asl_recognizer.ipynb

{
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    "# Artificial Intelligence Engineer Nanodegree - Probabilistic Models\n",
    "## Project: Sign Language Recognition System\n",
    "- [Introduction](#intro)\n",
    "- [Part 1 Feature Selection](#part1_tutorial)\n",
    "    - [Tutorial](#part1_tutorial)\n",
    "    - [Features Submission](#part1_submission)\n",
    "    - [Features Unittest](#part1_test)\n",
    "- [Part 2 Train the models](#part2_tutorial)\n",
    "    - [Tutorial](#part2_tutorial)\n",
    "    - [Model Selection Score Submission](#part2_submission)\n",
    "    - [Model Score Unittest](#part2_test)\n",
    "- [Part 3 Build a Recognizer](#part3_tutorial)\n",
    "    - [Tutorial](#part3_tutorial)\n",
    "    - [Recognizer Submission](#part3_submission)\n",
    "    - [Recognizer Unittest](#part3_test)\n",
    "- [Part 4 (OPTIONAL) Improve the WER with Language Models](#part4_info)"
   ]
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   "source": [
    "<a id='intro'></a>\n",
    "## Introduction\n",
    "The overall goal of this project is to build a word recognizer for American Sign Language video sequences, demonstrating the power of probabalistic models.  In particular, this project employs  [hidden Markov models (HMM's)](https://en.wikipedia.org/wiki/Hidden_Markov_model) to analyze a series of measurements taken from videos of American Sign Language (ASL) collected for research (see the [RWTH-BOSTON-104 Database](http://www-i6.informatik.rwth-aachen.de/~dreuw/database-rwth-boston-104.php)).  In this video, the right-hand x and y locations are plotted as the speaker signs the sentence.\n",
    "[![ASLR demo](http://www-i6.informatik.rwth-aachen.de/~dreuw/images/demosample.png)](https://drive.google.com/open?id=0B_5qGuFe-wbhUXRuVnNZVnMtam8)\n",
    "\n",
    "The raw data, train, and test sets are pre-defined.  You will derive a variety of feature sets (explored in Part 1), as well as implement three different model selection criterion to determine the optimal number of hidden states for each word model (explored in Part 2). Finally, in Part 3 you will implement the recognizer and compare the effects the different combinations of feature sets and model selection criteria.  \n",
    "\n",
    "At the end of each Part, complete the submission cells with implementations, answer all questions, and pass the unit tests.  Then submit the completed notebook for review!"
   ]
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    "<a id='part1_tutorial'></a>\n",
    "## PART 1: Data\n",
    "\n",
    "### Features Tutorial\n",
    "##### Load the initial database\n",
    "A data handler designed for this database is provided in the student codebase as the `AslDb` class in the `asl_data` module.  This handler creates the initial [pandas](http://pandas.pydata.org/pandas-docs/stable/) dataframe from the corpus of data included in the `data` directory as well as dictionaries suitable for extracting data in a format friendly to the [hmmlearn](https://hmmlearn.readthedocs.io/en/latest/) library.  We'll use those to create models in Part 2.\n",
    "\n",
    "To start, let's set up the initial database and select an example set of features for the training set.  At the end of Part 1, you will create additional feature sets for experimentation. "
   ]
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>left-x</th>\n",
       "      <th>left-y</th>\n",
       "      <th>right-x</th>\n",
       "      <th>right-y</th>\n",
       "      <th>nose-x</th>\n",
       "      <th>nose-y</th>\n",
       "      <th>speaker</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>video</th>\n",
       "      <th>frame</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
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       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th rowspan=\"5\" valign=\"top\">98</th>\n",
       "      <th>0</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      "text/plain": [
       "             left-x  left-y  right-x  right-y  nose-x  nose-y  speaker\n",
       "video frame                                                           \n",
       "98    0         149     181      170      175     161      62  woman-1\n",
       "      1         149     181      170      175     161      62  woman-1\n",
       "      2         149     181      170      175     161      62  woman-1\n",
       "      3         149     181      170      175     161      62  woman-1\n",
       "      4         149     181      170      175     161      62  woman-1"
      ]
     },
     "execution_count": 1,
     "metadata": {},
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   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from asl_data import AslDb\n",
    "\n",
    "\n",
    "asl = AslDb() # initializes the database\n",
