ubnt-intrepid/gmm_examples.ipynb

## gmm_examples.ipynb
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  "signature": "sha256:fb9e39de7dcdf847a1feaedf91e6285a187f9273d5d61d87046ba7ac3d367b03"
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 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import itertools\n",
      "\n",
      "import numpy as np\n",
      "from scipy import linalg\n",
      "import matplotlib.pyplot as plt\n",
      "import matplotlib as mpl\n",
      "%matplotlib inline\n",
      "\n",
      "from sklearn import mixture"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Number of samples per component\n",
      "n_samples = 500\n",
      "\n",
      "# Generate random sample, two components\n",
      "np.random.seed(0)\n",
      "C = np.array([[0., -0.5], [1.7, .4]])\n",
      "X = np.r_[np.dot(np.random.randn(n_samples, 2), C),\n",
      "          .7 * np.random.randn(n_samples, 2) + np.array([-4, 2])]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#n_components=12\n",
      "#\n",
      "#print(np.array([ mixture.GMM(n_components=n, covariance_type='full').fit(X).aic(X) \n",
      "#        for n in range(1, n_components + 1)]))\n",
      "#print(np.array([ mixture.GMM(n_components=n, covariance_type='full').fit(X).bic(X) \n",
      "#        for n in range(1, n_components + 1)]))\n",
      "\n",
      "n_components=5\n",
      "\n",
      "# Fit a mixture of Gaussians with EM using five components\n",
      "gmm = mixture.GMM(n_components=n_components, covariance_type='full')\n",
      "gmm.fit(X);\n",
      "print('GMM: AIC={:0.4f}, BIC={:0.4f}'.format(gmm.aic(X), gmm.bic(X)))\n",
      "\n",
      "# Fit a Variational Bayes mixture of Gaussians using five components\n",
      "vbgmm = mixture.VBGMM(n_components=n_components, covariance_type='full')\n",
      "vbgmm.fit(X);\n",
      "print('VBGMM: AIC={:0.4f}, BIC={:0.4f}'.format(vbgmm.aic(X), vbgmm.bic(X)))\n",
      "\n",
      "# Fit a Dirichlet process mixture of Gaussians using five components\n",
      "dpgmm = mixture.DPGMM(n_components=n_components, covariance_type='full')\n",
      "dpgmm.fit(X);\n",
      "print('DPGMM: AIC={:0.4f}, BIC={:0.4f}'.format(dpgmm.aic(X), dpgmm.bic(X)))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "GMM: AIC=6128.8666, BIC=6271.1915\n",
        "VBGMM: AIC=-2400.9650, BIC=-2258.6401"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "DPGMM: AIC=-1013.8372, BIC=-871.5122"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "color_iter = itertools.cycle(['r', 'g', 'b', 'c', 'm'])\n",
      "\n",
      "plt.figure(figsize=(10, 15))\n",
      "for i, (clf, title) in enumerate([(gmm, 'GMM'),\n",
      "                                  (vbgmm, 'Variational Bayes GMM'),\n",
      "                                  (dpgmm, 'Dirichlet Process GMM')]):\n",
      "    splot = plt.subplot(3, 1, 1+i)\n",
      "    Y_ = clf.predict(X)\n",
      "    for i, (mean, covar, color) in enumerate(zip(\n",
      "            clf.means_, clf._get_covars(), color_iter)):\n",
      "        v, w = linalg.eigh(covar)\n",
      "        u = w[0] / linalg.norm(w[0])\n",
      "        # as the DP will not use every component it has access to\n",
      "        # unless it needs it, we shouldn't plot the rdundant\n",
      "        # components.\n",
      "        if not np.any(Y_ == i):\n",
      "            continue\n",
      "        plt.scatter(X[Y_ == i, 0], X[Y_ == i, 1], .8, color=color)\n",
      "\n",
      "        # Plot an ellipse to show the Gaussian component\n",
      "        angle = np.arctan(u[1] / u[0])\n",
      "        angle = 180 * angle / np.pi \n",
      "        ell = mpl.patches.Ellipse(mean, v[0], v[1], 180 + angle, color=color)\n",
      "        ell.set_clip_box(splot.bbox)\n",
      "        ell.set_alpha(0.5)\n",
      "        splot.add_artist(ell)\n",
      "\n",
      "    plt.xlim(-10, 10)\n",
      "    plt.ylim(-3, 6)\n",
      "    plt.xticks(())\n",
      "    plt.yticks(())\n",
      "    plt.title(title)\n",
      "\n",
      "plt.show()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
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H70vS3e2G2MLNz1UOjuEKEOEFmJlYeBCzV5pximqpxptstYNOuFE47phgirl/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       "text": [
        "<matplotlib.figure.Figure at 0x7afa828>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    }
   ],
   "metadata": {}
  }
 ]
}