visual explanation of PRIM modification

illustration.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Visual explanation\n",
    "\n",
    "In this notebook, I offer a brief visual explanation of why the procedure suggested by Guivarch et al will help in identifying multiple boxes which are distinct. \n",
    "\n",
    "Imagine we have a simple data set with 2 uncertain variables, where the red dots are cases of interest"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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uHzFiBMsDPYLtdQHATF2GgKeeekqffvqpLrroIl100UUKtrrk6f79+20tDonB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\nRK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109ab01d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "np.random.seed(123456789)\n",
    "\n",
    "x = np.random.rand(150)\n",
    "y = np.random.rand(150)\n",
    "\n",
    "c_rand = np.random.rand(150) * 0.7\n",
    "logical = (x>c_rand) & (y>c_rand)\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, aspect='equal')\n",
    "ax.scatter(x[logical],y[logical], c='r', label='of interest')\n",
    "ax.scatter(x[logical==False],y[logical==False], c='b', label='not of interest')\n",
    "ax.set_xlabel('$U_1$')\n",
    "ax.set_ylabel('$U_2$')\n",
    "ax.legend()\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As can be seen, there is a large concentration of cases of interest in the upper right corner. Prim will be able to find a box where x is larger than 0.6, and y is larger than 0.4. That is, PRIM will find a box as shown below"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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AwD7d9gTU1NSopKRETU1NCgaDuuKKK9o9Pn36dNuKQ2q4eXtdAIB9ug0BP/vZ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\nAGCo/w+zMuEBhR+mTQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10946e550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.patches import Rectangle\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, aspect='equal')\n",
    "ax.scatter(x[logical],y[logical], c='r', label='of interest')\n",
    "ax.scatter(x[logical==False],y[logical==False], c='b', label='not of interest')\n",
    "\n",
    "ax.add_patch(Rectangle((0.6, 0.4), 0.35, 0.6, fill=None))\n",
    "\n",
    "ax.set_xlabel('$U_1$')\n",
    "ax.set_ylabel('$U_2$')\n",
    "ax.legend()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the default procedure of PRIM, we would remove these cases, and run PRIM on the remaining data. If we remove the data, we end up with the following"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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CQgBcjbNKALAP6wQABonHYioPhbQ0N1cLQyHFa2udLgmAg+gJAAyyvLhYBYsWtcysqKpS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\nAAAADEUIAADAUP8fGISQci9YZgQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1091cbb90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "remove = (x>0.6) & (y>0.4) & (x<0.95)\n",
    "\n",
    "x_plot = x[remove==False]\n",
    "y_plot = y[remove==False]\n",
    "logical_plot = logical[remove==False]\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, aspect='equal')\n",
    "ax.scatter(x_plot[logical_plot],y_plot[logical_plot], c='r',label='of interest')\n",
    "ax.scatter(x_plot[logical_plot==False],y_plot[logical_plot==False], c='b', label='not of interest')\n",
    "\n",
    "ax.set_xlim(xmin=-.2, xmax=1.2)\n",
    "ax.set_ylim(ymin=-.2, ymax=1.2)\n",
    "\n",
    "ax.set_xlabel('$U_1$')\n",
    "ax.set_ylabel('$U_2$')\n",
    "ax.legend()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we run PRIM in order to find a second box, we plausible end of with something like the following"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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MFsXFkyWVqqoqVcFgnYqLr3S6JABHQQiAq31zVlmr5i1/OLt0u0AgnV4aIEkQAuBqLWeV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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x109466e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, aspect='equal')\n",
    "ax.scatter(x_plot[logical_plot],y_plot[logical_plot], c='r', label='of interest')\n",
    "ax.scatter(x_plot[logical_plot==False],y_plot[logical_plot==False], c='b',label='not of interest')\n",
    "\n",
    "ax.add_patch(Rectangle((0.4, 0.2), 0.6, 0.8, fill=None))\n",
    "\n",
    "ax.set_xlim(xmin=-.2, xmax=1.2)\n",
    "ax.set_ylim(ymin=-.2, ymax=1.2)\n",
    "\n",
    "ax.set_xlabel('$U_1$')\n",
    "ax.set_ylabel('$U_2$')\n",
    "ax.legend()\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As can be seen, this second box contains the empty space left by removing the previous box. The result is overlapping boxes. The reason for this is that we are not forcing the hill climbing optimization algorithm in PRIM in any way to consider the impact of the previously removed data points. \n",
    "\n",
    "The clever idea of Guivarch et al is now to do exactly this. They achieve this by changing the cases of interest based on the first box, rather than removing them. That is, the data that this contained in the first box are no longer of interest, but are not removed from the dataset. So, the dataset after the first box now looks like this"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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mmdNcXbodY9uQmBviFYQAuFrzVeXmzQF99dVCffvb/6gxYw5ydQm4HHNDvIEQAFfjqhLw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\nAAAw1P8HRAatS61U4osAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1091a5390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "remove = (x>0.6) & (y>0.4)\n",
    "\n",
    "x_plot = x[remove==False]\n",
    "y_plot = y[remove==False]\n",
    "logical_plot = logical[remove==False]\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, aspect='equal')\n",
    "ax.scatter(x_plot[logical_plot],y_plot[logical_plot], c='r',label='of interest')\n",
    "ax.scatter(x_plot[logical_plot==False],y_plot[logical_plot==False], c='b', label='not of interest')\n",
    "ax.scatter(x[remove],y[remove], c='b')\n",
    "\n",
    "ax.set_xlabel('$U_1$')\n",
    "ax.set_ylabel('$U_2$')\n",
    "ax.legend()\n",
    "\n",
    "ax.set_xlim(xmin=-.2, xmax=1.2)\n",
    "ax.set_ylim(ymin=-.2, ymax=1.2)\n",
    "plt.show()\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Becase the upper right corner is now not removed, but simply no longer of interest, the hill climbing optimization algorithm used by PRIM suddenly has to account for these data points as well. A possible box that PRIM might find is shown below"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Wo0fv5+rSxRjbBryDEABX++aqskTS/dq+PaCPP+bq0s3C4eojPQABMbYNuBshAK72zVUl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\nAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1094663d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "remove = (x>0.6) & (y>0.4)\n",
    "\n",
    "x_plot = x[remove==False]\n",
    "y_plot = y[remove==False]\n",
    "logical_plot = logical[remove==False]\n",
    "\n",
    "fig = plt.figure()\n",
    "ax = fig.add_subplot(111, aspect='equal')\n",
    "ax.scatter(x_plot[logical_plot],y_plot[logical_plot], c='r', label='of interest')\n",
    "ax.scatter(x_plot[logical_plot==False],y_plot[logical_plot==False], c='b', label='not of interest')\n",
    "ax.scatter(x[remove],y[remove], c='b')\n",
    "\n",
    "ax.add_patch(Rectangle((0.4, 0.2), 0.2, 0.8, fill=None))\n",
    "\n",
    "ax.set_xlabel('$U_1$')\n",
    "ax.set_ylabel('$U_2$')\n",
    "ax.legend()\n",
    "\n",
    "ax.set_xlim(xmin=-.2, xmax=1.2)\n",
    "ax.set_ylim(ymin=-.2, ymax=1.2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As can be seen, this new box now borders the first box, rather than overlapping with it. Including any overlap between the first and the second box means a lower density because any cases that are included in the first box will negatively affect the density of the second box. "
   ]
  },
  {
   "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",
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