hierarchy cluster.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%reload_ext autoreload\n",
    "%autoreload 2\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Many thanks to this awesome tutorial: https://joernhees.de/blog/2015/08/26/scipy-hierarchical-clustering-and-dendrogram-tutorial/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.cluster.hierarchy import dendrogram, linkage\n",
    "np.set_printoptions(precision=5, suppress=True)  # suppress scientific float notation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generate sample data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(150, 2)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f10c274bcf8>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(42)\n",
    "a = np.random.multivariate_normal([10,0], [[3,1],[1,4]], size = [100,])\n",
    "b = np.random.multivariate_normal([0, 10], [[2,1],[1,4]], size = [50,])\n",
    "X = np.concatenate((a,b), )\n",
    "print(X.shape)\n",
    "plt.scatter(X[:,0], X[:,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(149, 4)\n"
     ]
    }
   ],
   "source": [
    "#generate linkage matrix\n",
    "Z = linkage(X, 'centroid')\n",
    "print(Z.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9588434598315442"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.cluster.hierarchy import cophenet\n",
    "from scipy.spatial.distance import pdist\n",
    "\n",
    "c, coph_dists = cophenet(Z, pdist(X))\n",
    "c"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([66.     , 91.     ,  0.02299,  2.     ])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Z[i] tells us which clusters were merged in i-1th iteration\n",
    "# idx1, idx2, distance, sample count\n",
    "Z[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([17.     , 69.     ,  0.02481,  2.     ])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 66.     ,  91.     ,   0.02299,   2.     ],\n",
       "       [ 17.     ,  69.     ,   0.02481,   2.     ],\n",
       "       [ 72.     ,  87.     ,   0.07878,   2.     ],\n",
       "       [  6.     ,  18.     ,   0.10092,   2.     ],\n",
       "       [ 40.     ,  57.     ,   0.10392,   2.     ],\n",
       "       [  0.     ,  93.     ,   0.11289,   2.     ],\n",
       "       [109.     , 134.     ,   0.11337,   2.     ],\n",
       "       [ 28.     ,  68.     ,   0.12189,   2.     ],\n",
       "       [  4.     ,  44.     ,   0.13721,   2.     ],\n",
       "       [ 52.     , 154.     ,   0.15013,   3.     ],\n",
       "       [119.     , 146.     ,   0.1522 ,   2.     ],\n",
       "       [108.     , 120.     ,   0.15921,   2.     ],\n",
       "       [ 48.     ,  75.     ,   0.16427,   2.     ],\n",
       "       [ 43.     ,  82.     ,   0.16567,   2.     ],\n",
       "       [121.     , 129.     ,   0.17229,   2.     ],\n",
       "       [138.     , 144.     ,   0.17445,   2.     ],\n",
       "       [ 16.     ,  58.     ,   0.17723,   2.     ],\n",
       "       [ 34.     ,  77.     ,   0.18201,   2.     ],\n",
       "       [ 99.     , 166.     ,   0.18276,   3.     ],\n",
       "       [ 36.     ,  88.     ,   0.20104,   2.     ]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z[:20]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[10.22066, -0.69132],\n",
       "       [10.17857, -0.59631],\n",
       "       [10.34825, -0.62268]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#we see that there is an index of 154, which means it's the 5th cluster formed by 40 and 57\n",
    "X[[40, 57,52]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f0fd197f320>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "idxs = [40,52,57]\n",
    "plt.figure(figsize = (10,6))\n",
    "plt.scatter(X[:,0],X[:,1])\n",
    "plt.scatter(X[idxs, 0],X[idxs,1], color = 'r')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f0fd1947f28>"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#idx = 166 corrspond to 16 and 58, check out their distance to 99\n",
    "idxs = [16,58,99]\n",
    "plt.figure(figsize=(10,6))\n",
    "plt.scatter(X[:,0], X[:,1])\n",
    "plt.scatter(X[idxs, 0],X[idxs, 1], color = 'g')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plot dendrogram"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1296x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (18,6))\n",
    "plt.title(\"Hierarchical Clustering Dendrogram\")\n",
    "plt.xlabel(\"sample index\")\n",
    "plt.ylabel(\"distance\")\n",
    "dendrogram(Z, leaf_rotation=90, leaf_font_size=8)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. horizontal lines are cluster merges\n",
    "2. vertical line tells you which clusters/labels were part of merge\n",
    "3. heights of horizontal line tells the distance between two clusters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4.97156,  5.57279,  7.34446, 14.36102])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Z[-4:,2]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.6.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}