examples/Example.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "from time import time\n",
    "from timeit import timeit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from xlines import utils, KLines, XLines"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def rotated_cov(a, l1, l2, radians = False):\n",
    "    r = utils.rotation_matrix(a, radians)\n",
    "    d = np.diag([l1, l2])\n",
    "    return np.dot(r, np.dot(d, r.T))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example with 4 lines"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\MyPrograms\\Anaconda\\lib\\site-packages\\matplotlib\\collections.py:571: FutureWarning: elementwise comparison failed; returning scalar instead, but in the future will perform elementwise comparison\n",
      "  if self._edgecolors == str('face'):\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXoAAAEACAYAAAC9Gb03AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAFHRJREFUeJzt3XuMnFd5x/Hfr3Yt7ybtRMh0bZIgJ3Io2KJcqqa4dcVQ\n6guoIrUQSvgDxdCgSuklqixEHCS8Uf8oCLltWhQJiYuRVUKQSiJHAdYLzaisaoKiODSN49or101c\nnIWIsI2zu7JjP/1j3l2P9zK7c3ln3jnz/Ugjzfu+s3POyTqPzj7n5ogQACBdv9LtCgAA8kWgB4DE\nEegBIHEEegBIHIEeABJHoAeAxLUc6G1/1faE7Wdr7r3B9qjtk7aP2L6u1XIAAM1pR4/+a5J2zbt3\nr6TRiHiLpB9k1wCALnA7FkzZ3ijpsYh4e3Z9QtJ7I2LC9npJlYh4a8sFAQAalleOfigiJrL3E5KG\ncioHALCM3Adjo/onA/ssAECXrM7peydsr4+Il2xvkPSz+R+wTfAHgCZEhBv5fF49+sOS7sze3ynp\n0cU+FBHJvvbv39/1OtA+2teP7Uu5bRHN9Y/bMb3yIUn/Luk3bb9o++OSPidpu+2Tkv4wuwYAdEHL\nqZuI+OgSj/6o1e8GALSOlbE5KZfL3a5Crmhfb0u5fSm3rVltmUffVMF2dKtsAOhVthUFGYwFABQE\ngR4AEkegB4DEEegBIHEEegBIHIEeABJHoAeAxBHoASBxBHoASByBHgASR6AHgMQR6AEgcQR6AEgc\ngR4AEkegB4DEEegBIHEEegBIHIEeABJHoAeAxBHoASBxBHoASNzqPL/c9hlJ/yfpkqSLEXFrnuUB\nABbKNdBLCknliPhFzuUAAJbQidSNO1AGAGAJeQf6kPR920/Z/mTOZQEAFpF36ub3I+Kc7TdKGrV9\nIiJ+OPtweHh47oPlclnlcjnn6gBAb6lUKqpUKi19hyOiPbVZriB7v6TzEXEgu45OlQ0AqbCtiGgo\nJZ5b6sb2oO1fy95fI2mHpGfzKg8AsLg8UzdDkh6xPVvOP0fEkRzLA4C2G5ua0sHJSUnSnlJJ2wYH\nu1yjxnUsdbOgYFI3AApubGpK90xMaCaLVWttPTA01NVgX6jUDQD0uoOTk3NBXpJmIuZ6972EQA8A\niSPQA8AS9pRKWusrWZK1tvaUSl2sUXPI0QNAHUUbjG0mR0+gB4AewmAsAGABAj0AJI5ADwCJI9AD\nQOII9ACQOAI9ACSOQA8AiSPQA0DiCPQAkDgCPQAkjkAPAIkj0ANA4gj0AJA4Aj0AJI5ADwCJI9AD\nyxgfkQ7tqL7GR7pdG6BxHDyCvjA+Ih09UH2/da+0aefKf+7h3dLr09Xr1QPS7Y+s/OeBduOEKWAR\nrQTrQzuk06NX37t5u/SxI+2vJ7AShTphyvYu2ydsn7L96bzKAZZz9MCVIC9V38/27oF+kEugt71K\n0hcl7ZK0WdJHbb8tj7KAPG3dW/0LYNbqgeo9oJfk1aO/VdJ4RJyJiIuSvinptpzKAupqJVhv2llN\n89y8vfoiP49etDqn771e0os112cl/W5OZQF1zQbrZgZjZ3+e4I5ellegX9Eo6/Dw8Nz7crmscrmc\nU3XQ7wjW6FWVSkWVSqWl78hl1o3t90gajohd2fU+SZcj4vM1n2HWDQA0qEizbp6SdIvtjbbXSLpd\n0uGcygIA1JFL6iYiXrf9F5JGJK2S9JWIeD6PsgAA9bFgCgB6SJFSNwCAgiDQo6ewwRjQOFI36Bls\nMAaQukHiVrpnDb1+4Gp5LZhC4prd9jdv83v9L4zR6y+K81PjennyqCRpXWmrrh3c1OUa9Q969GjY\nbDA9PVp9Pby7Mz3nlexZw06VxXR+alwvTDys16ZP67Xp03ph4mGdnxrvdrX6BoEeDetWMGWDsd71\n8uRRRbw+dx3x+lzvHvkjdYOestyeNVv3VtM1tQO2bCuMfkePHg1rZdvfvAdK6fUX07rSVtlX+pX2\naq0rbe1ijfoL0yvRlGYGY5ke2d8YjG0PzoxFoXH+KtA65tEDABYg0KNjOH8V6A5SN+iooi60SsnY\n1JQOTk5KkvaUSto2ONjlGqGdyNGjawjgxTA2NaV7JiY0k/2/tdbWA0NDBPuENBPomUePlrHtQHEc\nnJycC/KSNBOhg5OTXQ30zLbpPnL0aBnbDiw0NjWlu86d013nzmlsaqrb1ekatj4oBnr0QJvNT588\nNT2tTWvW6LpVq3LPme8plXRsZuaq1M2eUim38paz1NYH9Oo7ix49WsZsmqvNT59clPT8hQs6Oj2t\neyYmcu3hbxsc1ANDQ9o6MKCtAwPk5yGJHj3aYHbbAQZjl9eJnPm2wcGWvr+dOfV1pa2amnlhrlfP\n1gfdwawboM3mp27m2zowoC9v2NDhWq3MbE69NjC/eej2loI9g7HtxawboABm0ycHJyf1y0uXNH7h\ngi5mz7qdM19OHjn1awc3Edy7jEAP5KA2fcICJnRbLoHe9rCkuyT9PLu1LyK+l0dZQNG1mjPvJHLq\nacolR297v6RXI+Lv6nyGHD1QQOTUi61oOfqGKgKgGMippyfPefR/afsntr9i+7ocy8Ei8j7JqRfV\nW63KSlakrOnUje1RSesXefQZST/Slfz830jaEBF/Ou/nY//+/XPX5XJZ5XK5qbrgapzktFC9zb7Y\nCAxFVqlUVKlU5q7vv//+4u1eaXujpMci4u3z7pOjzwknOS1017lzOjo9fdW92fns9Z4BRVOYHL3t\nDRFxLrvcLenZPMpJHVv/YqUYQEU9eQ3Gft72OyWFpP+W9Gc5lZOsVrb+3bq3+vna1E0/7z0j1d/s\nq2gbgTVq/mrWqZkXWl7NirSwBUJBtZp+4a+BheotXOrlRU1nzh3Sa9Onr7p3zcDN2rjhY12qEfJU\nmNQNum/TToL7fPUWLvXSoiagUWxTXFBs/YuVWlfaKvtKn2251aznp8Z15twhnTl3iENA+gSpmwIj\n/YKVWulgbB67U6KzOBwcQF3k83tfM4Ge1A0AJI7B2AIhVYNZec2LZ3fK/kTqpiDYtgCz8s6js7iq\ntzG9socdPXAlyEvV90cPEOj7UR6nPNVid8r+Q44eABJHoC8I5s33n6Xmszc6Lx5YDjn6AmEwtn8s\nl4cnj46lMI8e6BHMZ0ezmEcP9LDXL/XQyVYjI9KOHdXXCEeYFR2zboAuWFfaqtemz0i6PHfvwoWf\n6/zUePHTNCMj0u7d0uxhLWNj0iOPSDvJNRYVPXpIyu/MVM5iXdy1g5u0ds1vXHUvdGkuL19oBw5c\nCfJS9f2BA92rD5ZFjx4Lzkw9NjPTljNT8/revHVqIHTVqmL/d0A66NFDBycn54KxJM1EzB3CUcTv\nzdPsbJjXpk/rtenTemHi4dy28u3ZaZR790oDNXOBBwaq91BYBHqgxlKrUvNw7eAmvXnodl0zcLOu\nGbi5d7YL3rmzmpPfvr36Ij9feKRukNuZqb1wFuv8NE2n9ex2BDt3Etx7CPPoE9Hqmad5nZla5LNY\nF1u09Mbr/kA//+UPOZgDhcWCqT41f9Bzrd0Tg57dttSipXWlraxKRWGxe2WfWmrQk0DfnJ5NpwBL\nYDAWfatnZ70ADWo60Nv+iO3nbF+y/e55z/bZPmX7hO0drVcT9ewplbTWV/6SK+KgZxH17KwXoEFN\n5+htv1XV9dtfkrQ3Ip7O7m+W9A1JvyPpeknfl/SWiLg87+fJ0bdRkQc9AbRPR3P0EXFittB5bpP0\nUERclHTG9rikWyX9qNmysLxtg4MEdwCLyiNH/yZJZ2uuz6raswcAdEHdHr