dep-parser/mst/mst.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# MST tutorial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from collections import defaultdict\n",
    "import matplotlib\n",
    "import matplotlib.pyplot as plt\n",
    "import networkx as nx\n",
    "%matplotlib inline  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def mst(scores):\n",
    "    \"\"\"\n",
    "    Chu-Liu-Edmonds' algorithm for finding minimum spanning arborescence in graphs.\n",
    "    Calculates the arborescence with node 0 as root.\n",
    "    Source: https://github.com/chantera/biaffineparser/blob/master/utils.py\n",
    "    \n",
    "    WARNING: mind the comment below. This mst function expects scores[i][j] to be the score from j to i, \n",
    "    not from i to j (as you would probably expect!). If you use a graph where you have the convention\n",
    "    that a head points to its dependent, you will need to transpose it before calling this function.\n",
    "    That is, call `mst(scores.T)` instead of `mst(scores)`.\n",
    "\n",
    "    :param scores: `scores[i][j]` is the weight of edge from node `j` to node `i`\n",
    "    :returns an array containing the head node (node with edge pointing to current node) for each node,\n",
    "             with head[0] fixed as 0\n",
    "    \"\"\"\n",
    "    length = scores.shape[0]\n",
    "    scores = scores * (1 - np.eye(length))\n",
    "    heads = np.argmax(scores, axis=1)\n",
    "    heads[0] = 0\n",
    "    tokens = np.arange(1, length)\n",
    "    roots = np.where(heads[tokens] == 0)[0] + 1\n",
    "    \n",
    "    # print initial heads\n",
    "    print(\"initial heads:\", heads)\n",
    "    \n",
    "    # deal with roots\n",
    "    if len(roots) < 1:\n",
    "        print(\"no node is pointing to root, choosing one\")\n",
    "        root_scores = scores[tokens, 0]\n",
    "        head_scores = scores[tokens, heads[tokens]]\n",
    "        new_root = tokens[np.argmax(root_scores / head_scores)]\n",
    "        print(\"new root is:\", new_root)\n",
    "        heads[new_root] = 0\n",
    "    elif len(roots) > 1:\n",
    "        print(\"multiple nodes are pointing to root, choosing one\")\n",
    "        root_scores = scores[roots, 0]\n",
    "        scores[roots, 0] = 0\n",
    "        new_heads = np.argmax(scores[roots][:, tokens], axis=1) + 1\n",
    "        new_root = roots[np.argmin(scores[roots, new_heads] / root_scores)]\n",
    "        print(\"new root is:\", new_root)\n",
    "        heads[roots] = new_heads\n",
    "        heads[new_root] = 0\n",
    "\n",
    "    # construct edges and vertices\n",
    "    edges = defaultdict(set)\n",
    "    vertices = set((0,))\n",
    "    for dep, head in enumerate(heads[tokens]):\n",
    "        vertices.add(dep + 1)\n",
    "        edges[head].add(dep + 1)\n",
    "        \n",
    "    # identify cycles & contract\n",
    "    for cycle in _find_cycle(vertices, edges):\n",
    "        print(\"Found cycle!\", cycle)\n",
    "        dependents = set()\n",
    "        to_visit = set(cycle)\n",
    "        while len(to_visit) > 0:\n",
    "            node = to_visit.pop()\n",
    "            print(\"Contraction, visiting node:\", node)\n",
    "            if node not in dependents:\n",
    "                dependents.add(node)\n",
    "                to_visit.update(edges[node])\n",
    "        cycle = np.array(list(cycle))\n",
    "        old_heads = heads[cycle]\n",
    "        old_scores = scores[cycle, old_heads]\n",
    "        non_heads = np.array(list(dependents))\n",
    "        scores[np.repeat(cycle, len(non_heads)),\n",
    "               np.repeat([non_heads], len(cycle), axis=0).flatten()] = 0\n",
    "        new_heads = np.argmax(scores[cycle][:, tokens], axis=1) + 1\n",
    "        new_scores = scores[cycle, new_heads] / old_scores\n",
    "        change = np.argmax(new_scores)\n",
    "        changed_cycle = cycle[change]\n",
    "        old_head = old_heads[change]\n",
    "        new_head = new_heads[change]\n",
    "        heads[changed_cycle] = new_head\n",
    "        edges[new_head].add(changed_cycle)\n",
    "        edges[old_head].remove(changed_cycle)\n",
    "\n",
