gap_validation.ipynb

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  "name": "",
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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Gap Joining Validation"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%load_ext autoreload\n",
      "%autoreload 2\n",
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import print_function, division\n",
      "import six, sys\n",
      "sys.path.append('..'); import pathcustomize, about\n",
      "about.about()\n",
      "\n",
      "import math\n",
      "import operator\n",
      "\n",
      "import numpy as np\n",
      "import pandas as pd\n",
      "import matplotlib.pyplot as plt\n",
      "import matplotlib.patches as patches\n",
      "\n",
      "import waldo"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Python 2.7.8 (default, Jul 31 2014 17:07:51) [GCC 4.8.2] on linux2, Host: liverpool\n"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#ex_id = '20130702_135704' # many pics\n",
      "ex_id = '20130702_135652' # many pics\n",
      "\n",
      "experiment = waldo.Experiment(experiment_id=ex_id)\n",
      "graph = experiment.graph.copy()\n",
      "removed = waldo.collider.remove_nodes_outside_roi(graph, experiment)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "screen = pd.read_csv('../../data/prep/gap_validate.csv')\n",
      "screen = screen[screen['eid'] == ex_id]\n",
      "print('{} gaps checked'.format(len(screen)))\n",
      "\n",
      "sa = {a: screen[screen['ans'] == a] for a in ['valid', 'invalid', 'unclear']}\n",
      "for a in sa:\n",
      "    print('{:<10}: {:>4}'.format(a.capitalize(), len(sa[a])))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "1090 gaps checked\n",
        "Unclear   :   65\n",
        "Valid     :  782\n",
        "Invalid   :  243\n"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "FIELDS = 'xytf'\n",
      "    \n",
      "def column_map(terminal):\n",
      "    try:\n",
      "        suffix = {'start': '0', 'end': 'N'}[terminal]\n",
      "    except KeyError:\n",
      "        raise ValueError('')\n",
      "    return {field + suffix: field for field in FIELDS}\n",
      "\n",
      "def terminal_endian(terminals, terminal, bid):\n",
      "    t = terminals.loc[bid].to_dict()\n",
      "    cm = column_map(terminal)\n",
      "    return {cn: t[co] for co, cn in cm.items()}\n",
      "\n",
      "def describe_gap(terminals, from_bid, to_bid):\n",
      "    from_data = terminal_endian(terminals, 'end', from_bid)\n",
      "    to_data = terminal_endian(terminals, 'start', to_bid)\n",
      "    gap = {field: to_data[field] - from_data[field] for field in FIELDS}\n",
      "    gap['s'] = math.sqrt(gap['x']**2 + gap['y']**2)\n",
      "    return gap "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "taper = waldo.tape.Taper(experiment, graph)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# load terminals preprocessed data\n",
      "terminals = experiment.prepdata.terminals\n",
      "terminals.set_index('bid', inplace=True)\n",
      "\n",
      "# pull data for screened gap pairs\n",
      "gapidxs = []\n",
      "gapdata = []\n",
      "for idx, gap in screen.iterrows():\n",
      "    from_blob, to_blob = gap['from_blob'], gap['to_blob']\n",
      "    g = describe_gap(terminals, from_blob, to_blob)\n",
      "    g['from_blob'] = from_blob\n",
      "    g['to_blob'] = to_blob\n",
      "    g['score'] = taper.score(g['s'], g['f'])\n",
      "    gapdata.append(g)\n",
      "    gapidxs.append(idx)\n",
      "\n",
      "# join the data with the valid/invalid (drop unclear for now)\n",
      "gapdata = pd.DataFrame(gapdata, index=gapidxs)\n",
      "gapdata = gapdata.join(pd.concat([sa['valid'], sa['invalid']]), how='inner', rsuffix='_r')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def tpfpfn(df, key, op, threshold, valid=None):\n",
      "    if not callable(op):\n",