3tUUnrF3l0X0Q81kA5\ni+ZohoeH596Xy2WVy+UGvhIA0lepVFSpVFr6jpbn0dt+Qlfn6O+VpIj4XHb9PUn7I+LJeT9Hjh4A\nGtTNg0dqCz0s6Q7ba2zfJOkWST9uUzkAgAa1Mr1yt+0XJb1H0uO2vytJEXFc0rckHZf0XUl303UH\nmsRJTmgDtkAAimr+SU4DA+wUCc6MBZLCSU5oEwI9UFQvv9ztGiARBHqgiEZGpOeeu/remjWc5ISm\nEOiBIjpwQLpw4ep7W7aQn0dTCPRAr1i3rts1QI8i0AOdtNLpkhzAjTZieiXQKY1OlxwZuTLLZu9e\n0jaQxPRKoNgamS5JkEcbcZQgUDTze/5jYyyUQkvo0QOdstK8Owul0GYEeqBTdu6s9sy3b6++6KWj\nQxiMBZbT6Xw5e9ygjmYGYwn0QD3dCroMxmIJBHqg3XbskEZHr763fbt05Eh36oO+x/RKAMACBHqg\nHlaoIgGkblowNjWlg5OTkqQ9pZK2DQ52uUbIBflyFAg5+g4am5rSPRMTmsnasNbWA0NDBHsAuSJH\n30EHJyfngrwkzUTM9e4BoEgI9ACQOAJ9k/aUSlrrK389rbW1p1TqYo0AYHHk6FvAYCyATmMwFgAS\n19HBWNsfsf2c7Uu2311zf6PtadvHsteDzZYBLGulJzYBfayV/eiflbRb0pcWeTYeEe9q4buB5bFv\nO7AiTffoI+JERJxsZ2WAhrBvO7Aiec26uSlL21Rsb8upDADACtRN3dgelbR+kUf3RcRjS/zYTyXd\nGBGvZLn7R21viYhX539weHh47n25XFa5XF5pvYHqdgRjY1dvIcw+NEhMpVJRpVJp6TtannVj+wlJ\neyPi6UaeM+sGbcE+NOgzzcy6adfh4HOF2l4n6ZWIuGT7Zkm3SDrdpnLQDxoJ3jt3EtyBZTTdo7e9\nW9I/SlonaVLSsYj4gO0PS7pf0kVJlyV9NiIeX+Tn6dFjIY7RA+piwRR6Hyc6AXWxeyUAYAECPdqj\nXStUOdEJaDtSN2hdu/PqzKQBlkSOHt1BXh3oGHL0AIAFCPRoHXl1oNBI3aA9yKsDHUGOHgASR44e\nALAAgR4AEkegB4DEEegBIHEEegBIHIEeABJHoAeAxBHoASBxBPp+1q6thQEUGitj+xVH9gE9iZWx\nWLkDB64Eean6fnavGgBJIdADQOII9P2KrYWBvkGOvp+xtTDQc9imGAAS19HBWNtfsP287Z/Y/rbt\nUs2zfbZP2T5he0ezZQAAWtdKjv6IpC0R8Q5JJyXtkyTbmyXdLmmzpF2SHrTNWAAAdEnTATgiRiPi\ncnb5pKQbsve3SXooIi5GxBlJ45JubamWAICmtaun/QlJ38nev0nS2ZpnZyVd36ZyAAANWl3voe1R\nSesXeXRfRDyWfeYzki5ExDfqfNWio67Dw8Nz78vlssrl8jLVBYD+UqlUVKlUWvqOlmbd2N4j6ZOS\n3h8RM9m9eyUpIj6XXX9P0v6IeHLezzLrBgAa1OlZN7skfUrSbbNBPnNY0h2219i+SdItkn7cbDkA\ngNbUTd0s458krZE0aluSjkbE3RFx3Pa3JB2X9Lqku+m6A0D3sGAKAHoIu1cCABYg0ANA4gj0AJA4\nAj0AJI5ADwCJI9ADQOII9ACQOAI9ACSOQA8AiSPQA0DiCPQAkDgCPQAkjkAPAIkj0ANA4gj0AJA4\nAj0AJI5ADwCJI9ADQOII9ACQOAI9ACSOQA8AiSPQA0Dimg70tr9g+3nbP7H9bdul7P5G29O2j2Wv\nB9tXXQBAo1rp0R+RtCUi3iHppKR9Nc/GI+Jd2evulmrYoyqVSrerkCva19tSbl/KbWtW04E+IkYj\n4nJ2+aSkG9pTpTSk/o+N9vW2lNuXctua1a4c/Sckfafm+qYsbVOxva1NZQAAmrC63kPbo5LWL/Lo\nvoh4LPvMZyRdiIhvZM9+KunGiHjF9rslPWp7S0S82s6KAwBWxhHR/A/beyR9UtL7I2Jmic88IWlv\nRDw9737zBQNAH4sIN/L5uj36emzvkvQpSe+tDfK210l6JSIu2b5Z0i2STrdaUQBAc5ru0ds+JWmN\npF9kt45GxN22PyzpfkkXJV2W9NmIeLwdlQUANK6l1A0AoPg6vjJ2qYVW2bN9tk/ZPmF7R6fr1g62\nP2L7OduXssHo2mc93z6pmrbL2nDK9qe7XZ9W2P6q7Qnbz9bce4PtUdsnbR+xfV0369gK2zfafiL7\nN/mftv8qu59EG22vtf2k7WdsH7f9t9n9JNonSbZXZbMYZyfANNy2bmyBsOhCK9ubJd0uabOkXZIe\ntN2LWzQ8K