Baayen et al. (2011).ipynb

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   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Baayen, R. H. and Milin, P. and Filipovic Durdevic, D. and Hendrix, P. and Marelli, M. 2011. \"An amorphous model for morphological processing in visual comprehension based on naive discriminative learning.\" *Psychological Review* 118:438-482."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pandas as pd\n",
      "import pandas.rpy.common as com\n",
      "import numpy as np\n",
      "from sklearn.feature_extraction import DictVectorizer\n",
      "\n",
      "%load_ext autoreload\n",
      "%autoreload 2\n",
      "\n",
      "%load_ext rmagic\n",
      "\n",
      "%precision 2\n",
      "pd.set_option('display.precision', 3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%%R\n",
      "library(ndl)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "text": [
        "This is ndl version 0.2.16. \n",
        "For an overview of the package, type 'help(\"ndl.package\")'.\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "data = com.load_data('plurals')\n",
      "data['Cues'] = [list(w) for w in data['WordForm']]\n",
      "data['Outcomes'] = [w.split('_') for w in data['Outcomes']]\n",
      "data"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>WordForm</th>\n",
        "      <th>Frequency</th>\n",
        "      <th>Outcomes</th>\n",
        "      <th>Cues</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>1 </th>\n",
        "      <td>  hand</td>\n",
        "      <td>  10</td>\n",
        "      <td>    [hand, NIL]</td>\n",
        "      <td>    [h, a, n, d]</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2 </th>\n",
        "      <td> hands</td>\n",
        "      <td>  20</td>\n",
        "      <td> [hand, PLURAL]</td>\n",
        "      <td> [h, a, n, d, s]</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3 </th>\n",
        "      <td>  land</td>\n",
        "      <td>   8</td>\n",
        "      <td>    [land, NIL]</td>\n",
        "      <td>    [l, a, n, d]</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4 </th>\n",
        "      <td> lands</td>\n",
        "      <td>   3</td>\n",
        "      <td> [land, PLURAL]</td>\n",
        "      <td> [l, a, n, d, s]</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>5 </th>\n",
        "      <td>   and</td>\n",
        "      <td>  35</td>\n",
        "      <td>     [and, NIL]</td>\n",
        "      <td>       [a, n, d]</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>6 </th>\n",
        "      <td>   sad</td>\n",
        "      <td>  18</td>\n",
        "      <td>     [sad, NIL]</td>\n",
        "      <td>       [s, a, d]</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>7 </th>\n",
        "      <td>    as</td>\n",
        "      <td>  35</td>\n",
        "      <td>      [as, NIL]</td>\n",
        "      <td>          [a, s]</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>8 </th>\n",
        "      <td>   lad</td>\n",
        "      <td> 102</td>\n",
        "      <td>     [lad, NIL]</td>\n",
        "      <td>       [l, a, d]</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>9 </th>\n",
        "      <td>   lad</td>\n",
        "      <td>  54</td>\n",
        "      <td>  [lad, PLURAL]</td>\n",
        "      <td>       [l, a, d]</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>10</th>\n",
        "      <td>  lass</td>\n",
        "      <td> 134</td>\n",
        "      <td>    [lass, NIL]</td>\n",
        "      <td>    [l, a, s, s]</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "<p>10 rows \u00d7 4 columns</p>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "   WordForm  Frequency        Outcomes             Cues\n",
        "1      hand         10     [hand, NIL]     [h, a, n, d]\n",
        "2     hands         20  [hand, PLURAL]  [h, a, n, d, s]\n",
        "3      land          8     [land, NIL]     [l, a, n, d]\n",
        "4     lands          3  [land, PLURAL]  [l, a, n, d, s]\n",
        "5       and         35      [and, NIL]        [a, n, d]\n",