    "asl.df.head() # displays the first five rows of the asl database, indexed by video and frame"
   ]
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   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
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    {
     "data": {
      "text/plain": [
       "left-x         149\n",
       "left-y         181\n",
       "right-x        170\n",
       "right-y        175\n",
       "nose-x         161\n",
       "nose-y          62\n",
       "speaker    woman-1\n",
       "Name: (98, 1), dtype: object"
      ]
     },
     "execution_count": 3,
     "metadata": {},
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   "source": [
    "asl.df.ix[98,1]  # look at the data available for an individual frame"
   ]
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   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The frame represented by video 98, frame 1 is shown here:\n",
    "![Video 98](http://www-i6.informatik.rwth-aachen.de/~dreuw/database/rwth-boston-104/overview/images/orig/098-start.jpg)"
   ]
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   "source": [
    "##### Feature selection for training the model\n",
    "The objective of feature selection when training a model is to choose the most relevant variables while keeping the model as simple as possible, thus reducing training time.  We can use the raw features already provided or derive our own and add columns to the pandas dataframe `asl.df` for selection. As an example, in the next cell a feature named `'grnd-ry'` is added. This feature is the difference between the right-hand y value and the nose y value, which serves as the \"ground\" right y value. "
   ]
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   "cell_type": "code",
   "execution_count": 4,
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       "      <td>woman-1</td>\n",
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       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
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       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
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      "text/plain": [
       "             left-x  left-y  right-x  right-y  nose-x  nose-y  speaker  \\\n",
       "video frame                                                              \n",
       "98    0         149     181      170      175     161      62  woman-1   \n",
       "      1         149     181      170      175     161      62  woman-1   \n",
       "      2         149     181      170      175     161      62  woman-1   \n",
       "      3         149     181      170      175     161      62  woman-1   \n",
       "      4         149     181      170      175     161      62  woman-1   \n",
       "\n",
       "             grnd-ry  \n",
       "video frame           \n",
       "98    0          113  \n",
       "      1          113  \n",
       "      2          113  \n",
       "      3          113  \n",
       "      4          113  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "asl.df['grnd-ry'] = asl.df['right-y'] - asl.df['nose-y']\n",
    "asl.df.head()  # the new feature 'grnd-ry' is now in the frames dictionary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Try it!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "asl.df sample\n"
     ]
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       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
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       "      <td>119</td>\n",
       "      <td>-12</td>\n",
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       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
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       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
       "      <td>9</td>\n",
       "      <td>119</td>\n",
       "      <td>-12</td>\n",
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      "text/plain": [
       "             left-x  left-y  right-x  right-y  nose-x  nose-y  speaker  \\\n",
       "video frame                                                              \n",
       "98    0         149     181      170      175     161      62  woman-1   \n",
       "      1         149     181      170      175     161      62  woman-1   \n",
       "      2         149     181      170      175     161      62  woman-1   \n",
       "      3         149     181      170      175     161      62  woman-1   \n",
       "      4         149     181      170      175     161      62  woman-1   \n",
       "\n",
       "             grnd-ry  grnd-rx  grnd-ly  grnd-lx  \n",
       "video frame                                      \n",
       "98    0          113        9      119      -12  \n",
       "      1          113        9      119      -12  \n",
