04-Hopfield-Network.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "import ANN\n",
    "import numpy as np\n",
    "import copy\n",
    "from pprint import pprint\n",
    "from collections import defaultdict as ddict"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "numNeurons = 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "class hopfieldNetwork:\n",
    "    ''' This creates a Hopfield network class '''\n",
    "    def __init__(self, Input):\n",
    "        self.Input = Input\n",
    "        self.InputComplement = -1 * Input\n",
    "        self.numNeurons = self.Input.shape[1]\n",
    "        self.neuronList = [hopfieldNeuron(1,i) for i in range(self.numNeurons)]\n",
    "        self.mapInputToNeurons(self.Input)\n",
    "        self.connections = ddict(list)\n",
    "        self.connect_neurons()\n",
    "        self.compute()\n",
    "        \n",
    "    \n",
    "    def mapInputToNeurons(self, Input):\n",
    "        ''' Mapping of the inputs to different subsets of neurons'''\n",
    "        for index, neuron in enumerate(self.neuronList):\n",
    "            neuron.input = Input[:,index]\n",
    "        \n",
    "    def connect_neurons(self):\n",
    "        for i, neuron in enumerate(self.neuronList):\n",
    "            for j, neuron_2 in enumerate(self.neuronList, i+1):\n",
    "                self.connections[neuron].append((neuron_2, int(neuron.input*neuron_2.input)))\n",
    "                self.connections[neuron_2].append((neuron, int(neuron.input*neuron_2.input)))\n",
    "    \n",
    "    def compute(self, mode ='async'):\n",
    "        if mode == 'sync':\n",
    "            new_output = []\n",
    "            for neuron in self.connections:\n",
    "                for neuron_in, weight in self.connections[neuron]:\n",
    "                    neuron.localField += weight*neuron_in.input\n",
    "                neuron.output = neuron.activation(neuron.localField)\n",
    "                new_output.append(neuron.output)\n",
    "                neuron.localField = 0\n",
    "            \n",
    "            new_output = np.array([new_output])\n",
    "            self.mapInputToNeurons(new_output)\n",
    "            \n",
    "                \n",
    "        elif mode == 'async':\n",
    "            for neuron in self.connections:\n",
    "                for neuron_in, weight in self.connections[neuron]:\n",
    "                    neuron.localField += weight*neuron_in.input\n",
    "                neuron.output = neuron.activation(neuron.localField)\n",
    "                neuron.localField = 0\n",
    "                neuron.input = neuron.output\n",
    "            \n",
    "            new_output = np.array([[i.output for i in self.neuronList]])\n",
    "            \n",
    "        return new_output\n",
    "    \n",
    "    def runHopfieldNetwork(self, test, count=25):\n",
    "        hop.mapInputToNeurons(test)\n",
    "        curr_state = test\n",
    "        states = [curr_state]\n",
    "        \n",
    "        while not ((curr_state == self.Input).all() or\n",
    "                   (curr_state == self.InputComplement).all() or\n",
    "                  count == 0):            \n",
    "            curr_state = self.compute()\n",
    "            states.append(curr_state)\n",
    "            count -= 1\n",
    "            \n",
    "        return states\n",
    "                \n",
    "class hopfieldNeuron(ANN.neuron):\n",
    "    def __init__(self, layer, index, activation_method='step'):\n",
    "        self.input = []\n",
    "        self.localField = 0\n",
    "        self.activation_method= activation_method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "a = np.array([[-1,1,1,1,-1,1,-1,1]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "hop = hopfieldNetwork(a)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[array([[-1, -1,  1,  1,  1,  1,  1,  1]]),\n",
      " array([[-1,  1,  1,  1, -1,  1, -1,  1]])]\n"
     ]
    }
   ],
   "source": [
