{
 "metadata": {
  "name": "",
  "signature": "sha256:b093fe7870269c846fb132031385f739da0699b7d50ff86bcff4e1e88f95c0b1"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "from sklearn.cluster.hierarchical import ward_tree\n",
      "from sklearn.neighbors import kneighbors_graph\n",
      "import pylab as pl\n",
      "\n",
      "%pylab inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "dim = 10\n",
      "npoints = 100"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# very simple simulation: two blobs\n",
      "mean1 = -5 * np.ones(dim)\n",
      "cov1 = np.diag(np.ones(dim))\n",
      "mean2 = 5 * np.ones(dim)\n",
      "cov2 = cov1\n",
      "    \n",
      "X1 = np.random.multivariate_normal(mean1,cov1,npoints)\n",
      "X2 = np.random.multivariate_normal(mean2,cov2,npoints)\n",
      "    \n",
      "X = np.vstack((X1, X2))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "connectivity = kneighbors_graph(X, n_neighbors=5)\n",
      "pl.figure(figsize=(5, 5))\n",
      "pl.imshow(connectivity.todense(), interpolation='nearest');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10c37b250>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# ward_tree fails when the connectivity matrix is sparse\n",
      "out = ward_tree(X, connectivity)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "/usr/local/lib/python2.7/site-packages/sklearn/cluster/hierarchical.py:167: UserWarning: the number of connected components of the connectivity matrix is 2 > 1. Completing it to avoid stopping the tree early.\n",
        "  n_components=n_components)\n"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "connectivity_1 = kneighbors_graph(X, n_neighbors=npoints)\n",
      "pl.figure(figsize=(5,5))\n",
      "pl.imshow(connectivity_1.todense(), interpolation='nearest');"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAToAAAE3CAYAAAA63I2CAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10c37b590>"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# ward_tree doesn't fail now\n",
      "out = ward_tree(X, connectivity_1)\n",
      "print out[0][:10]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[195 169]\n",
        " [164 113]\n",
        " [ 91  24]\n",
        " [ 20  11]\n",
        " [158 133]\n",
        " [197 185]\n",
        " [120 116]\n",
        " [162 144]\n",
        " [193 125]\n",
        " [ 99  15]]\n"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print out[0][:10]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[195 169]\n",
        " [164 113]\n",
        " [ 91  24]\n",
        " [ 20  11]\n",
        " [158 133]\n",
        " [197 185]\n",
        " [120 116]\n",
        " [162 144]\n",
        " [193 125]\n",
        " [ 99  15]]\n"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}