som.ipynb

{
  "metadata": {
    "name": "Self-organizing Maps"
  }, 
  "nbformat": 3, 
  "nbformat_minor": 0, 
  "worksheets": [
    {
      "cells": [
        {
          "cell_type": "heading", 
          "level": 1, 
          "metadata": {}, 
          "source": [
            "Self-organizing Maps"
          ]
        }, 
        {
          "cell_type": "markdown", 
          "metadata": {}, 
          "source": [
            "\n\n", 
            "This is a demonstration of how a self-organizing map (SOM), also known\nas a Kohonen network, can be used to map high-dimensional data into a\ntwo-dimensional representation. For the sake of an easy visualization\n'high-dimensional' in this case is 3D.\n\n", 
            "In general, SOMs might be useful for visualizing high-dimensional data\nin terms of its similarity structure. Especially large SOMs (i.e. with\nlarge number of Kohonen units) are known to perform mappings that\npreserve the topology of the original data, i.e. neighboring data\npoints in input space will also be represented in adjacent locations\non the SOM.\n\n", 
            "The following code shows the 'classic' color mapping example, i.e. the\nSOM will map a number of colors into a rectangular area."
          ]
        }, 
        {
          "cell_type": "code", 
          "collapsed": false, 
          "input": [
            "from mvpa2.suite import *"
          ], 
          "language": "python", 
          "metadata": {}, 
          "outputs": []
        }, 
        {
          "cell_type": "markdown", 
          "metadata": {}, 
          "source": [
            "\n\n", 
            "First, we define some colors as RGB values from the interval (0,1),\ni.e. with white being (1, 1, 1) and black being (0, 0, 0). Please\nnote, that a substantial proportion of the defined colors represent\nvariations of 'blue', which are supposed to be represented in more\ndetail in the SOM."
          ]
        }, 
        {
          "cell_type": "code", 
          "collapsed": false, 
          "input": [
            "colors = np.array(\n         [[0., 0., 0.],\n          [0., 0., 1.],\n          [0., 0., 0.5],\n          [0.125, 0.529, 1.0],\n          [0.33, 0.4, 0.67],\n          [0.6, 0.5, 1.0],\n          [0., 1., 0.],\n          [1., 0., 0.],\n          [0., 1., 1.],\n          [1., 0., 1.],\n          [1., 1., 0.],\n          [1., 1., 1.],\n          [.33, .33, .33],\n          [.5, .5, .5],\n          [.66, .66, .66]])\n\n# store the names of the colors for visualization later on\ncolor_names = \\\n        ['black', 'blue', 'darkblue', 'skyblue',\n         'greyblue', 'lilac', 'green', 'red',\n         'cyan', 'violet', 'yellow', 'white',\n         'darkgrey', 'mediumgrey', 'lightgrey']"
          ], 
          "language": "python", 
          "metadata": {}, 
          "outputs": []
        }, 
        {
          "cell_type": "markdown", 
          "metadata": {}, 
          "source": [
            "\n\n", 
            "Now we can instantiate the mapper. It will internally use a so-called\nKohonen layer to map the data onto. We tell the mapper to use a\nrectangular layer with 20 x 30 units. This will be the output space of\nthe mapper. Additionally, we tell it to train the network using 400\niterations and to use custom learning rate."
          ]
        }, 
        {
          "cell_type": "code", 
          "collapsed": false, 
          "input": [
            "som = SimpleSOMMapper((20, 30), 400, learning_rate=0.05)"
          ], 
          "language": "python", 
          "metadata": {}, 
          "outputs": []
        }, 
        {
          "cell_type": "markdown", 
          "metadata": {}, 
          "source": [
            "\n\n", 
            "Finally, we train the mapper with the previously defined 'color' dataset."
          ]
        }, 
        {
          "cell_type": "code", 
          "collapsed": false, 
          "input": [
            "som.train(colors)"
          ], 
          "language": "python", 
          "metadata": {}, 
          "outputs": []
        }, 
        {
          "cell_type": "markdown", 
          "metadata": {}, 
          "source": [
            "\n\n", 
            "Each unit in the Kohonen layer can be treated as a pointer into the\nhigh-dimensional input space, that can be queried to inspect which\ninput subspaces the SOM maps onto certain sections of its 2D output\nspace.  The color-mapping generated by this example's SOM can be shown\nwith a single matplotlib call:"
          ]
        }, 
        {
          "cell_type": "code", 
          "collapsed": false, 
          "input": [
            "pl.imshow(som.K, origin='lower')"
          ], 
          "language": "python", 
          "metadata": {}, 
          "outputs": []
        }, 
        {
          "cell_type": "markdown", 
          "metadata": {}, 
          "source": [
            "\n\n", 
            "And now, let's take a look onto which coordinates the initial training\nprototypes were mapped to. The get those coordinates we can simply feed\nthe training data to the mapper and plot the output."
          ]
        }, 
        {
          "cell_type": "code", 
          "collapsed": false, 
          "input": [
            "mapped = som(colors)\n\npl.title('Color SOM')\n# SOM's kshape is (rows x columns), while matplotlib wants (X x Y)\nfor i, m in enumerate(mapped):\n    pl.text(m[1], m[0], color_names[i], ha='center', va='center',\n           bbox=dict(facecolor='white', alpha=0.5, lw=0))"
          ], 
          "language": "python", 
          "metadata": {}, 
          "outputs": []
        }, 
        {
          "cell_type": "markdown", 
          "metadata": {}, 
          "source": [
            "\n\n", 
            "The text labels of the original training colors will appear at the 'mapped'\nlocations in the SOM -- and should match with the underlying color."
          ]
        }, 
        {
          "cell_type": "code", 
          "collapsed": false, 
          "input": [
            "# show the figure"
          ], 
          "language": "python", 
          "metadata": {}, 
          "outputs": []
        }, 
        {
          "cell_type": "markdown", 
          "metadata": {}, 
          "source": [
            "\n\n", 
            "The following figure shows an exemplary solution of the SOM mapping of the\n3D color-space onto the 2D SOM node layer:\n\n\\[Visit [http://pymvpa.org/examples/som.html](http://pymvpa.org/examples/som.html) to view this figure\\]"
          ]
        }
      ], 
      "metadata": {}
    }
  ]
}