view notebook/gmm-list-analysis.ipynb @ 13:cc8ceb270e79

add some gmm ipynbs

{
 "metadata": {
  "name": "",
  "signature": "sha256:71e3c2bb9a7d67a9a397b725f0c1114f05dbe56d1991ef5cb863257aa88a6988"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%bash\n",
      "\n",
      "ls ../cache"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1000-contrast6-dct-pca-2048_1024-wl20-ss10-ssm.txt\n",
        "1002-contrast6-dct-pca-2048_1024-wl20-ss10-ssm.txt\n",
        "Cache-1000-contrast6-dct-pca-2048_1024-wl20-ss10.txt-f_getGMMs-pickle.txt\n",
        "Cache-1000-contrast6-dct-pca-2048_1024-wl50-ss50.txt-f_getGMMs-pickle.txt\n",
        "Cache-1002-contrast6-dct-pca-2048_1024-wl20-ss10.txt-f_getGMMs-pickle.txt\n",
        "Cache-10hongniang01-contrast6-dct-pcamean--wl20-ss10.txt-f_getGMMs-pickle.txt\n"
       ]
      }
     ],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import sys\n",
      "sys.path.insert(0,\"../\")\n",
      "sys.path.insert(0, '/Users/mitian/Documents/hg/segmenter/utils/')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import utils.gmmplot as gp"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%bash\n",
      "\n",
      "#rm ../cache/gmm_list.txt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import cPickle as p\n",
      "with open(\"../cache/Cache-10hongniang01-contrast6-dct-pcamean--wl20-ss10.txt-f_getGMMs-pickle.txt\",\"r\") as f:\n",
      "    gmm_list = p.load(f)\n",
      "print len(gmm_list)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1235\n"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "g0 = gmm_list[0]\n",
      "len(g0.components)\n",
      "#print g0.components[0].covars\n",
      "#dir(g0.gmm)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "1"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "len(gmm_list[49].gmm.means_[0])\n",
      "print gmm_list[49].gmm.means_[0]\n",
      "print gmm_list[49].gmm.covars_[0][:2,:2]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 0.85296231  0.53451746  0.21546676  0.59680386  0.56988481  0.53920114\n",
        "  0.7503756   0.52364793  0.34387062  0.29799375  0.26085172  0.30439882\n",
        "  0.30225178  0.42498073  0.57177275  0.48702445  0.58831181  0.69667595\n",
        "  0.57755405  0.52266616]\n",
        "[[ 0.00221093 -0.00087832]\n",
        " [-0.00087832  0.01219112]]\n"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "from numpy.linalg import eigh\n",
      "from pylab import plt\n",
      "from matplotlib.patches import Ellipse\n",
      "import itertools\n",
      "\n",
      "def plot_gmm(gmm,sl=0):\n",
      "    '''Plot gaussians associated with a GMM.'''\n",
      "    splot = plt.subplot(111, aspect='equal')\n",
      "    X = gmm.sample(500)\n",
      "    Y = gmm.predict(X)\n",
      "    for i, (mean, covar, color) in enumerate(zip(gmm.means_, gmm.covars_, itertools.cycle (['r', 'g', 'b', 'c']))):\n",
      "        mean = mean[sl:sl+2]\n",
      "        covar = 10*covar[sl:sl+2,sl:sl+2]\n",
      "        v, w = eigh(covar)\n",
      "        u = w[0] / np.linalg.norm(w[0])\n",
      "        angle = 180 * np.arctan(u[1]/u[0]) / np.pi\n",
      "        plt.scatter(X[Y==i, 0], X[Y==i, 1], .1, color=color)\n",
      "        ellipse = Ellipse(mean, v[0], v[1], 180 + angle, color=color)\n",
      "        ellipse.set_alpha(0.6)\n",
      "        ellipse.set_clip_box(splot.bbox)        \n",
      "        splot.add_artist(ellipse)\n",
      "    plt.show()\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figure(figsize=(8,8))\n",
      "plot_gmm(gmm_list[60].gmm)\n"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x1041e75d0>"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## 1) Visualising a sequence of fitted GMMs \n",
      "\n",
      "The code below generates a video taking a 2D slice from the data. The data in this case are generated by drawing samples from the fitted models. "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from matplotlib import animation\n",
      "from matplotlib.patches import Ellipse\n",
      "import matplotlib.gridspec as gridspec\n",
      "import itertools\n",
      "\n",
      "def print_progress(counter=\"\", message=\"\"):\n",
      "    sys.stdout.write(\"%(counter)s: %(message)s\" %vars())\n",
      "    sys.stdout.flush()\n",
      "    sys.stdout.write(\"\\r\\r\")\n",
      "\n",
      "fig = plt.figure(figsize=(8, 8), dpi=220)\n",
      "\n",
      "SL = 0\n",
      "    \n",
      "def setup_gmm(gmm,sl=SL):\n",
      "    '''Plot gaussians associated with a GMM.'''\n",
      "    splot = plt.subplot(111, aspect='equal')\n",
      "    X = gmm.sample(500)\n",
      "    Y = gmm.predict(X)\n",
      "    #scatters = [None,None]\n",
      "    scatters = splot.scatter(X[:,0],X[:,1], alpha=0.1)\n",
      "    for i, (mean, covar, color) in enumerate(zip(gmm.means_, gmm.covars_, itertools.cycle (['r', 'g', 'b', 'c']))):\n",
      "        mean = mean[sl:sl+2]\n",
      "        covar = 15*covar[sl:sl+2,sl:sl+2]\n",
      "        v, w = eigh(covar)\n",
      "        u = w[0] / np.linalg.norm(w[0])\n",
      "        angle = 180 * np.arctan(u[1]/u[0]) / np.pi\n",
      "        #scatters[i] = splot.scatter(X[Y==i, 0], X[Y==i, 1], .1, color=color)\n",