2m3pH+rvZlK+2yvkvRFVduwWdJHbb+tu7VqyddUbUuteyWNRsRbJP0gu+5VFyX9dURs\nkfQeSX+e/b6SaGM2Pvi+iHinpN+S9L5sSncS7cvcI+m4pNn0S8Nt63igqbPQ6jZJD0XExYg4I2lc\n0q2drl+rIuJERJxc5FES7VO1zuMRcSYiLkr6pqpt60kR8UNJr8y7/SFJX8/ef13Sn3S0Um0UES9F\nxDPZ+/OSnpd0vdJq41T2do2kVar+PpNon+0bJH1Q0pclzU5gabht3e5R1i60epOkszXPzqr6DzIV\nqbTvekkv1lz3ajvqGYqIiez9hKShblamXWxvlPQuVTtYybTR9q/YfkbVdjwREc8pnfb9vaqzGy/X\n3Gu4bU1Pr6ynyYVWiynkSPFK2rdChWzfMnqxzk2LiEhhzYftayX9i6R7IuJV+8rs5l5vY5YheGc2\n3jdi+33znvdk+2z/saSfRcQx2+XFPrPStuUS6CNie73n2UKrD0p6f83t/5V0Y831Ddm9wlmufUvo\nmfYtY347btTVf6mkYML2+oh4yfYGST/rdoVaYftXVQ3yhyLi0ex2Um2UpIiYtP24pN9WGu37PUkf\nsv1BSWsl/brtQ2qibd2YdTO70Oq2eatpD0u6w/Ya2zeputDqx52uX5vVLgpLpX1PSbol2456jaoD\nzIe7XKd2Oyzpzuz9nZIerfPZQnO16/4VSccj4h9qHiXRRtvrZmed2B6QtF3SMSXQvoi4LyJujIib\nJN0h6V8j4mNqpm0R0dGXpFOS/kfVX8YxSQ/WPLtP1UHKE5J2drpubWrfblVz2NOSXpL03ZTal7Xj\nA5L+K2vLvm7Xp8W2PKTq/kwXst/bxyW9QdL3VZ0VdkTSdd2uZwvt26ZqfveZmv/ndqXSRklvl/R0\n1r7/kPSp7H4S7atp53slHW62bSyYAoDEdXvWDQAgZwR6AEgcgR4AEkegB4DEEegBIHEEegBIHIEe\nABJHoAeAxP0/9KKy/RnQmUIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x8d967f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Number of samples per component\n",
    "n_samples = 10\n",
    "\n",
    "# Generate random sample, 4 components\n",
    "np.random.seed(0)\n",
    "COV = rotated_cov(20, 100., 0.5)  # covariance matrix\n",
    "origins = [[10., 0.], [10., -5.], [10., -9.], [8., -14.]]\n",
    "# origins = [[10., 0.], [10., -5.], [8., -20.]]\n",
    "\n",
    "# Data\n",
    "Xs = [np.random.multivariate_normal(O, COV, size=n_samples) for O in origins]\n",
    "X = np.concatenate(Xs, axis=0)\n",
    "\n",
    "colors = mpl.cm.rainbow(np.linspace(0, 1, len(Xs)))\n",
    "for x,c in zip(Xs,colors):\n",
    "    plt.scatter(x[:, 0], x[:, 1], color=c)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## KLines with k=4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Selected alpha=40.0 at init\n",
      "Kmeans w/ proj 40.00: -91.99\n",
      "Kmeans w/ proj 34.51: -64.73\n",
      "Kmeans w/ proj 29.91: -57.83\n",
      "Kmeans w/ proj 26.06: -36.82\n",
      "Kmeans w/ proj 22.56: -19.34\n",
      "Kmeans w/ proj 21.10: -15.93\n",
      "\n",
      "Converged with orientation: 21.10\n",
      "Line centroids:\n",
      "[[  5.86781727 -15.20455437]\n",
      " [  1.16602816  -3.0213856 ]\n",
      " [  4.36984832 -11.32305135]\n",
