social_learning.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Social Learning"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Voter Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This model of social learning was independently introduced in Clifford and Sudbury (1973), Holley and Liggett (1975). The setting and dynamic process are the following:\n",
    "* Each agent has its own opinion\n",
    "* On each iteration a randoly choosen agent chooses its neighbour and adopts its side"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It was shown that agents' states reach a consensus over any connected graph $G$ (Coalescing Random Walks)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy as sp\n",
    "import networkx as nx\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Implement the Voter Model and check how the number of agents' states changes with time.\n",
    "Run it for Karate club and [Political Blogs](https://www.dropbox.com/s/fj70uuph47hoc3v/polblogs.gml?dl=0) networks."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "G = nx.karate_club_graph()\n",
    "y = range(G.number_of_nodes())\n",
    "\n",
    "maxIter = 1000\n",
    "numStates = np.zeros((maxIter,), dtype=int)\n",
    "path = []\n",
    "\n",
    "for i in xrange(maxIter):\n",
    "    numStates[i] = len(np.unique(y))\n",
    "    agent = np.random.choice(G.nodes())\n",
    "    adopt = np.random.choice(G.neighbors(agent))\n",
    "    y[agent] = y[adopt]\n",
    "    path.append((adopt, agent))\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f439625f050>]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f43962bfa10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(numStates)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "numStates[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Some preprocessing for polblogs\n",
    "A = nx.adj_matrix(nx.read_gml('polblogs.gml'))\n",
    "G = nx.Graph(A)\n",
    "for n,d in G.degree_iter():\n",
    "    if d == 0: \n",
    "        G.remove_node(n)\n",
    "\n",
    "mapping = {}\n",
    "i = 0\n",
    "for n in G.nodes_iter():\n",
    "    mapping[n] = i\n",
    "    i+=1\n",
    "G = nx.relabel_nodes(G,mapping)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f4361143710>]"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4396209c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(numStates)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Task 2*"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Try to write a code that identifies the path of opinion adoption starting from a particular node "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "G = nx.karate_club_graph()\n",
    "y = range(G.number_of_nodes())\n",
    "\n",
    "maxIter = 1000\n",
    "numStates = np.zeros((maxIter,), dtype=int)\n",
    "path = []\n",
    "\n",
    "for i in xrange(maxIter):\n",
    "    numStates[i] = len(np.unique(y))\n",
    "    agent = np.random.choice(G.nodes())\n",
    "    adopt = np.random.choice(G.neighbors(agent))\n",
    "    y[agent] = y[adopt]\n",
    "    path.append((adopt, agent))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[(16, 5), (3, 12), (2, 0)]"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "path[0:3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6depka1xAsip99+OP6C6XI9yA46IBtFIoMGLUKLi4uGR7fIFuhPItRJQrVw6O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\nk+ArhBBCmJgEXyGEEMLEJPgKIYQQJvb/auiqes9XflQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4360360850>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "nx.draw(G, with_labels=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "start = 6\n",
    "\n",
    "rw = []\n",
    "time = []\n",
    "t = 0\n",
    "\n",
    "for hop in path:\n",
    "    if hop[0] == start:\n",
    "        rw.append(hop)\n",
    "        time.append(t)\n",
    "        start = hop[1]\n",
    "    t+=1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "pltrw = []\n",
    "plttime = []\n",
    "\n",
    "for i in xrange(len(rw)-1):\n",
    "    pltrw.extend((rw[i][0], rw[i][1], rw[i][1]))\n",
    "    plttime.extend((time[i], time[i], time[i+1]))\n",
    "\n",
    "pltrw.extend((rw[-1][0], rw[1][1]))\n",
    "plttime.extend((time[-1], time[-1]))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pltrw2 = pltrw[:]\n",
    "plttime2 = plttime[:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f4360d83710>,\n",
       " <matplotlib.lines.Line2D at 0x7f4360d83990>]"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4395106490>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(5,10))\n",
    "plt.plot(pltrw, plttime, pltrw2, plttime2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## References"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. Clifford, P., and A. Sudbury, \"A model for spatial conflict\", 1973.\n",
    "2. Holley R and Liggett T M, \"Ergodic Theorems for Weakly Interacting Infinite Systems and the Voter Model\", 1975.\n",
    "3. Ercan Yildiz , Daron Acemoglu , Asuman Ozdaglar , Amin Saberi , Anna Scaglione, \"Discrete Opinion Dynamics with Stubborn Agents\", 2011\n",
    "4. Abhimanyu Das, Sreenivas Gollapudi, and Kamesh Munagala, \"Modeling Opinion Dynamics in Social Networks\", 2014\n"
   ]
  }
 ],
 "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": "2.7.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}