       "      2          113        9      119      -12  \n",
       "      3          113        9      119      -12  \n",
       "      4          113        9      119      -12  "
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      "text/html": [
       "<font color=green>Correct!</font><br/>"
      ],
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       "<IPython.core.display.HTML object>"
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     "execution_count": 5,
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   ],
   "source": [
    "from asl_utils import test_features_tryit\n",
    "# TODO add df columns for 'grnd-rx', 'grnd-ly', 'grnd-lx' representing differences between hand and nose locations\n",
    "asl.df['grnd-rx'] = asl.df['right-x'] - asl.df['nose-x']\n",
    "asl.df['grnd-ly'] = asl.df['left-y'] - asl.df['nose-y']\n",
    "asl.df['grnd-lx'] = asl.df['left-x'] - asl.df['nose-x']\n",
    "\n",
    "# test the code\n",
    "test_features_tryit(asl)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[9, 113, -12, 119]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# collect the features into a list\n",
    "features_ground = ['grnd-rx','grnd-ry','grnd-lx','grnd-ly']\n",
    " #show a single set of features for a given (video, frame) tuple\n",
    "[asl.df.ix[98,1][v] for v in features_ground]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Build the training set\n",
    "Now that we have a feature list defined, we can pass that list to the `build_training` method to collect the features for all the words in the training set.  Each word in the training set has multiple examples from various videos.  Below we can see the unique words that have been loaded into the training set:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training words: ['STOLEN', 'TELL', 'VEGETABLE', 'BUT', 'FRANK', 'LIVE', 'GIVE3', 'BUY', 'COAT', 'SAY', 'WOMAN', 'TOMORROW', 'ANN', 'THROW', 'JANA', 'CAN', 'DECIDE', 'CAR', 'FINISH', 'GIRL', 'HOUSE', 'FUTURE1', 'LAST-WEEK', 'LOVE', 'GIVE', 'SAY-1P', 'VIDEOTAPE', 'LIKE', 'ARRIVE', 'BREAK-DOWN', 'TEACHER', 'STUDENT', 'SHOULD', 'PARTY', 'EAT', 'FRED', 'PUTASIDE', 'MOVIE', 'BLUE', 'HAVE', 'READ', 'JOHN', 'GO1', 'HOMEWORK', 'BLAME', 'SEARCH-FOR', 'PEOPLE', 'FIND', 'WHO', 'WANT', 'SUE', 'MOTHER', 'YESTERDAY', 'CHINA', 'NAME', 'KNOW', 'HERE', 'SOMETHING-ONE', 'GIVE2', 'NEW', 'LEG', 'CHOCOLATE', 'IX-1P', 'LEAVE', 'HIT', 'POTATO', 'CORN', 'WONT', 'FISH', 'PREFER', 'BUY1', 'CHICAGO', 'GO', 'BOOK', 'PAST', 'SELF', 'SEE', 'TOY', 'GROUP', 'IX', 'FRIEND', 'OLD', 'ALL', 'BILL', 'TOY1', 'SHOOT', 'NOT', 'MARY', 'VISIT', 'SELL', 'BOX', 'CANDY', 'POSS', 'APPLE', 'BOY', 'THINK', 'CHICKEN', 'BORROW', 'NEW-YORK', 'GO2', 'GET', 'WILL', 'WRITE', 'MAN', 'FUTURE', 'GIVE1', 'WHAT', 'CORN1', 'MANY', 'NEXT-WEEK', 'BROCCOLI', 'BROTHER']\n"
     ]
    }
   ],
   "source": [
    "training = asl.build_training(features_ground)\n",
    "print(\"Training words: {}\".format(training.words))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The training data in `training` is an object of class `WordsData` defined in the `asl_data` module.  in addition to the `words` list, data can be accessed with the `get_all_sequences`, `get_all_Xlengths`, `get_word_sequences`, and `get_word_Xlengths` methods. We need the `get_word_Xlengths` method to train multiple sequences with the `hmmlearn` library.  In the following example, notice that there are two lists; the first is a concatenation of all the sequences(the X portion) and the second is a list of the sequence lengths(the Lengths portion)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[-11,  48,   7, 120],\n",
       "        [-11,  48,   8, 109],\n",
       "        [ -8,  49,  11,  98],\n",
       "        [ -7,  50,   7,  87],\n",
       "        [ -4,  54,   7,  77],\n",
       "        [ -4,  54,   6,  69],\n",
       "        [ -4,  54,   6,  69],\n",
       "        [-13,  52,   6,  69],\n",
       "        [-13,  52,   6,  69],\n",
       "        [ -8,  51,   6,  69],\n",
       "        [ -8,  51,   6,  69],\n",
       "        [ -8,  51,   6,  69],\n",
       "        [ -8,  51,   6,  69],\n",
       "        [ -8,  51,   6,  69],\n",
       "        [-10,  59,   7,  71],\n",
       "        [-15,  64,   9,  77],\n",
       "        [-17,  75,  13,  81],\n",
       "        [ -4,  48,  -4, 113],\n",
       "        [ -2,  53,  -4, 113],\n",
       "        [ -4,  55,   2,  98],\n",
       "        [ -4,  58,   2,  98],\n",
       "        [ -1,  59,   2,  89],\n",
       "        [ -1,  59,  -1,  84],\n",
       "        [ -1,  59,  -1,  84],\n",
       "        [ -7,  63,  -1,  84],\n",
       "        [ -7,  63,  -1,  84],\n",
       "        [ -7,  63,   3,  83],\n",
       "        [ -7,  63,   3,  83],\n",
       "        [ -7,  63,   3,  83],\n",