    "pprint(hop.runHopfieldNetwork(np.array([[-1,-1,1,1,1,1,1,1]])))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Let's memorize some digits!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from sklearn import datasets\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#Load the digits dataset\n",
    "digits = datasets.load_digits()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Binarize the dataset\n",
    "for digit_im, digit_data in zip(digits['images'], digits['data']):\n",
    "    digit_im[digit_im>0] = 1\n",
    "    digit_data[digit_data>0] = 1\n",
    "    digit_data[digit_data==0] = -1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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6qwEH+66H0eziABya5AjguVLKkx2NuRZYAZwBPJ9k61bUbCmlk5m2Sb4K3EpzmvRdNAe/\nltPsU3eilPI88KbjLkmeB7aUUka7UUlFkq8DN9N8SH8L+EvgFaDLG0uuAe5Jsprm9OTRwEqa08Gd\nGVuLz0meztnBaZ4/ppma/iLNEfkjOx5vOc2pyVfnLf/Y4ZjbGu9V4A87HPPvgUcHv9efA7cDJ0zg\n73sX3Z4eXU9zSv1F4AngeuCQMfxcpwE/AV4A/gM4fwxjnjx43xzW5ThOM5dU1atjFJL6yaCQVGVQ\nSKoyKCRVGRSSqgwKSVUGhaQqg0JSlUEhqcqgkFRlUEiqMigkVf0/0zibPVVtQhgAAAAASUVORK5C\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f23683bc358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Display the first digit\n",
    "plt.figure(1, figsize=(3, 3))\n",
    "plt.imshow(digits.images[0], cmap=plt.cm.gray_r, interpolation='nearest')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "hop = hopfieldNetwork(np.matrix(digits.data[0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-1. -1.  1.  1.  1.  1. -1. -1. -1. -1.  1.  1.  1.  1.  1. -1. -1.  1.\n",
      "  1.  1. -1.  1.  1. -1. -1.  1.  1. -1. -1.  1.  1. -1. -1.  1.  1. -1.\n",
      " -1.  1.  1. -1. -1.  1.  1. -1.  1.  1.  1. -1. -1.  1.  1.  1.  1.  1.\n",
      " -1. -1. -1. -1.  1.  1.  1. -1. -1. -1.]\n"
     ]
    }
   ],
   "source": [
    "print(digits.data[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1]\n"
     ]
    }
   ],
   "source": [
    "print([i.output for i in hop.neuronList])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "output = np.array([i.output for i in hop.neuronList])\n",
    "image_out = output.reshape((8,8))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6qwEH+66H0eziABya5AjguVLKkx2NuRZYAZwBPJ9k61bUbCmlk5m2Sb4K3EpzmvRdNAe/\nltPsU3eilPI88KbjLkmeB7aUUka7UUlFkq8DN9N8SH8L+EvgFaDLG0uuAe5Jsprm9OTRwEqa08Gd\nGVuLz0meztnBaZ4/ppma/iLNEfkjOx5vOc2pyVfnLf/Y4ZjbGu9V4A87HPPvgUcHv9efA7cDJ0zg\n73sX3Z4eXU9zSv1F4AngeuCQMfxcpwE/AV4A/gM4fwxjnjx43xzW5ThOM5dU1atjFJL6yaCQVGVQ\nSKoyKCRVGRSSqgwKSVUGhaQqg0JSlUEhqcqgkFRlUEiqMigkVf0/0zibPVVtQhgAAAAASUVORK5C\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f23683bc240>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Display the first digit\n",
    "plt.figure(1, figsize=(3, 3))\n",
    "plt.imshow(image_out, cmap=plt.cm.gray_r, interpolation='nearest')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "output[3:6] = -1\n",
    "image_out = output.reshape((8,8))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ZB3YAm+k2uF3dquDos+sJdB9xAI5PchLwYCnlvkY1twIbgfOAh5LsXYtaLKU0OdM2yYeA\nL9HtJn023cav0+k+UzdRSnkIeMp2lyQPAXtKKZNdqKQiyUeAL9C9SX8L+EvgcaDlhSWvBG5LsoVu\n9+SpwCa63cHNTG3E5yx35xxgN88f052a/gjdFvmTG9c7nW7X5C+W3f6xYc191fsF8IcNa/498L3R\n6/pj4CbgTTP4/d5C292j2+l2qT8C/BC4DnjxFH6uc4FvAQ8D/wFcNIWaZ43+bk5oWcfTzCVVDWob\nhaRhMigkVRkUkqoMCklVBoWkKoNCUpVBIanKoJBUZVBIqjIoJFUZFJKqDApJVf8Pq6+pp5q75BEA\nAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f2368272ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Display the first digit\n",
    "plt.figure(1, figsize=(3, 3))\n",
    "plt.imshow(image_out, cmap=plt.cm.gray_r, interpolation='nearest')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [],
   "source": [
    "hop.mapInputToNeurons(np.matrix(output))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1, -1,  1,  1,  1,  1, -1, -1, -1, -1,  1,  1,  1,  1,  1, -1, -1,\n",
       "         1,  1,  1, -1,  1,  1, -1, -1,  1,  1, -1, -1,  1,  1, -1, -1,  1,\n",
       "         1, -1, -1,  1,  1, -1, -1,  1,  1, -1,  1,  1,  1, -1, -1,  1,  1,\n",
       "         1,  1,  1, -1, -1, -1, -1,  1,  1,  1, -1, -1, -1]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hop.compute()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "output = np.array([i.output for i in hop.neuronList])\n",