        "6       sad         18      [sad, NIL]        [s, a, d]\n",
        "7        as         35       [as, NIL]           [a, s]\n",
        "8       lad        102      [lad, NIL]        [l, a, d]\n",
        "9       lad         54   [lad, PLURAL]        [l, a, d]\n",
        "10     lass        134     [lass, NIL]     [l, a, s, s]\n",
        "\n",
        "[10 rows x 4 columns]"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "---\n",
      "\n",
      "Appendix\n",
      "========\n",
      "\n",
      "The first step is to construct the co-occurrence matrix $C$ (eq. 37), where $C_{ij}$ is the frequency with which cue $i$ co-occurs with cue $j$ ($C_{ii}$ is the marginal frequency of cue $i$)."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "cues = DictVectorizer(dtype=float,sparse=False)\n",
      "D = cues.fit_transform({}.fromkeys(c,True) for c in data.Cues) * data.Frequency[:,np.newaxis]\n",
      "D "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "array([[  10.,   10.,   10.,    0.,   10.,    0.],\n",
        "       [  20.,   20.,   20.,    0.,   20.,   20.],\n",
        "       [   8.,    8.,    0.,    8.,    8.,    0.],\n",
        "       [   3.,    3.,    0.,    3.,    3.,    3.],\n",
        "       [  35.,   35.,    0.,    0.,   35.,    0.],\n",
        "       [  18.,   18.,    0.,    0.,    0.,   18.],\n",
        "       [  35.,    0.,    0.,    0.,    0.,   35.],\n",
        "       [ 102.,  102.,    0.,  102.,    0.,    0.],\n",
        "       [  54.,   54.,    0.,   54.,    0.,    0.],\n",
        "       [ 134.,    0.,    0.,  134.,    0.,  134.]])"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "cues.get_feature_names()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "['a', 'd', 'h', 'l', 'n', 's']"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now sum up to get $C$:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "n = len(cues.get_feature_names())\n",
      "C = np.zeros((n,n))\n",
      "for row in D:\n",
      "    for nz in np.nonzero(row):\n",
      "        C[nz] += row\n",
      "C"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "array([[ 419.,  250.,   30.,  301.,   76.,  210.],\n",
        "       [ 250.,  250.,   30.,  167.,   76.,   41.],\n",
        "       [  30.,   30.,   30.,    0.,   30.,   20.],\n",
        "       [ 301.,  167.,    0.,  301.,   11.,  137.],\n",
        "       [  76.,   76.,   30.,   11.,   76.,   23.],\n",
        "       [ 210.,   41.,   20.,  137.,   23.,  210.]])"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Then we normalize to get $C'$, the conditional probabilty matrix (eqs. 38 and 39), where:  $$C'_{ij}=p(j|i)=\\frac{C_{ij}}{\\sum_kC_{ik}}$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Z = C.sum(axis=1)\n",
      "C1 = C / Z[:,np.newaxis]\n",
      "C1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 7,
       "text": [
        "array([[ 0.33,  0.19,  0.02,  0.23,  0.06,  0.16],\n",
        "       [ 0.31,  0.31,  0.04,  0.21,  0.09,  0.05],\n",
        "       [ 0.21,  0.21,  0.21,  0.  ,  0.21,  0.14],\n",
        "       [ 0.33,  0.18,  0.  ,  0.33,  0.01,  0.15],\n",
        "       [ 0.26,  0.26,  0.1 ,  0.04,  0.26,  0.08],\n",
        "       [ 0.33,  0.06,  0.03,  0.21,  0.04,  0.33]])"
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Next, Outcome matrix $O$, where $O_{ij}$ is number of types cue $i$ occurred with outcome $j$:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "out = DictVectorizer(dtype=float,sparse=False)\n",
      "X = out.fit_transform([{}.fromkeys(c,True) for c in data.Outcomes]) * data.Frequency[:,np.newaxis]\n",
      "X"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "array([[  10.,    0.,    0.,    0.,   10.,    0.,    0.,    0.,    0.],\n",
        "       [   0.,   20.,    0.,    0.,   20.,    0.,    0.,    0.,    0.],\n",
        "       [   8.,    0.,    0.,    0.,    0.,    0.,    8.,    0.,    0.],\n",
        "       [   0.,    3.,    0.,    0.,    0.,    0.,    3.,    0.,    0.],\n",