      "        ellipse = Ellipse(mean, v[0], v[1], 180 + angle, color=color)\n",
      "        ellipse.set_url(str(i))\n",
      "        ellipse.set_alpha(0.6)\n",
      "        ellipse.set_clip_box(splot.bbox)        \n",
      "        splot.add_artist(ellipse)         \n",
      "    return splot,scatters\n",
      "\n",
      "def update_gmm(gmm,splot,scatters,sl=SL):\n",
      "    '''Update gaussians associated with a GMM.'''\n",
      "    X = gmm.sample(500)\n",
      "    Y = gmm.predict(X)\n",
      "    scatters.set_offsets(X)\n",
      "    for i, (mean, covar, color) in enumerate(zip(gmm.means_, gmm.covars_, itertools.cycle (['r', 'g', 'b', 'c']))):\n",
      "        mean = mean[sl:sl+2]\n",
      "        covar = 15*covar[sl:sl+2,sl:sl+2]\n",
      "        v, w = eigh(covar)\n",
      "        u = w[0] / np.linalg.norm(w[0])\n",
      "        angle = 180 * np.arctan(u[1]/u[0]) / np.pi\n",
      "        #scatters[i].set_offsets(X[Y==i, :])\n",
      "        e = [x for x in splot.artists if x.get_url() == str(i)][0]\n",
      "        splot.artists.remove(e)\n",
      "        ellipse = Ellipse(mean, v[0], v[1], 180 + angle, color=color)\n",
      "        ellipse.set_url(str(i))\n",
      "        ellipse.set_alpha(0.6)\n",
      "        ellipse.set_clip_box(splot.bbox)        \n",
      "        splot.add_artist(ellipse)         \n",
      "    return splot,scatters\n",
      "\n",
      "splot,scatters = setup_gmm(gmm_list[0].gmm)\n",
      "\n",
      "def animate(i) :\n",
      "    print_progress(i)\n",
      "    update_gmm(gmm_list[i].gmm, splot,scatters)\n",
      "    \n",
      "frames = len(gmm_list)\n",
      "\n",
      "a=animation.FuncAnimation(fig, animate, frames=frames, interval=10, blit=True)\n",
      "#a.save('/Users/mitian/Documents/hg/seg/notebooks/gmm_list2.mp4', fps=5, extra_args=['-vcodec', 'libx264'])\n",
      "a.save('../figs/Cache-10hongniang01-contrast6-dct-pcamean--wl20-ss10.mp4', fps=3)\n"
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        "553: "
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        "556: "
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        "558: "
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        "559: "
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        "561: "
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        "562: "
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        "\r",
        "\r",
        "563: "
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        "564: "
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        "\r",
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        "565: "
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       "text": [
        "\r",
        "\r",
        "566: "
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       "text": [
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        "567: "
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        "568: "
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        "569: "
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        "\r",
        "\r",
        "570: "
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        "571: "
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        "\r",
        "\r",
        "572: "
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        "\r",
        "\r",
        "573: "
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        "\r",
        "\r",
        "574: "
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        "\r",
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        "575: "
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        "\r",
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        "576: "
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       "text": [
        "\r",
        "\r",
        "577: "
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       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "\r",
        "578: "
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       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "\r",
        "579: "
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       "stream": "stdout",
       "text": [
        "\r",
        "\r",
        "580: "
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       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "\r",
        "581: "
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       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "\r",
        "582: "
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       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
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        "583: "
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       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "\r",
        "584: "
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       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "\r",
        "585: "
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      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        "\r",
        "586: "
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      {