      " [  2.98301772  -7.72952753]]\n"
     ]
    }
   ],
   "source": [
    "model = KLines(n_components=4, init_alpha=True, max_iter=15, verbose=1)\n",
    "model.fit(X)\n",
    "a = model.alpha_ # orientation in radians\n",
    "\n",
    "print(\"\\nConverged with orientation: {:.2f}\".format(utils.rad2deg(a)))\n",
    "print(\"Line centroids:\\n{}\".format(model.centroids_))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## XLines with candidates: [4,2,3,5,6]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-Test 4 components\n",
      "Selected alpha=40.0 at init\n",
      "Kmeans w/ proj 40.00: -91.99\n",
      "Kmeans w/ proj 34.51: -64.73\n",
      "Kmeans w/ proj 29.91: -57.83\n",
      "Kmeans w/ proj 26.06: -36.82\n",
      "Kmeans w/ proj 22.56: -19.34\n",
      "Kmeans w/ proj 21.10: -15.93\n",
      "-Test 2 components\n",
      "Kmeans w/ proj 21.10: -229.82\n",
      "Kmeans w/ proj 23.06: -226.11\n",
      "Kmeans w/ proj 24.18: -225.72\n",
      "Kmeans w/ proj 26.05: -216.64\n",
      "-Test 3 components\n",
      "Kmeans w/ proj 21.10: -92.24\n",
      "Kmeans w/ proj 22.05: -94.05\n",
      "Kmeans w/ proj 22.98: -96.11\n",
      "-Test 5 components\n",
      "Kmeans w/ proj 21.10: -12.29\n",
      "Kmeans w/ proj 18.86: -11.92\n",
      "Kmeans w/ proj 19.81: -11.58\n",
      "-Test 6 components\n",
      "Kmeans w/ proj 21.10: -9.26\n",
      "-Results:\n",
      "Candidate scores: [0.80366761617576254, 0.66726385123590215, 0.62515825909242806, 0.73288783035788452, 0.72186833098641578]\n",
      "Best model with 4 components\n",
      "Best model with orientation: 21.10\n"
     ]
    }
   ],
   "source": [
    "tol = 0.01\n",
    "clustering_n_init = 3\n",
    "clustering_init = \"estimate\"\n",
    "\n",
    "xmodel = XLines(candidates=[4,2,3,5,6], init_alpha=\"one\", metric=\"silhouette\", tol=tol, clustering_n_init=clustering_n_init, clustering_init=clustering_init, verbose=2)\n",
    "best_model, best_k = xmodel.fit(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXYAAAEACAYAAACnJV25AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n/wM7kZakncEIJQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x8db69b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for x,y in best_model.centroids_:\n",
    "    plt.scatter(x,y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}