        "       [  35.,    0.,   35.,    0.,    0.,    0.,    0.,    0.,    0.],\n",
        "       [  18.,    0.,    0.,    0.,    0.,    0.,    0.,    0.,   18.],\n",
        "       [  35.,    0.,    0.,   35.,    0.,    0.,    0.,    0.,    0.],\n",
        "       [ 102.,    0.,    0.,    0.,    0.,  102.,    0.,    0.,    0.],\n",
        "       [   0.,   54.,    0.,    0.,    0.,   54.,    0.,    0.,    0.],\n",
        "       [ 134.,    0.,    0.,    0.,    0.,    0.,    0.,  134.,    0.]])"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "out.get_feature_names()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "['NIL', 'PLURAL', 'and', 'as', 'hand', 'lad', 'land', 'lass', 'sad']"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "O = np.zeros((len(cues.get_feature_names()),len(out.get_feature_names())))\n",
      "for i in xrange(len(X)):\n",
      "    for nz in np.nonzero(D[i]):\n",
      "        O[nz] += X[i]\n",
      "O"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "array([[ 342.,   77.,   35.,   35.,   30.,  156.,   11.,  134.,   18.],\n",
        "       [ 173.,   77.,   35.,    0.,   30.,  156.,   11.,    0.,   18.],\n",
        "       [  10.,   20.,    0.,    0.,   30.,    0.,    0.,    0.,    0.],\n",
        "       [ 244.,   57.,    0.,    0.,    0.,  156.,   11.,  134.,    0.],\n",
        "       [  53.,   23.,   35.,    0.,   30.,    0.,   11.,    0.,    0.],\n",
        "       [ 187.,   23.,    0.,   35.,   20.,    0.,    3.,  134.,   18.]])"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "As above, we renormalize $O$ to get the conditional outcome matrix $O'$, where: $$O'_{ij}=p(o_j|c_i)=\\frac{p(c_i,o_j)}{p(c_i)}=\\frac{O_{ij}}{\\sum_kC_{ik}}$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "O1 = O / Z[:,np.newaxis]\n",
      "O1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "array([[ 0.27,  0.06,  0.03,  0.03,  0.02,  0.12,  0.01,  0.1 ,  0.01],\n",
        "       [ 0.21,  0.09,  0.04,  0.  ,  0.04,  0.19,  0.01,  0.  ,  0.02],\n",
        "       [ 0.07,  0.14,  0.  ,  0.  ,  0.21,  0.  ,  0.  ,  0.  ,  0.  ],\n",
        "       [ 0.27,  0.06,  0.  ,  0.  ,  0.  ,  0.17,  0.01,  0.15,  0.  ],\n",
        "       [ 0.18,  0.08,  0.12,  0.  ,  0.1 ,  0.  ,  0.04,  0.  ,  0.  ],\n",
        "       [ 0.29,  0.04,  0.  ,  0.05,  0.03,  0.  ,  0.  ,  0.21,  0.03]])"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Finally, we find the weight matrix *W* by solving equation (47): $C'W=O'$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.linalg.solve(C1,O1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 12,
       "text": [
        "array([[  1.45e+00,  -4.49e-01,   3.75e-01,   1.03e+00,   2.57e-16,\n",
        "          4.09e-01,  -3.75e-01,  -3.41e-02,  -4.09e-01],\n",
        "       [ -5.31e-01,   5.31e-01,  -1.62e-01,  -4.44e-01,  -1.98e-16,\n",
        "          3.95e-01,   1.62e-01,  -5.56e-01,   6.05e-01],\n",
        "       [ -4.91e-01,   4.91e-01,  -6.89e-01,   5.35e-02,   1.00e+00,\n",
        "          3.65e-01,  -3.11e-01,  -5.35e-02,  -3.65e-01],\n",
        "       [ -2.23e-01,   2.23e-01,  -2.15e-01,  -6.20e-01,  -5.38e-17,\n",
        "          1.65e-01,   2.15e-01,   6.20e-01,  -1.65e-01],\n",
        "       [  8.83e-02,  -8.83e-02,   6.12e-01,  -4.20e-01,  -4.31e-17,\n",
        "         -8.08e-01,   3.88e-01,   4.20e-01,  -1.92e-01],\n",
        "       [ -2.72e-01,   2.72e-01,  -2.05e-01,  -3.35e-01,  -2.03e-16,\n",
        "         -5.41e-01,   2.05e-01,   3.35e-01,   5.41e-01]])"
       ]
      }
     ],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Alternatively, find weight matrix $W$ using the pseudoinverse $C^+$ as in equation (48): $W=C^+O'$ This has the advantage of working even when $C$ is singular."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "W = np.linalg.pinv(C1).dot(O1)\n",
      "W"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 13,
       "text": [
        "array([[  1.45e+00,  -4.49e-01,   3.75e-01,   1.03e+00,  -4.88e-15,\n",
        "          4.09e-01,  -3.75e-01,  -3.41e-02,  -4.09e-01],\n",
