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  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Simple Clustering With SciPy\n",
      "\n",
      "- **Author:** [Chris Albon](http://www.chrisalbon.com/), [@ChrisAlbon](https://twitter.com/chrisalbon)\n",
      "- **Date:** -\n",
      "- **Repo:** [Python 3 code snippets for data science](https://github.com/chrisalbon/code_py)\n",
      "- **Note:**"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Import modules"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "%matplotlib inline\n",
      "import matplotlib.pyplot as plt\n",
      "from scipy.cluster import vq"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 42
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Create coordinates for battles for each year of the war"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# create 100 coordinate pairs (i.e. two values), then add 5 to all of them\n",
      "year_1 = np.random.randn(100, 2) + 5\n",
      "\n",
      "# create 30 coordinatee pairs (i.e. two values), then subtract 5 to all of them\n",
      "year_2 = np.random.randn(30, 2) - 5\n",
      "\n",
      "# create 50 coordinatee pairs (i.e. two values)\n",
      "year_3 = np.random.randn(50, 2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### View the first 3 entries of each year of battles"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print('year 1 battles:',  year_1[0:3])\n",
      "print('year 2 battles:', year_2[0:3])\n",
      "print('year 3 battles:', year_3[0:3])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "year 1 battles: [[ 3.87032104  4.93418141]\n",
        " [ 4.47603646  3.23230121]\n",
        " [ 6.15905943  4.55274026]]\n",
        "year 2 battles: [[-3.55642932 -3.13125097]\n",
        " [-5.83295449 -5.75787649]\n",
        " [-5.12144789 -5.00466761]]\n",
        "year 3 battles: [[-0.27557365 -0.65002898]\n",
        " [ 0.94593878 -0.46056352]\n",
        " [ 0.91003511  0.27888337]]\n"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Pool all three years of coordinates"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# vertically stack year_1, year_2, and year_3 elements\n",
      "battles = np.vstack([year_1, year_2, year_3])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Cluster the battle locations into three groups"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# calculate the centroid coordinates of each cluster \n",
      "# and the variance of all the clusters\n",
      "centroids, variance  = vq.kmeans(battles, 3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 30
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### View the centroid coordinate for each of the three clusters"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "centroids"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 32,
       "text": [
        "array([[ 4.89478443,  5.00806609],\n",
        "       [ 0.16770004,  0.01639683],\n",
        "       [-5.06447231, -4.99956259]])"
       ]
      }
     ],
     "prompt_number": 32
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### View the variance of the clusters (they all share the same)"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "variance"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 35,
       "text": [
        "1.2382236882037887"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Seperate the battle data into clusters"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "identified, distance = vq.vq(battles, centroids)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 36
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### View the cluster of each battle"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "identified"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### View the distance of each individual battle from their cluster's centroid"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "distance"
     ],
     "language": "python",
     "metadata": {},
     "outputs": []
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Index the battles data by the cluster to which they belong"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "cluster_1 = battles[identified == 0]\n",
      "cluster_2 = battles[identified == 1]\n",
      "cluster_3 = battles[identified == 2]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 39
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Print the first three coordinate pairs of each cluster"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "print(cluster_1[0:3])\n",
      "print(cluster_2[0:3])\n",
      "print(cluster_3[0:3])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[[ 3.87032104  4.93418141]\n",
        " [ 4.47603646  3.23230121]\n",
        " [ 6.15905943  4.55274026]]\n",
        "[[-0.27557365 -0.65002898]\n",
        " [ 0.94593878 -0.46056352]\n",
        " [ 0.91003511  0.27888337]]\n",
        "[[-3.55642932 -3.13125097]\n",
        " [-5.83295449 -5.75787649]\n",
        " [-5.12144789 -5.00466761]]\n"
       ]
      }
     ],
     "prompt_number": 43
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Plot all the battles, color each battle by cluster"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# create a scatter plot there the x-axis is the first column of battles\n",
      "# the y-axis is the second column of battles, the size is 100, and\n",
      "# the color of each point is determined by the indentified variable\n",
      "plt.scatter(battles[:,0], battles[:,1], s=100, c=identified)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 58,
       "text": [
        "<matplotlib.collections.PathCollection at 0x10771b890>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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V50YHrADUeHtbEhh4AoDdu3fTr98Y4uOHGNvtRxjrbgiPkROImXUqwoCORSTHijf+s0RE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\neZYj8kIkFjbm/DN6B3f2BVO5ayVcG7t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       "text": [
        "<matplotlib.figure.Figure at 0x10729a190>"
       ]
      }
     ],
     "prompt_number": 58
    }
   ],
   "metadata": {}
  }
 ]
}