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       "stream": "stdout",
       "text": [
        "\r",
        "\r"
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      {
       "ename": "LinAlgError",
       "evalue": "unrecoverable internal error.",
       "output_type": "pyerr",
       "traceback": [
        "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m\n\u001b[0;31mLinAlgError\u001b[0m                               Traceback (most recent call last)",
        "\u001b[0;32m<ipython-input-19-fb46ff615b3c>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     65\u001b[0m \u001b[0ma\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0manimation\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mFuncAnimation\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mfig\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0manimate\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mframes\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mframes\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0minterval\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m10\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mblit\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     66\u001b[0m \u001b[0;31m#a.save('/Users/mitian/Documents/hg/seg/notebooks/gmm_list2.mp4', fps=5, extra_args=['-vcodec', 'libx264'])\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 67\u001b[0;31m \u001b[0ma\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msave\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'../figs/Cache-10hongniang01-contrast6-dct-pcamean--wl20-ss10.mp4'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfps\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
        "\u001b[0;32m/Library/Python/2.7/site-packages/matplotlib/animation.pyc\u001b[0m in \u001b[0;36msave\u001b[0;34m(self, filename, writer, fps, dpi, codec, bitrate, extra_args, metadata, extra_anim, savefig_kwargs)\u001b[0m\n\u001b[1;32m    764\u001b[0m                 \u001b[0;32mfor\u001b[0m \u001b[0manim\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0md\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mzip\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mall_anim\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdata\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    765\u001b[0m                     \u001b[0;31m# TODO: Need to see if turning off blit is really necessary\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 766\u001b[0;31m                     \u001b[0manim\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_draw_next_frame\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0md\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mblit\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    767\u001b[0m                 \u001b[0mwriter\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgrab_frame\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0msavefig_kwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    768\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
        "\u001b[0;32m/Library/Python/2.7/site-packages/matplotlib/animation.pyc\u001b[0m in \u001b[0;36m_draw_next_frame\u001b[0;34m(self, framedata, blit)\u001b[0m\n\u001b[1;32m    801\u001b[0m         \u001b[0;31m# post- draw, as well as the drawing of the frame itself.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    802\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_pre_draw\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mframedata\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mblit\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 803\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_draw_frame\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mframedata\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    804\u001b[0m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_post_draw\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mframedata\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mblit\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    805\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
        "\u001b[0;32m/Library/Python/2.7/site-packages/matplotlib/animation.pyc\u001b[0m in \u001b[0;36m_draw_frame\u001b[0;34m(self, framedata)\u001b[0m\n\u001b[1;32m   1104\u001b[0m         \u001b[0;31m# Call the func with framedata and args. If blitting is desired,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1105\u001b[0m         \u001b[0;31m# func needs to return a sequence of any artists that were modified.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1106\u001b[0;31m         \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_drawn_artists\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_func\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mframedata\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_args\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