        "       [ -5.31e-01,   5.31e-01,  -1.62e-01,  -4.44e-01,   2.44e-15,\n",
        "          3.95e-01,   1.62e-01,  -5.56e-01,   6.05e-01],\n",
        "       [ -4.91e-01,   4.91e-01,  -6.89e-01,   5.35e-02,   1.00e+00,\n",
        "          3.65e-01,  -3.11e-01,  -5.35e-02,  -3.65e-01],\n",
        "       [ -2.23e-01,   2.23e-01,  -2.15e-01,  -6.20e-01,   2.80e-15,\n",
        "          1.65e-01,   2.15e-01,   6.20e-01,  -1.65e-01],\n",
        "       [  8.83e-02,  -8.83e-02,   6.12e-01,  -4.20e-01,   7.77e-16,\n",
        "         -8.08e-01,   3.88e-01,   4.20e-01,  -1.92e-01],\n",
        "       [ -2.72e-01,   2.72e-01,  -2.05e-01,  -3.35e-01,   3.00e-15,\n",
        "         -5.41e-01,   2.05e-01,   3.35e-01,   5.41e-01]])"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pd.DataFrame(W,columns=out.get_feature_names(),index=cues.get_feature_names())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>NIL</th>\n",
        "      <th>PLURAL</th>\n",
        "      <th>and</th>\n",
        "      <th>as</th>\n",
        "      <th>hand</th>\n",
        "      <th>lad</th>\n",
        "      <th>land</th>\n",
        "      <th>lass</th>\n",
        "      <th>sad</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>a</th>\n",
        "      <td> 1.45</td>\n",
        "      <td>-0.45</td>\n",
        "      <td> 0.38</td>\n",
        "      <td> 1.03</td>\n",
        "      <td>-4.88e-15</td>\n",
        "      <td> 0.41</td>\n",
        "      <td>-0.38</td>\n",
        "      <td>-0.03</td>\n",
        "      <td>-0.41</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>d</th>\n",
        "      <td>-0.53</td>\n",
        "      <td> 0.53</td>\n",
        "      <td>-0.16</td>\n",
        "      <td>-0.44</td>\n",
        "      <td> 2.44e-15</td>\n",
        "      <td> 0.39</td>\n",
        "      <td> 0.16</td>\n",
        "      <td>-0.56</td>\n",
        "      <td> 0.61</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>h</th>\n",
        "      <td>-0.49</td>\n",
        "      <td> 0.49</td>\n",
        "      <td>-0.69</td>\n",
        "      <td> 0.05</td>\n",
        "      <td> 1.00e+00</td>\n",
        "      <td> 0.36</td>\n",
        "      <td>-0.31</td>\n",
        "      <td>-0.05</td>\n",
        "      <td>-0.36</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>l</th>\n",
        "      <td>-0.22</td>\n",
        "      <td> 0.22</td>\n",
        "      <td>-0.21</td>\n",
        "      <td>-0.62</td>\n",
        "      <td> 2.80e-15</td>\n",
        "      <td> 0.17</td>\n",
        "      <td> 0.21</td>\n",
        "      <td> 0.62</td>\n",
        "      <td>-0.17</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>n</th>\n",
        "      <td> 0.09</td>\n",
        "      <td>-0.09</td>\n",
        "      <td> 0.61</td>\n",
        "      <td>-0.42</td>\n",
        "      <td> 7.77e-16</td>\n",
        "      <td>-0.81</td>\n",
        "      <td> 0.39</td>\n",
        "      <td> 0.42</td>\n",
        "      <td>-0.19</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>s</th>\n",
        "      <td>-0.27</td>\n",
        "      <td> 0.27</td>\n",
        "      <td>-0.21</td>\n",
        "      <td>-0.34</td>\n",
        "      <td> 3.00e-15</td>\n",
        "      <td>-0.54</td>\n",
        "      <td> 0.21</td>\n",
        "      <td> 0.34</td>\n",
        "      <td> 0.54</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "<p>6 rows \u00d7 9 columns</p>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 17,
       "text": [
        "    NIL  PLURAL   and    as      hand   lad  land  lass   sad\n",
        "a  1.45   -0.45  0.38  1.03 -4.88e-15  0.41 -0.38 -0.03 -0.41\n",
        "d -0.53    0.53 -0.16 -0.44  2.44e-15  0.39  0.16 -0.56  0.61\n",
        "h -0.49    0.49 -0.69  0.05  1.00e+00  0.36 -0.31 -0.05 -0.36\n",
        "l -0.22    0.22 -0.21 -0.62  2.80e-15  0.17  0.21  0.62 -0.17\n",
        "n  0.09   -0.09  0.61 -0.42  7.77e-16 -0.81  0.39  0.42 -0.19\n",
        "s -0.27    0.27 -0.21 -0.34  3.00e-15 -0.54  0.21  0.34  0.54\n",
        "\n",