    "image_out = output.reshape((8,8))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false,
    "deletable": true,
    "editable": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6qwEH+66H0eziABya5AjguVLKkx2NuRZYAZwBPJ9k61bUbCmlk5m2Sb4K3EpzmvRdNAe/\nltPsU3eilPI88KbjLkmeB7aUUka7UUlFkq8DN9N8SH8L+EvgFaDLG0uuAe5Jsprm9OTRwEqa08Gd\nGVuLz0meztnBaZ4/ppma/iLNEfkjOx5vOc2pyVfnLf/Y4ZjbGu9V4A87HPPvgUcHv9efA7cDJ0zg\n73sX3Z4eXU9zSv1F4AngeuCQMfxcpwE/AV4A/gM4fwxjnjx43xzW5ThOM5dU1atjFJL6yaCQVGVQ\nSKoyKCRVGRSSqgwKSVUGhaQqg0JSlUEhqcqgkFRlUEiqMigkVf0/0zibPVVtQhgAAAAASUVORK5C\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f23681b5668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Display the first digit\n",
    "plt.figure(1, figsize=(3, 3))\n",
    "plt.imshow(image_out, cmap=plt.cm.gray_r, interpolation='nearest')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1, -1, -1, -1,  1, -1,  1, -1]])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a * -1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Let's Visualize the state changes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[matrix([[-1., -1., -1., -1., -1., -1., -1., -1., -1., -1., -1., -1., -1.,\n",
      "         -1., -1., -1., -1., -1., -1., -1., -1., -1., -1., -1., -1., -1.,\n",
      "         -1., -1., -1., -1., -1., -1., -1.,  1.,  1., -1., -1.,  1.,  1.,\n",
      "         -1., -1.,  1.,  1., -1.,  1.,  1.,  1., -1., -1.,  1.,  1.,  1.,\n",
      "          1.,  1., -1., -1., -1., -1.,  1.,  1.,  1., -1., -1., -1.]]),\n",
      " array([[-1, -1,  1,  1,  1,  1, -1, -1, -1, -1,  1,  1,  1,  1,  1, -1, -1,\n",
      "         1,  1,  1, -1,  1,  1, -1, -1,  1,  1, -1, -1,  1,  1, -1, -1,  1,\n",
      "         1, -1, -1,  1,  1, -1, -1,  1,  1, -1,  1,  1,  1, -1, -1,  1,  1,\n",
      "         1,  1,  1, -1, -1, -1, -1,  1,  1,  1, -1, -1, -1]])]\n"
     ]
    }
   ],
   "source": [
    "start_image = np.matrix(digits.data[0])\n",
    "perturb_image = copy.deepcopy(digits.data[0])\n",
    "perturb_image[0:32] = -1\n",
    "\n",
    "\n",
    "hop = hopfieldNetwork(start_image)\n",
    "states = hop.runHopfieldNetwork( np.matrix(perturb_image))\n",
    "pprint(states)\n",
    "\n",
    "image_out = states[0].reshape(8,8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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VcB5QAR6WNNTbejoiNhcqcJwcTGZmCSormCJiSX7P0nlkQ3r3kfWEnsw3mQ1sq9nlQ2Sz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\ni9tmVfd9AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f236819d898>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from IPython import display\n",
    "plt.ion()\n",
    "\n",
    "f, ax = plt.subplots(1,1)\n",
    "im = ax.imshow(states[0].reshape(8,8), cmap=plt.cm.gray_r, interpolation = 'nearest')\n",
    "\n",
    "f.colorbar(im)\n",
    "f.canvas.draw()\n",
    "\n",
    "for i in range(len(states)):  \n",
    "    try:\n",
    "        im.set_data(states[i].reshape(8,8)) \n",
    "        f.canvas.draw()\n",
    "        display.display(f)\n",
    "        display.clear_output(wait=True) \n",
    "        plt.pause(0.1)\n",
    "\n",
    "    except KeyboardInterrupt:\n",
    "        break\n",
    "plt.ioff()\n",
    "plt.close()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6qwEH+66H0eziABya5AjguVLKkx2NuRZYAZwBPJ9k61bUbCmlk5m2Sb4K3EpzmvRdNAe/\nltPsU3eilPI88KbjLkmeB7aUUka7UUlFkq8DN9N8SH8L+EvgFaDLG0uuAe5Jsprm9OTRwEqa08Gd\nGVuLz0meztnBaZ4/ppma/iLNEfkjOx5vOc2pyVfnLf/Y4ZjbGu9V4A87HPPvgUcHv9efA7cDJ0zg\n73sX3Z4eXU9zSv1F4AngeuCQMfxcpwE/AV4A/gM4fwxjnjx43xzW5ThOM5dU1atjFJL6yaCQVGVQ\nSKoyKCRVGRSSqgwKSVUGhaQqg0JSlUEhqcqgkFRlUEiqMigkVf0/0zibPVVtQhgAAAAASUVORK5C\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f236834a8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.ion()\n",
    "\n",
    "f = plt.figure(1, figsize=(3, 3))\n",
    "im = plt.imshow(start_image.reshape((8,8)), cmap=plt.cm.gray_r, interpolation='nearest')\n",
    "plt.show()\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}