view notebook/Gaussian-KLdiv-study.ipynb @ 19:890cfe424f4a tip

added annotations

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   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Demonstrating KL divergence between Gaussian models \n",
      "\n",
      "This script helps to assess the behaviour of the KL divergence under basic transformations of data such as \n",
      "- rotation\n",
      "- shift\n",
      "- scaling\n",
      "    \n",
      "and a few basic combinations of these.\n",
      "\n",
      "Notes:\n",
      "- The JSAnimation package is required to display the animation inside the notebook. \n",
      "- Uncomment the relevant animation function at the bottom of the script to generate video or display in the notebook.\n",
      "- At the moment 1800 frames are generated for various transformations, (360 degrees each). This takes a while to compute or render."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#from JSAnimation import IPython_display\n",
      "from matplotlib import animation\n",
      "\n",
      "from matplotlib.patches import Ellipse\n",
      "import matplotlib.gridspec as gridspec\n",
      "import itertools\n",
      "\n",
      "import sys\n",
      "sys.path.insert(0, '../')\n",
      "from gmmdist import _skl_full as skl_full\n",
      "from gmmdist import kldiv_full\n",
      "\n",
      "from scipy.stats import norm\n",
      "from scipy.signal import sawtooth\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",
      "save = True\n",
      "    \n",
      "if save :\n",
      "    fig = plt.figure(figsize=(14, 10), dpi=220)\n",
      "    pad = 9.0\n",
      "else :\n",
      "    fig = plt.figure(figsize=(8, 6), dpi=100, facecolor=\"0.95\", tight_layout=False)\n",
      "    pad = 3.0\n",
      "suptitle(\"KL divergence between Gaussian distributions\", fontsize=\"16\", fontweight=\"medium\")\n",
      "gs = gridspec.GridSpec(2, 1, width_ratios=[2.5,1])\n",
      "splot = plt.subplot(gs[0], aspect='equal', xlim=(-10, 10))\n",
      "title(\"Op: none frame: 0\", fontsize=\"14\", family=\"monospace\") # this will be changed in animation\n",
      "splot2 = plt.subplot(gs[1], xlim=(0, 360), ylim=(-0.1, 3.0), xlabel=\"frame\", ylabel=\"divergence\")\n",
      "title(\"KL divergence\", fontsize=\"14\", family=\"monospace\")\n",
      "#gs.tight_layout(fig, rect=[0.15, 0.0, 1.05, 1.0], h_pad=5.5)\n",
      "gs.tight_layout(fig, rect=[0.15, 0.0, 1.05, 1.0], h_pad=pad)\n",
      "#gs = gridspec.GridSpec(2, 1, width_ratios=[2,2],height_ratios=[2,2.2])\n",
      "\n",
      "def setup_gaussians(X, gaussians, nlines=1 ):\n",
      "    '''Plot individual gaussians [(m,c),(m,c),...,(m,c)].'''\n",
      "    ellipses = []\n",
      "    lines = []\n",
      "    for line in xrange(nlines) :\n",
      "        l, = splot2.plot([], [], lw=2)\n",
      "        lines.append(l)\n",
      "    if len(lines) == 3:\n",
      "        lines[0].set_label(\"Symm\")\n",
      "        lines[1].set_label(\"kl12\")\n",
      "        lines[2].set_label(\"kl21\")\n",
      "        lines[1].set_linestyle(\"--\")\n",
      "        lines[1].set_linewidth(1.5)\n",
      "        lines[2].set_linestyle(\"--\")\n",
      "        lines[2].set_linewidth(1.5)\n",
      "        plt.legend(handles=lines)\n",
      "\n",
      "    scat = splot.scatter(X[:,0],X[:,1], alpha=0.03)\n",
      "    for i, ((mean, covar), color) in enumerate(zip(gaussians, itertools.cycle (['r', 'g', 'b', 'c']))):\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",
      "        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",
      "        ellipses.append(ellipse)\n",
      "    #plt.show()\n",
      "    return ellipses,scat,lines\n",
      "\n",
      "mu1, scale1 = 0.0, 1.0\n",
      "X1 = np.array(map(lambda x: norm.rvs(mu1, scale1, size=2),xrange(1000)))\n",
      "\n",
      "#scale the x dimemsion\n",
      "X1[:,0] = X1[:,0] * 2.0\n",
      "#X1 = shift(X1,20)\n",
      "\n",
      "a = 0\n",
      "fi = pi*-a/180\n",
      "C = np.array([[cos(fi), -sin(fi)], [sin(fi), cos(fi)]])\n",
      "X1 = np.dot(X1, C)\n",
      "\n",
      "m1 = mean(X1,axis=0)\n",
      "c1 = cov(X1.T)\n",
      "\n",
      "ellipses,scat,lines = setup_gaussians(X1,[(m1,c1),(m1,c1)], nlines=3)\n",
      "\n",
      "def update_gaussians(X, gaussians, ellipses, scat, splot):\n",
      "    '''Update individual gaussians [(m,c),(m,c),...,(m,c)].'''\n",
