cluster_assignment,\n",
    "            cmap=rand_cmap(num_clusters, type='bright',\n",
    "                           first_color_black=False,\n",
    "                           last_color_black=False,\n",
    "                           verbose=False))\n",
    "plt.axis('equal')\n",
    "\n",
    "linkage = 'single'\n",
    "\n",
    "while num_clusters > 1:\n",
    "    # find the two clusters that are ``closest'' according to some rule\n",
    "    min_dist = np.inf\n",
    "    arg_min = None\n",
    "    for cluster_idx1 in range(num_clusters):\n",
    "        cluster1_points = points[cluster_assignment == cluster_idx1]\n",
    "        for cluster_idx2 in range(cluster_idx1 + 1, num_clusters):\n",
    "            cluster2_points = points[cluster_assignment == cluster_idx2]\n",
    "            \n",
    "            if linkage == 'centroid':\n",
    "                dist = np.linalg.norm(cluster1_points.mean(axis=0)\n",
    "                                      - cluster2_points.mean(axis=0))\n",
    "            elif linkage == 'single':\n",
    "                dist = cdist(cluster1_points, cluster2_points).min()\n",
    "            elif linkage == 'complete':\n",
    "                dist = cdist(cluster1_points, cluster2_points).max()\n",
    "            else:\n",
    "                raise NotImplementedError('Unsupported linkage type')\n",
    "            \n",
    "            if dist < min_dist:\n",
    "                min_dist = dist\n",
    "                arg_min = (cluster_idx1, cluster_idx2)\n",
    "    \n",
    "    cluster_idx1, cluster_idx2 = arg_min\n",
    "    \n",
    "    # merge arg_min clusters\n",
    "    cluster_assignment[cluster_assignment == cluster_idx2] = cluster_idx1\n",
    "    mask = (cluster_assignment > cluster_idx2)\n",
    "    if mask.sum() > 0:\n",
    "        cluster_assignment[mask] -= 1\n",
    "    num_clusters -= 1\n",
    "    \n",
    "    plt.figure()\n",
    "    plt.title('Number of clusters: ' + str(num_clusters))\n",
    "    if num_clusters > 1:\n",
    "        plt.scatter(points[:, 0], points[:, 1], c=cluster_assignment,\n",
    "                    cmap=rand_cmap(num_clusters, type='bright',\n",
    "                                   first_color_black=False,\n",
    "                                   last_color_black=False,\n",
    "                                   verbose=False))\n",
    "    else:\n",
    "        plt.scatter(points[:, 0], points[:, 1], c=cluster_assignment)\n",
    "    plt.axis('equal')"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}