       "        [ -7,  63,   3,  83],\n",
       "        [ -7,  63,   3,  83],\n",
       "        [ -7,  63,   3,  83],\n",
       "        [ -7,  63,   3,  83],\n",
       "        [ -4,  70,   3,  83],\n",
       "        [ -4,  70,   3,  83],\n",
       "        [ -2,  73,   5,  90],\n",
       "        [ -3,  79,  -4,  96],\n",
       "        [-15,  98,  13, 135],\n",
       "        [ -6,  93,  12, 128],\n",
       "        [ -2,  89,  14, 118],\n",
       "        [  5,  90,  10, 108],\n",
       "        [  4,  86,   7, 105],\n",
       "        [  4,  86,   7, 105],\n",
       "        [  4,  86,  13, 100],\n",
       "        [ -3,  82,  14,  96],\n",
       "        [ -3,  82,  14,  96],\n",
       "        [  6,  89,  16, 100],\n",
       "        [  6,  89,  16, 100],\n",
       "        [  7,  85,  17, 111]], dtype=int64), [17, 20, 12])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "training.get_word_Xlengths('CHOCOLATE')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###### More feature sets\n",
    "So far we have a simple feature set that is enough to get started modeling.  However, we might get better results if we manipulate the raw values a bit more, so we will go ahead and set up some other options now for experimentation later.  For example, we could normalize each speaker's range of motion with grouped statistics using [Pandas stats](http://pandas.pydata.org/pandas-docs/stable/api.html#api-dataframe-stats) functions and [pandas groupby](http://pandas.pydata.org/pandas-docs/stable/generated/pandas.DataFrame.groupby.html).  Below is an example for finding the means of all speaker subgroups."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>left-x</th>\n",
       "      <th>left-y</th>\n",
       "      <th>right-x</th>\n",
       "      <th>right-y</th>\n",
       "      <th>nose-x</th>\n",
       "      <th>nose-y</th>\n",
       "      <th>grnd-ry</th>\n",
       "      <th>grnd-rx</th>\n",
       "      <th>grnd-ly</th>\n",
       "      <th>grnd-lx</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>speaker</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>man-1</th>\n",
       "      <td>206.248203</td>\n",
       "      <td>218.679449</td>\n",
       "      <td>155.464350</td>\n",
       "      <td>150.371031</td>\n",
       "      <td>175.031756</td>\n",
       "      <td>61.642600</td>\n",
       "      <td>88.728430</td>\n",
       "      <td>-19.567406</td>\n",
       "      <td>157.036848</td>\n",
       "      <td>31.216447</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>woman-1</th>\n",
       "      <td>164.661438</td>\n",
       "      <td>161.271242</td>\n",
       "      <td>151.017865</td>\n",
       "      <td>117.332462</td>\n",
       "      <td>162.655120</td>\n",
       "      <td>57.245098</td>\n",
       "      <td>60.087364</td>\n",
       "      <td>-11.637255</td>\n",
       "      <td>104.026144</td>\n",
       "      <td>2.006318</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>woman-2</th>\n",
       "      <td>183.214509</td>\n",
       "      <td>176.527232</td>\n",
       "      <td>156.866295</td>\n",
       "      <td>119.835714</td>\n",
       "      <td>170.318973</td>\n",
       "      <td>58.022098</td>\n",
       "      <td>61.813616</td>\n",
       "      <td>-13.452679</td>\n",
       "      <td>118.505134</td>\n",
       "      <td>12.895536</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             left-x      left-y     right-x     right-y      nose-x  \\\n",
       "speaker                                                               \n",
       "man-1    206.248203  218.679449  155.464350  150.371031  175.031756   \n",
       "woman-1  164.661438  161.271242  151.017865  117.332462  162.655120   \n",
       "woman-2  183.214509  176.527232  156.866295  119.835714  170.318973   \n",
       "\n",
       "            nose-y    grnd-ry    grnd-rx     grnd-ly    grnd-lx  \n",
       "speaker                                                          \n",
       "man-1    61.642600  88.728430 -19.567406  157.036848  31.216447  \n",
       "woman-1  57.245098  60.087364 -11.637255  104.026144   2.006318  \n",
       "woman-2  58.022098  61.813616 -13.452679  118.505134  12.895536  "
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_means = asl.df.groupby('speaker').mean()\n",
    "df_means"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To select a mean that matches by speaker, use the pandas [map](http://pandas.pydata.org/pandas-docs/stable/generated/pandas.Series.map.html) method:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th>grnd-ly</th>\n",
       "      <th>grnd-lx</th>\n",
       "      <th>left-x-mean</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>video</th>\n",
       "      <th>frame</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "      <th rowspan=\"5\" valign=\"top\">98</th>\n",