        "[6 rows x 9 columns]"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Compute activations.  Let $u$ be a vector of cues that are active for a given input.  For example, for the input *hands*, we have:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "u=cues.transform([{}.fromkeys(list('hands'),True)]).T\n",
      "u"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 20,
       "text": [
        "array([[ 1.],\n",
        "       [ 1.],\n",
        "       [ 1.],\n",
        "       [ 0.],\n",
        "       [ 1.],\n",
        "       [ 1.]])"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Given $u$, the activation $a_j$ of a meaning $j$ is: $$a_j=\\sum_iW_{ij}=W^Tu$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "W.T.dot(u)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 21,
       "text": [
        "array([[ 0.24],\n",
        "       [ 0.76],\n",
        "       [-0.07],\n",
        "       [-0.11],\n",
        "       [ 1.  ],\n",
        "       [-0.18],\n",
        "       [ 0.07],\n",
        "       [ 0.11],\n",
        "       [ 0.18]])"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pd.DataFrame(W.T.dot(u),index=out.get_feature_names())"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>0</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>NIL</th>\n",
        "      <td> 0.24</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>PLURAL</th>\n",
        "      <td> 0.76</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>and</th>\n",
        "      <td>-0.07</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>as</th>\n",
        "      <td>-0.11</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>hand</th>\n",
        "      <td> 1.00</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>lad</th>\n",
        "      <td>-0.18</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>land</th>\n",
        "      <td> 0.07</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>lass</th>\n",
        "      <td> 0.11</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>sad</th>\n",
        "      <td> 0.18</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "<p>9 rows \u00d7 1 columns</p>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 22,
       "text": [
        "           0\n",
        "NIL     0.24\n",
        "PLURAL  0.76\n",
        "and    -0.07\n",
        "as     -0.11\n",
        "hand    1.00\n",
        "lad    -0.18\n",
        "land    0.07\n",
        "lass    0.11\n",
        "sad     0.18\n",
        "\n",
        "[9 rows x 1 columns]"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "targets = ['hands','hand']\n",
      "pd.DataFrame(W.T.dot(cues.transform([{}.fromkeys(list(t),True) for t in targets]).T),index=out.get_feature_names(),columns=targets)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>hands</th>\n",
        "      <th>hand</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>NIL</th>\n",
        "      <td> 0.24</td>\n",
        "      <td> 0.51</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>PLURAL</th>\n",
        "      <td> 0.76</td>\n",
        "      <td> 0.49</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>and</th>\n",
        "      <td>-0.07</td>\n",
        "      <td> 0.14</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>as</th>\n",
        "      <td>-0.11</td>\n",
        "      <td> 0.22</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>hand</th>\n",
        "      <td> 1.00</td>\n",
        "      <td> 1.00</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>lad</th>\n",
        "      <td>-0.18</td>\n",
        "      <td> 0.36</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>land</th>\n",
        "      <td> 0.07</td>\n",
        "      <td>-0.14</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>lass</th>\n",
        "      <td> 0.11</td>\n",
        "      <td>-0.22</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>sad</th>\n",
        "      <td> 0.18</td>\n",
        "      <td>-0.36</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "<p>9 rows \u00d7 2 columns</p>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 27,