        "\u001b[0;32m<ipython-input-19-fb46ff615b3c>\u001b[0m in \u001b[0;36manimate\u001b[0;34m(i)\u001b[0m\n\u001b[1;32m     59\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0manimate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     60\u001b[0m     \u001b[0mprint_progress\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 61\u001b[0;31m     \u001b[0mupdate_gmm\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgmm_list\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mgmm\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msplot\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mscatters\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     62\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     63\u001b[0m \u001b[0mframes\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgmm_list\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
        "\u001b[0;32m<ipython-input-19-fb46ff615b3c>\u001b[0m in \u001b[0;36mupdate_gmm\u001b[0;34m(gmm, splot, scatters, sl)\u001b[0m\n\u001b[1;32m     36\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0mupdate_gmm\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mgmm\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0msplot\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mscatters\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0msl\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mSL\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     37\u001b[0m     \u001b[0;34m'''Update gaussians associated with a GMM.'''\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 38\u001b[0;31m     \u001b[0mX\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mgmm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msample\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m500\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     39\u001b[0m     \u001b[0mY\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mgmm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpredict\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     40\u001b[0m     \u001b[0mscatters\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mset_offsets\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
        "\u001b[0;32m/Library/Python/2.7/site-packages/sklearn/mixture/gmm.pyc\u001b[0m in \u001b[0;36msample\u001b[0;34m(self, n_samples, random_state)\u001b[0m\n\u001b[1;32m    409\u001b[0m                 X[comp_in_X] = sample_gaussian(\n\u001b[1;32m    410\u001b[0m                     \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmeans_\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mcomp\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcv\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcovariance_type\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 411\u001b[0;31m                     num_comp_in_X, random_state=random_state).T\n\u001b[0m\u001b[1;32m    412\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mX\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    413\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
        "\u001b[0;32m/Library/Python/2.7/site-packages/sklearn/mixture/gmm.pyc\u001b[0m in \u001b[0;36msample_gaussian\u001b[0;34m(mean, covar, covariance_type, n_samples, random_state)\u001b[0m\n\u001b[1;32m    100\u001b[0m         \u001b[0mrand\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdiag\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msqrt\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcovar\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mrand\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    101\u001b[0m     \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 102\u001b[0;31m         \u001b[0ms\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mU\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlinalg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0meigh\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcovar\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    103\u001b[0m         \u001b[0ms\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mclip\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mout\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m)\u001b[0m        \u001b[0;31m# get rid of tiny negatives\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    104\u001b[0m         \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msqrt\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mout\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0ms\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
        "\u001b[0;32m/Library/Python/2.7/site-packages/scipy/linalg/decomp.pyc\u001b[0m in \u001b[0;36meigh\u001b[0;34m(a, b, lower, eigvals_only, overwrite_a, overwrite_b, turbo, eigvals, type, check_finite)\u001b[0m\n\u001b[1;32m    399\u001b[0m                           \" fortran routine.\" % (-info))\n\u001b[1;32m    400\u001b[0m     \u001b[0;32melif\u001b[0m \u001b[0minfo\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m0\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mb1\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 401\u001b[0;31m         \u001b[0;32mraise\u001b[0m \u001b[0mLinAlgError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"unrecoverable internal error.\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    402\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    403\u001b[0m     \u001b[0;31m# The algorithm failed to converge.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
        "\u001b[0;31mLinAlgError\u001b[0m: unrecoverable internal error."