      "        op = getattr(operator, op)\n",
      "    if valid is None:\n",
      "        valid = gapdata['ans'] == 'valid'\n",
      "    \n",
      "    positive = op(gapdata[key], threshold)\n",
      "    true_positive = valid & positive\n",
      "    \n",
      "    yield sum(true_positive) # TP\n",
      "    yield sum(positive) - sum(true_positive) # FP\n",
      "    yield sum(valid) - sum(true_positive) # FN\n",
      "    \n",
      "def tpfpfns(df, key, op, thresholds):\n",
      "    valid = gapdata['ans'] == 'valid'\n",
      "    outputs = [], [], []\n",
      "    for th in thresholds:\n",
      "        for l, n in zip(outputs, tpfpfn(df, key, op, th, valid=valid)):\n",
      "            l.append(n)\n",
      "    return outputs\n",
      "\n",
      "def tpfpfns_plot(ax, df, key, op, thresholds):\n",
      "    tps, fps, fns = tpfpfns(df, key, op, thresholds)\n",
      "    outputs = tps, fns, fps # rearrange\n",
      "    stack_coll = ax.stackplot(thresholds, *outputs, baseline='zero', colors=['green', 'yellow', 'red'])\n",
      "    \n",
      "    # make proxy artists for legend\n",
      "    proxy_rects = [patches.Rectangle((0, 0), 1, 1, fc=pc.get_facecolor()[0]) for pc in stack_coll]\n",
      "    ax.legend(proxy_rects, ['TP', 'FN', 'FP'])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Score Thresholds"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "f, axs = plt.subplots(sharey=True, ncols=2)\n",
      "f.set_size_inches((10,8))\n",
      "f.subplots_adjust(wspace=0.05)\n",
      "threshold_ranges = np.logspace(-102, -4, 100), np.logspace(-4, 0, 100)\n",
      "for ax, trange in zip(axs, threshold_ranges):\n",
      "    ax.set_xscale('log')\n",
      "    ax.set_xlabel('Score')\n",
      "    tpfpfns_plot(ax, gapdata, 'score', 'gt', trange)\n",
      "\n",
      "axs[1].legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stderr",
       "text": [
        "/home/visitors/ntimkovich/.pyenv64/versions/waldo27/lib/python2.7/site-packages/matplotlib/axes/_axes.py:475: UserWarning: No labelled objects found. Use label='...' kwarg on individual plots.\n",
        "  warnings.warn(\"No labelled objects found. \"\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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SHPPud/NP3/0uU6ZMqXB1qhRDmKRKM4RJO7EO+K9Uin9ubeXMD36Q93/kI3R3d7PXXnv1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\nRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7ff7fb231710>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Distance Thresholds"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "f, ax = plt.subplots()\n",
      "f.set_size_inches((10,8))\n",
      "trange = np.logspace(-2, 3, 100)\n",
      "ax.set_xscale('log')\n",
      "ax.set_xlabel('Distance (px)')\n",
      "tpfpfns_plot(ax, gapdata, 's', 'lt', trange)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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iiDgbWD+ldHZxYP41FMaBbQrcCfxXWuHNI/pdjiRlZtYs2H57aP0csGHW1Ugq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\nAQAAAIBB/tbD2FMUATCQMACAQXdGIVXAd1YMAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7ff7fb231b90>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "Time Thresholds"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "f, ax = plt.subplots()\n",
      "f.set_size_inches((10,8))\n",
      "trange = np.logspace(-1, 2, 100)\n",
      "ax.set_xscale('log')\n",
      "ax.set_xlabel('Time (sec)')\n",
      "tpfpfns_plot(ax, gapdata, 't', 'lt', trange)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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wScrQr34V3H1vot5Z8aWK46+8JGVk0iT43vcS+YMSrJV1NZL6myFMkjLwxhsw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\n+2wtKaXo7j662wn7AnA08Fx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       "text": [
        "<matplotlib.figure.Figure at 0x7ff7f7df5f10>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    }
   ],
   "metadata": {}
  }
 ]
}