    "    return heads"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def _find_cycle(vertices, edges):\n",
    "    \"\"\"\n",
    "    Finds cycles in given graph, where the graph is provided as (vertices, edges).\n",
    "    https://en.wikipedia.org/wiki/Tarjan%27s_strongly_connected_components_algorithm  # NOQA\n",
    "    https://github.com/tdozat/Parser/blob/0739216129cd39d69997d28cbc4133b360ea3934/lib/etc/tarjan.py  # NOQA\n",
    "    \"\"\"\n",
    "    _index = [0]\n",
    "    _stack = []\n",
    "    _indices = {}\n",
    "    _lowlinks = {}\n",
    "    _onstack = defaultdict(lambda: False)\n",
    "    _SCCs = []\n",
    "\n",
    "    def _strongconnect(v):\n",
    "        _indices[v] = _index[0]\n",
    "        _lowlinks[v] = _index[0]\n",
    "        _index[0] += 1\n",
    "        _stack.append(v)\n",
    "        _onstack[v] = True\n",
    "\n",
    "        for w in edges[v]:\n",
    "            if w not in _indices:\n",
    "                _strongconnect(w)\n",
    "                _lowlinks[v] = min(_lowlinks[v], _lowlinks[w])\n",
    "            elif _onstack[w]:\n",
    "                _lowlinks[v] = min(_lowlinks[v], _indices[w])\n",
    "\n",
    "        if _lowlinks[v] == _indices[v]:\n",
    "            SCC = set()\n",
    "            while True:\n",
    "                w = _stack.pop()\n",
    "                _onstack[w] = False\n",
    "                SCC.add(w)\n",
    "                if not (w != v):\n",
    "                    break\n",
    "            _SCCs.append(SCC)\n",
    "\n",
    "    for v in vertices:\n",
    "        if v not in _indices:\n",
    "            _strongconnect(v)\n",
    "\n",
    "    return [SCC for SCC in _SCCs if len(SCC) > 1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 1: a short sentence\n",
    "\n",
    "Let's try it out on the example in McDonald et al. (2005): \"John saw Mary.\""
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['root', 'john', 'saw', 'mary']\n",
      "[0, 1, 2, 3]\n",
      "4\n"
     ]
    }
   ],
   "source": [
    "w2i = defaultdict(lambda: len(w2i))\n",
    "sentence = \"root john saw mary\".split()\n",
    "sentence_ids = [w2i[token] for token in sentence]\n",
    "num_words = len(sentence)\n",
    "i2w = {i: w for w, i in w2i.items()}\n",
    "\n",
    "print(sentence)\n",
    "print(sentence_ids)\n",
    "print(num_words)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ -1.   9.  10.   9.]\n",
      " [ -1.  -1.  20.   3.]\n",
      " [ -1.  30.  -1.  30.]\n",
      " [ -1.  11.   0.  -1.]]\n"
     ]
    }
   ],
   "source": [
    "# define the scores\n",
    "scores = np.full([num_words, num_words], -1.)\n",
    "scores[w2i['root']][w2i['saw']] = 10.\n",
    "scores[w2i['root']][w2i['mary']] = 9.\n",
    "scores[w2i['root']][w2i['john']] = 9.\n",
    "scores[w2i['john']][w2i['saw']] = 20.\n",
    "scores[w2i['john']][w2i['mary']] = 3.\n",
    "scores[w2i['saw']][w2i['mary']] = 30.\n",
    "scores[w2i['saw']][w2i['john']] = 30.\n",
    "scores[w2i['mary']][w2i['john']] = 11.\n",
    "scores[w2i['mary']][w2i['saw']] = 0.\n",
    "\n",
    "print(scores)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAWoAAAD8CAYAAABekO4JAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nzcwyzonazCzjnKjNzDLu/wNhqOFngMBLtQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1065e7978>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_heatmap(scores):\n",
    "\n",
    "    # make heatmap with the scores\n",
    "    fig, ax = plt.subplots()\n",
    "    heatmap = ax.pcolor(scores, cmap='viridis')\n",
    "\n",
    "    # set tick labels to the words\n",
    "    ax.set_xticklabels(sentence, minor=False)\n",
    "    ax.set_yticklabels(sentence, minor=False)\n",
    "\n",
    "    # put the major ticks at the middle of each cell\n",
    "    # and the x-ticks on top\n",
    "    ax.xaxis.tick_top()\n",
    "    ax.set_xticks(np.arange(scores.shape[1]) + 0.5, minor=False)\n",
    "    ax.set_yticks(np.arange(scores.shape[0]) + 0.5, minor=False)\n",
    "    ax.invert_yaxis()\n",
    "\n",
    "    # display values\n",
    "    for y in range(scores.shape[0]):\n",
    "        for x in range(scores.shape[1]):\n",
    "            plt.text(x + 0.5, y + 0.5, '%.0f' % scores[y, x],\n",