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x109c9dd90>"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%bash\n",
      "\n",
      "ls -lah | grep mp4 "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "-rw-r--r--@   1 mitian  staff   6.7M 26 Sep 19:27 Innuendo-wl80-ss20-f_getGMMs-SL0.mp4\n",
        "-rw-r--r--@   1 mitian  staff   6.7M 26 Sep 19:22 Innuendo-wl80-ss20-f_getGMMs-SL1.mp4\n",
        "-rw-r--r--@   1 mitian  staff   2.1M 25 Sep 20:37 gmm_list.mp4\n",
        "-rw-r--r--@   1 mitian  staff   1.5M 16 Sep 17:59 kl_divergence-5.mp4\n"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### 2) Visualising a sequence of fitted GMMs using projection \n",
      "\n",
      "Try to visualise a projection of higher dimensional data"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from matplotlib import animation\n",
      "from matplotlib.patches import Ellipse\n",
      "import matplotlib.gridspec as gridspec\n",
      "import itertools\n",
      "from sklearn.decomposition import PCA\n",
      "\n",
      "\n",
      "def print_progress(counter=\"\", message=\"\"):\n",
      "    sys.stdout.write(\"%(counter)s: %(message)s\" %vars())\n",
      "    sys.stdout.flush()\n",
      "    sys.stdout.write(\"\\r\\r\")\n",
      "\n",
      "fig = plt.figure(figsize=(8, 8), dpi=220)\n",
      "\n",
      "SL = 0\n",
      "\n",
      "def setup_gmm(gmm,sl=SL):\n",
      "    '''Plot gaussians associated with a GMM.'''\n",
      "    splot = plt.subplot(111, aspect='equal')\n",
      "    X = gmm.sample(500)\n",
      "    Y = gmm.predict(X)\n",
      "    pca = PCA(n_components=2)\n",
      "    pca.fit(X)\n",
      "    Z = pca.transform(X)\n",
      "    #scatters = [None,None]\n",
      "    #scatters = splot.scatter(X[:,0],X[:,1], alpha=0.1)\n",
      "    scatters = splot.scatter(Z[:,0],Z[:,1], alpha=0.1)\n",
      "    for i, (mean, covar, color) in enumerate(zip(gmm.means_, gmm.covars_, itertools.cycle (['r', 'g', 'b', 'c']))):\n",
      "        mean = mean[sl:sl+2]\n",
      "        covar = 15*covar[sl:sl+2,sl:sl+2]\n",
      "        v, w = eigh(covar)\n",
      "        u = w[0] / np.linalg.norm(w[0])\n",
      "        angle = 180 * np.arctan(u[1]/u[0]) / np.pi\n",
      "        #scatters[i] = splot.scatter(X[Y==i, 0], X[Y==i, 1], .1, color=color)\n",
      "        ellipse = Ellipse(mean, v[0], v[1], 180 + angle, color=color)\n",
      "        ellipse.set_url(str(i))\n",
      "        ellipse.set_alpha(0.6)\n",
      "        ellipse.set_clip_box(splot.bbox)        \n",
      "        splot.add_artist(ellipse)         \n",
      "    return splot,scatters\n",