       "text": [
        "        hands  hand\n",
        "NIL      0.24  0.51\n",
        "PLURAL   0.76  0.49\n",
        "and     -0.07  0.14\n",
        "as      -0.11  0.22\n",
        "hand     1.00  1.00\n",
        "lad     -0.18  0.36\n",
        "land     0.07 -0.14\n",
        "lass     0.11 -0.22\n",
        "sad      0.18 -0.36\n",
        "\n",
        "[9 rows x 2 columns]"
       ]
      }
     ],
     "prompt_number": 27
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "---\n",
      "\n",
      "The same thing, but packaged up in a function:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from ndl import *"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ndl(data)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>NIL</th>\n",
        "      <th>PLURAL</th>\n",
        "      <th>and</th>\n",
        "      <th>as</th>\n",
        "      <th>hand</th>\n",
        "      <th>lad</th>\n",
        "      <th>land</th>\n",
        "      <th>lass</th>\n",
        "      <th>sad</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>a</th>\n",
        "      <td> 1.45</td>\n",
        "      <td>-0.45</td>\n",
        "      <td> 0.38</td>\n",
        "      <td> 1.03</td>\n",
        "      <td>-4.88e-15</td>\n",
        "      <td> 0.41</td>\n",
        "      <td>-0.38</td>\n",
        "      <td>-0.03</td>\n",
        "      <td>-0.41</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>d</th>\n",
        "      <td>-0.53</td>\n",
        "      <td> 0.53</td>\n",
        "      <td>-0.16</td>\n",
        "      <td>-0.44</td>\n",
        "      <td> 2.44e-15</td>\n",
        "      <td> 0.39</td>\n",
        "      <td> 0.16</td>\n",
        "      <td>-0.56</td>\n",
        "      <td> 0.61</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>h</th>\n",
        "      <td>-0.49</td>\n",
        "      <td> 0.49</td>\n",
        "      <td>-0.69</td>\n",
        "      <td> 0.05</td>\n",
        "      <td> 1.00e+00</td>\n",
        "      <td> 0.36</td>\n",
        "      <td>-0.31</td>\n",
        "      <td>-0.05</td>\n",
        "      <td>-0.36</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>l</th>\n",
        "      <td>-0.22</td>\n",
        "      <td> 0.22</td>\n",
        "      <td>-0.21</td>\n",
        "      <td>-0.62</td>\n",
        "      <td> 2.80e-15</td>\n",
        "      <td> 0.17</td>\n",
        "      <td> 0.21</td>\n",
        "      <td> 0.62</td>\n",
        "      <td>-0.17</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>n</th>\n",
        "      <td> 0.09</td>\n",
        "      <td>-0.09</td>\n",
        "      <td> 0.61</td>\n",
        "      <td>-0.42</td>\n",
        "      <td> 7.77e-16</td>\n",
        "      <td>-0.81</td>\n",
        "      <td> 0.39</td>\n",
        "      <td> 0.42</td>\n",
        "      <td>-0.19</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>s</th>\n",
        "      <td>-0.27</td>\n",
        "      <td> 0.27</td>\n",
        "      <td>-0.21</td>\n",
        "      <td>-0.34</td>\n",
        "      <td> 3.00e-15</td>\n",
        "      <td>-0.54</td>\n",
        "      <td> 0.21</td>\n",
        "      <td> 0.34</td>\n",
        "      <td> 0.54</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "<p>6 rows \u00d7 9 columns</p>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 29,
       "text": [
        "    NIL  PLURAL   and    as      hand   lad  land  lass   sad\n",
        "a  1.45   -0.45  0.38  1.03 -4.88e-15  0.41 -0.38 -0.03 -0.41\n",
        "d -0.53    0.53 -0.16 -0.44  2.44e-15  0.39  0.16 -0.56  0.61\n",
        "h -0.49    0.49 -0.69  0.05  1.00e+00  0.36 -0.31 -0.05 -0.36\n",
        "l -0.22    0.22 -0.21 -0.62  2.80e-15  0.17  0.21  0.62 -0.17\n",
        "n  0.09   -0.09  0.61 -0.42  7.77e-16 -0.81  0.39  0.42 -0.19\n",
        "s -0.27    0.27 -0.21 -0.34  3.00e-15 -0.54  0.21  0.34  0.54\n",
        "\n",
        "[6 rows x 9 columns]"
       ]
      }
     ],
     "prompt_number": 29
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}