    "                     horizontalalignment='center',\n",
    "                     verticalalignment='center',\n",
    "                     color='w')\n",
    "\n",
    "    plt.colorbar(heatmap)\n",
    "    plt.show()\n",
    "    \n",
    "plot_heatmap(scores)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "initial heads: [0 2 1 2]\n",
      "no node is pointing to root, choosing one\n",
      "new root is: 2\n",
      "final heads: [0 2 0 2]\n"
     ]
    }
   ],
   "source": [
    "heads = mst(scores.T)\n",
    "print(\"final heads:\", heads)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Example 2: a longer sentence\n",
    "\n",
    "Let's now try this on a longer sentence."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2 3 4 5 6 7 8 9]\n",
      "[0 1 2 3 4 5 6 7 8 9]\n",
      "10\n"
     ]
    }
   ],
   "source": [
    "# define a dummy sentence\n",
    "w2i = defaultdict(lambda: len(w2i))\n",
    "sentence = np.arange(10)\n",
    "sentence_ids = sentence\n",
    "num_words = len(sentence)\n",
    "i2w = {i: w for w, i in w2i.items()}\n",
    "\n",
    "print(sentence)\n",
    "print(sentence_ids)\n",
    "print(num_words)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 37.45401188  95.07143064  73.19939418  59.86584842  15.60186404\n",
      "   15.59945203   5.80836122  86.61761458  60.11150117  70.80725778]\n",
      " [  2.05844943  96.99098522  83.24426408  21.23391107  18.18249672\n",
      "   18.34045099  30.4242243   52.47564316  43.19450186  29.12291402]\n",
      " [ 61.18528947  13.94938607  29.21446485  36.63618433  45.60699842\n",
      "   78.51759614  19.96737822  51.42344384  59.24145689   4.64504127]\n",
      " [ 60.75448519  17.05241237   6.5051593   94.88855373  96.56320331\n",
      "   80.83973481  30.46137692   9.7672114   68.42330265  44.01524937]\n",
      " [ 12.20382348  49.51769101   3.43885211  90.93204021  25.87799816\n",
      "   66.25222844  31.17110761  52.00680212  54.67102793  18.48544555]\n",
      " [ 96.95846278  77.51328234  93.94989416  89.48273504  59.78999788\n",
      "   92.1874235    8.84925021  19.59828624   4.52272889  32.53303308]\n",
      " [ 38.86772897  27.13490318  82.87375092  35.67533267  28.09345097\n",
      "   54.26960832  14.0924225   80.21969808   7.45506437  98.68869366]\n",
      " [ 77.22447693  19.87156815   0.55221171  81.54614285  70.68573438\n",
      "   72.9007168   77.12703467   7.40446517  35.84657285  11.58690595]\n",
      " [ 86.31034259  62.32981268  33.08980249   6.35583503  31.09823217\n",
      "   32.5183322   72.96061783  63.75574714  88.72127426  47.22149252]\n",
      " [ 11.95942459  71.32447872  76.07850486  56.12771976  77.096718\n",
      "   49.37955964  52.27328294  42.75410184   2.54191267  10.7891427 ]]\n"
     ]
    }
   ],
   "source": [
    "# define the scores\n",
    "np.random.seed(seed=42)\n",
    "scores = 100 * np.random.rand(num_words, num_words)\n",
    "print(scores)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAVYAAAD8CAYAAAAsX4y/AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x10e013160>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_heatmap(scores)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "initial heads: [0 0 5 4 3 3 7 0 3 6]\n",
      "multiple nodes are pointing to root, choosing one\n",
      "new root is: 1\n",
      "Found cycle! {3, 4}\n",
      "Contraction, visiting node: 3\n",
      "Contraction, visiting node: 4\n",
      "Contraction, visiting node: 5\n",
      "Contraction, visiting node: 8\n",
      "Contraction, visiting node: 2\n",
      "Contraction, visiting node: 3\n",
      "Found cycle! {6, 7}\n",
      "Contraction, visiting node: 6\n",
      "Contraction, visiting node: 7\n",
      "Contraction, visiting node: 9\n",
      "Contraction, visiting node: 3\n",
      "Contraction, visiting node: 4\n",
      "Contraction, visiting node: 5\n",
      "Contraction, visiting node: 6\n",
      "Contraction, visiting node: 8\n",
      "Contraction, visiting node: 2\n",
      "final heads: [0 0 5 7 3 3 7 1 3 6]\n"
     ]
    }
   ],
   "source": [
    "heads = mst(scores.T)\n",
    "print(\"final heads:\", heads)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.6.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}