      "\n",
      "def update_gmm(gmm,splot,scatters,sl=SL):\n",
      "    '''Update gaussians associated with a GMM.'''\n",
      "    X = gmm.sample(500)\n",
      "    Y = gmm.predict(X)\n",
      "    pca = PCA(n_components=2)\n",
      "    pca.fit(X)\n",
      "    Z = pca.transform(X)\n",
      "    scatters.set_offsets(Z)\n",
      "    for i, (mean, covar, color) in enumerate(zip(gmm.means_, gmm.covars_, itertools.cycle (['r', 'g', 'b', 'c']))):\n",
      "        mean = mean[sl:sl+2]\n",
      "        covar = 15*covar[sl:sl+2,sl:sl+2]\n",
      "        v, w = eigh(covar)\n",
      "        u = w[0] / np.linalg.norm(w[0])\n",
      "        angle = 180 * np.arctan(u[1]/u[0]) / np.pi\n",
      "        #scatters[i].set_offsets(X[Y==i, :])\n",
      "        e = [x for x in splot.artists if x.get_url() == str(i)][0]\n",
      "        splot.artists.remove(e)\n",
      "        ellipse = Ellipse(mean, v[0], v[1], 180 + angle, color=color)\n",
      "        ellipse.set_url(str(i))\n",
      "        ellipse.set_alpha(0.6)\n",
      "        ellipse.set_clip_box(splot.bbox)        \n",
      "        splot.add_artist(ellipse)         \n",
      "    return splot,scatters\n",
      "\n",
      "splot,scatters = setup_gmm(gmm_list[0].gmm)\n",
      "\n",
      "def animate(i) :\n",
      "    print_progress(i)\n",
      "    update_gmm(gmm_list[i].gmm, splot,scatters)\n",
      "    \n",
      "frames = len(gmm_list)\n",
      "\n",
      "a=animation.FuncAnimation(fig, animate, frames=frames, interval=10, blit=True)\n",
      "#a.save('/Users/mitian/Documents/hg/seg/notebooks/gmm_list2.mp4', fps=5, extra_args=['-vcodec', 'libx264'])\n",
      "a.save('/Users/mitian/Documents/hg/seg/notebooks/10hongniang01-mfccs-wl40-ss10-f_getGMMs-pickle.mp4', fps=3)\n"
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45Vf9Mq86+qoDl3kugVsIceA1t15LJXvdrvJmzYF7enqOJ59MEgi4lhPdcrz0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\nm8eOWQKWrLXfM8akgN8FftZa+9Gx41Q5TeQlmnYp0/Hs6dM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LwO4ph/1R4GeMMT/FoNiw\nb4z569baP3faOd9///3x44cPH/Lw4cPzfwIRubWUGS6z5NGjRzx69OjK57lKVvmvAGVr7S8bY74J\nZK21ZyaoGWN+EvgPlFUuIueZZp211mLLrLuOrPJfAr5hjPkB8M8Nv8YYs2KM+XtnvEaRWUTONdqB\ny/dbuG4Vz7MEQePIPPdN2+5T5HVRARYRubEm9arP2xBF5Ka7jh63iMgrNalX/apqpYvcdNodTERm\n0mg4/UUg1/y23A4K3CJyY/l+kkqlQrUaUq8PetX5/PL4+ctsFyoy6zRULiI3luu6FAoe1WoRay3p\ndIFisaliLHKrqcctIjdaGPbI5+8eSUJTMRa5zdTjFhERmSEK3CJyoyl7XOQoreMWkRtPpU3li+iy\n67gVuEVERK6BCrCIiIjcAgrcIiIiM0SBW0REZIYocIuIiMwQBW4REZEZosAtIiIyQxS4RUREZogC\nt4iIyAxR4BYREZkhCtwiIiIzRIFbRERkhihwi4iIzBAFbhERkRmiwC0iIjJDFLhFRERmiAK3iIjI\nDFHgFhERmSEK3CIiIjNEgVtERGSGKHCLiIjMEAVuERGRGaLALSIiMkMUuEVERGaIAreIiMgMUeAW\nERGZIQrcIiIiM+TSgdsYs2CM+cAY8wNjzHeMMdkzjssaY37DGPORMeZDY8xPXL65IiIit9tVetzf\nBD6w1n4F+K3h16f5r4BvW2sfAH8E+OgK1xQREbnVjLX2ci805mPgJ621RWPMEvDIWvvOsWMywHet\ntfemOJ+9bFtERERmjTEGa6256Ouu0uMuWGuLw8dFoHDKMW8DJWPMXzPG/J4x5teMMckrXFNERORW\nmxi4h3PY3z/lv585fNywq3xadzkKfB34K9barwMHnD2kLiIiIueITnrSWvuNs54zxhSNMUvW2h1j\nzDKwe8phG8CGtfb/G379G0wI3O+///748cOHD3n48OGk5omIiMyMR48e8ejRoyuf5ypz3L8ClK21\nv2yM+SaQtdaeCMrGmH8E/Ly19gfGmPcBz1r7C6ccpzluERG5NS47x32VwL0A/DpwF3gC/Jy1tmKM\nWQF+zVr708PjfgT4q0Ac+Bz489ba6innU+AWEZFb47UH7pdNgVtERG6T68gqFxERkddMgVtERGSG\nKHCLiIjMEAVuERGRGaLALSIiMkMUuEVERGaIAreIiMgMUeAWERGZIQrcIiIiM0SBW0REZIYocIuI\niMwQBW4REZEZosAtIiIyQxS4RUREZogCt4iIyAxR4BYREZkhCtwiIiIzRIFbRERkhihwi4iIzBAF\nbhERkRmiwC0iIjJDFLhFRERmiAK3iIjIDFHgFhERmSEK3CIiIjNEgVtERGSGKHCLiIjMEAVuERGR\nGaLALSIiMkMUuEVERGaIAreIiMgMUeAWERGZIQrcIiIiM0SBW0REZIYocIuIiMwQBW4REZEZcunA\nbYxZMMZ8YIz5gTHmO8aY7BnH/WVjzD8zxnzfGPM/GWPcyzdXRETkdrtKj/ubwAfW2q8AvzX8+ghj\nzFvAXwS+bq39w0AE+JevcE25gR49enTdTZAr0Ps32/T+3T5XCdw/A3xr+PhbwM+eckwAdICkMSYK\nJIHNK1xTbiD94Zhtev9mm96/2+cqgbtgrS0OHxeBwvEDrLXPgf8CWAe2gIq19u9f4ZoiIiK3WnTS\nk8aYD4ClU576xcNfWGutMcae8vovAf8e8BZQBf6OMeZftdb+zUu3WERE5BYz1p6It9O90JiPgYfW\n2h1jzDLwD6y17xw75s8C37DW/vzw638d+Alr7b9zyvku1xAREZEZZa01F33NxB73Of4u8G8Avzz8\n/2+ecszHwH9qjPGAFvDHgf/3tJNdpvEiIiK3zVV63AvArwN3gSfAz1lrK8aYFeDXrLU/PTzuP2IQ\n2PvA7wE/b63tvIS2i4iI3DqXDtwiIiLy+l1b5TRjzL80LMzSM8Z8fcJxf8IY87Ex5lNjzC+8zjbK\n6S5QfOeJMeafGmO+a4w5dYpEXp9pPkvGmF8dPv/7xpj3Xncb5XTnvXfGmIfGmOrws/ZdY8x/ch3t\nlJOMMf+jMaZojPn+hGMu9Lm7zpKn3wf+DPCPzjrAGBMB/hvgTwDvAv+KMebB62meTHBu8Z0hyyCB\n8T1r7Y+9ttbJCdN8lowxPwXct9Z+Gfg3gf/2tTdUTrjA38F/OPysvWet/c9fayNlkr/G4L071WU+\nd9cWuK21H1trf3DOYT8GfGatfTKcF/9bwL/w6lsn55im+M6Ikg5vhmk+S+P31Vr720DWGHOiPoO8\ndtP+HdRn7Qay1v7fwP6EQy78ubvpm4ysAs8Ofb0x/J5cr3OL7wxZ4O8bY37HGPMXX0/T5AzTfJZO\nO2btFbdLzjfNe2eBPzocav22Mebd19Y6uaoLf+6ushzsXBMKuPzH1tr/fYpTKHPumly1+M7QH7PW\nbhtj8sAHxpiPh3ef8vpN+1k63mvTZ/D6TfMe/B7whrW2YYz5kwyW537l1TZLXqILfe5eaeC21n7j\niqfYBN449PUbDO5G5BWb9N4NEy2WDhXf2T3jHNvD/5eMMf8bgyE/Be7rMc1n6fgxa2hvgZvg3PfO\nWls79Pj/MMb8FWPMwrDstNxsF/7c3ZSh8rPmZn4H+LIx5i1jTBz4swwKv8j1GhXfgTOK7xhjksaY\n9PDxHPDPM0hIlOsxzWfp7wJ/DsAY8xMM9hYoItft3PfOGFMwxpjh4x9jsNRXQXs2XPhz90p73JMY\nY/4M8KtADvh7xpjvWmv/5OECLtbarjHm3wX+LwZbgv4P1tqPrqvNMvZLwK8bY/4Cw+I7AMeK7ywB\n/+vwb0kU+JvW2u9cT3PlrM+SMebfGj7/31lrv22M+SljzGfAAfDnr7HJMjTNewf8i8C/bYzpAg20\nffKNYYz5n4GfBHLGmGfAfwbE4PKfOxVgERERmSE3ZahcREREpqDALSIiMkMUuEVERGaIAreIiMgM\nUeAWERGZIQrcIiIiM0SBW0REZIYocIuIiMyQ/x+XsM2xcAqkywAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10fb45a90>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}