Coursera Data Analysis -- in Python

K-means Clustering

{
 "metadata": {
  "name": "k-means_clustering"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "K-means clustering -- in Python"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# as always, create the same data as in video in R"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%load_ext rmagic"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R -o x,y\n",
      "set.seed(1234); par(mar=c(0,0,0,0))\n",
      "x <- rnorm(12,mean=rep(1:3,each=4),sd=0.2)\n",
      "y <- rnorm(12,mean=rep(c(1,2,1),each=4),sd=0.2)\n",
      "plot(x,y,col='blue',pch=19,cex=2)\n",
      "text(x+0.05,y+0.05,labels=as.character(0:11))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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agQACCCAQmAABHFiHUV0EEEAAgTgECOA4+pFWIIAAAggEJkAAB9ZhVBcBBBBA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\n+n+BkunjqrR7ZQAAAABJRU5ErkJggg==\n"
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# perform k-means clustering\n",
      "from scipy.cluster.vq import kmeans, vq\n",
      "\n",
      "data = np.vstack(zip(x, y))\n",
      "\n",
      "centers, _ = kmeans(data, 3)\n",
      "cluster, _ = vq(data, centers)\n",
      "\n",
      "cluster"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 19,
       "text": [
        "array([2, 2, 2, 2, 1, 1, 1, 1, 0, 0, 0, 0])"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# plot the clusters\n",
      "plot(data[cluster==0,0], data[cluster==0,1], 'og',\n",
      "     data[cluster==1,0], data[cluster==1,1], 'or',\n",
      "     data[cluster==2,0], data[cluster==2,1], 'ok')\n",
      "\n",
      "plot(centers[:,0], centers[:,1], '+', markersize=15);"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# again generate data for plotting heatmap using R"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R -i x,y -o dataMatrix\n",
      "dataFrame <- data.frame(x=x,y=y)\n",
      "set.seed(1234)\n",
      "dataMatrix <- as.matrix(dataFrame)[sample(1:12),]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# show heatmaps of the original matrix and after reordered by cluster\n",
      "f, (ax1, ax2) = subplots(ncols=2)\n",
      "\n",
      "ax1.matshow(dataMatrix, aspect='auto', cmap='hot')\n",
      "\n",
      "centers, _ = kmeans(dataMatrix, 3)\n",
      "cluster, _ = vq(dataMatrix, centers)\n",
      "dataMatrixOrdered = np.vstack((dataMatrix[cluster==0,:], dataMatrix[cluster==1,:], dataMatrix[cluster==2,:]))\n",
      "ax2.matshow(dataMatrixOrdered, aspect='auto', cmap='hot')\n",
      "\n",
      "f.tight_layout();"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}