      "    scat.set_offsets(X)\n",
      "    for i, ((mean, covar), color) in enumerate(zip(gaussians, itertools.cycle (['r', 'g', 'b', 'c']))):\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",
      "        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 ellipses,scat\n",
      "\n",
      "\n",
      "\n",
      "PREV = 0\n",
      "ROTATE = 0\n",
      "SHIFT = 1\n",
      "SCALE = 2\n",
      "frames = 360\n",
      "div = frames/4\n",
      "\n",
      "divergences = zeros(frames)\n",
      "dkl12 = zeros(frames)\n",
      "dkl21 = zeros(frames)\n",
      "meta = {}\n",
      "\n",
      "def rotate(X, i, scale=1.0):\n",
      "    angle = i\n",
      "    fi = pi * -angle / 180.0\n",
      "    C = scale * np.array([[cos(fi), -sin(fi)], [sin(fi), cos(fi)]])\n",
      "    Y = np.dot(X, C)\n",
      "    meta[\"angle\"] = fi\n",
      "    meta[\"op\"] = meta.pop(\"op\",\"\") + \"rotation \"\n",
      "    return Y\n",
      "\n",
      "def shift(X,i):\n",
      "    fi = pi * (i+90.0) / 180.0\n",
      "    shift = 5.0 * sawtooth(fi, width=0.5)\n",
      "    Y = copy(X)\n",
      "    Y[:,0] += shift\n",
      "    meta[\"shift\"] = shift\n",
      "    meta[\"op\"] = meta.pop(\"op\",\"\") + \"shift \"\n",
      "    return Y\n",
      "\n",
      "def scale(X, i):\n",
      "    fi = pi * (i+90.0) / 180.0\n",
      "    scale = 1.0*sawtooth(fi, width=0.5)+1.0\n",
      "    if scale < 0.05 : scale = 0.05\n",
      "    C = scale * np.array([[1.0,0.0], [0.0,1.0]])\n",
      "    Y = np.dot(X, C)\n",
      "    meta[\"scale\"] = scale\n",
      "    meta[\"op\"] = meta.pop(\"op\",\"\") + \"scale \"\n",
      "    return Y\n",
      "\n",
      "def rotshift(X, i):\n",
      "    meta[\"mult\"] = 0.1\n",
      "    return shift(rotate(X,i),i)\n",
      "\n",
      "def rotscale(X, i):\n",
      "    meta[\"mult\"] = 0.2\n",
      "    return scale(rotate(X,i),i)\n",
      "\n",
      "transforms = {0:rotate, 1:shift, 2:scale, 3:rotshift, 4:rotscale}\n",
      "start_from = 0\n",
      "\n",
      "def animate(i) :\n",
      "    i = i + (start_from*frames)\n",
      "    print_progress(i)\n",
      "    meta.clear()\n",
      "    t1 = fig.axes[0].title\n",
      "    t2 = fig.axes[1].title\n",
      "    sel = int(i/frames)\n",
      "    transform = transforms[sel]\n",
      "    X2 = transform(X1,i%frames)\n",
      "    m2 = mean(X2,axis=0)\n",
      "    c2 = cov(X2.T)\n",
      "    d=skl_full(m1,m2,c1,c2)\n",
      "    d12=kldiv_full(m1,m2,c1,c2)\n",
      "    d21=kldiv_full(m2,m1,c2,c1)\n",
      "    t1.set_text(\"Op: %s frame %3i\" %(meta.pop(\"op\",\"unknown\"),i))\n",
      "    t1.set_family(\"monospace\")\n",
      "    props = \" \".join([\"%s: %3.2f\" %(k,v) for k,v in meta.iteritems()])\n",
      "    t2.set_text(\"KL divergence:  %3.2f  %s\" %(d,props))\n",
      "    t2.set_family(\"monospace\")\n",
      "    dscale = float(meta.pop(\"mult\",1.0))\n",
      "    divergences[i%frames] = d * dscale\n",
      "    dkl12[i%frames] = d12 * dscale\n",
      "    dkl21[i%frames] = d21 * dscale\n",
      "    update_gaussians(X2, [(mean(X1,axis=0),cov(X1.T)),(m2,c2)], ellipses, scat, splot)\n",
      "    lines[0].set_data(np.linspace(0, frames-1, frames)[0:i%frames],divergences[0:i%frames])\n",
      "    lines[1].set_data(np.linspace(0, frames-1, frames)[0:i%frames],dkl12[0:i%frames])\n",
      "    lines[2].set_data(np.linspace(0, frames-1, frames)[0:i%frames],dkl21[0:i%frames])\n",
      "    return None\n",
      "\n",
      "#animation.FuncAnimation(fig, animate, frames=frames, interval=10, blit=True)\n",
      "\n",
      "if not save :\n",
      "    pass\n",
      "    #animation.FuncAnimation(fig, animate, frames=5*frames, interval=10, blit=True)\n",
      "else :\n",
      "    #a=animation.FuncAnimation(fig, animate, frames=5*frames, interval=10, blit=True)\n",
      "    #a.save('kl_divergence-5.mp4', fps=30, extra_args=['-vcodec', 'libx264'])\n",
      "    pass"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
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       "output_type": "display_data",
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olzoqJBXlEuE4JzTtRgzu1bxkWcbGRh+IylCN4yTUJzHLD0BjDINBjkgTgMEg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\ngg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x4694a10>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}