       "      <th>0</th>\n",
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       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
       "      <td>9</td>\n",
       "      <td>119</td>\n",
       "      <td>-12</td>\n",
       "      <td>164.661438</td>\n",
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       "      <td>149</td>\n",
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       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
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       "      <td>9</td>\n",
       "      <td>119</td>\n",
       "      <td>-12</td>\n",
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       "      <td>149</td>\n",
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       "      <td>175</td>\n",
       "      <td>161</td>\n",
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       "      <td>175</td>\n",
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       "      <td>woman-1</td>\n",
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       "      <td>9</td>\n",
       "      <td>119</td>\n",
       "      <td>-12</td>\n",
       "      <td>164.661438</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>149</td>\n",
       "      <td>181</td>\n",
       "      <td>170</td>\n",
       "      <td>175</td>\n",
       "      <td>161</td>\n",
       "      <td>62</td>\n",
       "      <td>woman-1</td>\n",
       "      <td>113</td>\n",
       "      <td>9</td>\n",
       "      <td>119</td>\n",
       "      <td>-12</td>\n",
       "      <td>164.661438</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             left-x  left-y  right-x  right-y  nose-x  nose-y  speaker  \\\n",
       "video frame                                                              \n",
       "98    0         149     181      170      175     161      62  woman-1   \n",
       "      1         149     181      170      175     161      62  woman-1   \n",
       "      2         149     181      170      175     161      62  woman-1   \n",
       "      3         149     181      170      175     161      62  woman-1   \n",
       "      4         149     181      170      175     161      62  woman-1   \n",
       "\n",
       "             grnd-ry  grnd-rx  grnd-ly  grnd-lx  left-x-mean  \n",
       "video frame                                                   \n",
       "98    0          113        9      119      -12   164.661438  \n",
       "      1          113        9      119      -12   164.661438  \n",
       "      2          113        9      119      -12   164.661438  \n",
       "      3          113        9      119      -12   164.661438  \n",
       "      4          113        9      119      -12   164.661438  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "asl.df['left-x-mean']= asl.df['speaker'].map(df_means['left-x'])\n",
    "asl.df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Try it!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "df_std\n"
     ]
    },
    {
     "data": {
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       "      <th>right-y</th>\n",
       "      <th>nose-x</th>\n",
       "      <th>nose-y</th>\n",
       "      <th>grnd-ry</th>\n",
       "      <th>grnd-rx</th>\n",
       "      <th>grnd-ly</th>\n",
       "      <th>grnd-lx</th>\n",
       "      <th>left-x-mean</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>speaker</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>man-1</th>\n",
       "      <td>15.154425</td>\n",
       "      <td>36.328485</td>\n",
       "      <td>18.901917</td>\n",
       "      <td>54.902340</td>\n",
       "      <td>6.654573</td>\n",
       "      <td>5.520045</td>\n",
       "      <td>53.487999</td>\n",
       "      <td>20.269032</td>\n",
       "      <td>36.572749</td>\n",
       "      <td>15.080360</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>woman-1</th>\n",
       "      <td>17.573442</td>\n",
       "      <td>26.594521</td>\n",
       "      <td>16.459943</td>\n",
       "      <td>34.667787</td>\n",
       "      <td>3.549392</td>\n",
       "      <td>3.538330</td>\n",
       "      <td>33.972660</td>\n",
       "      <td>16.764706</td>\n",
       "      <td>27.117393</td>\n",
       "      <td>17.328941</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>woman-2</th>\n",
       "      <td>15.388711</td>\n",
       "      <td>28.825025</td>\n",
       "      <td>14.890288</td>\n",
       "      <td>39.649111</td>\n",
       "      <td>4.099760</td>\n",
       "      <td>3.416167</td>\n",
       "      <td>39.128572</td>\n",
       "      <td>16.191324</td>\n",
       "      <td>29.320655</td>\n",
       "      <td>15.050938</td>\n",
       "      <td>0.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "            left-x     left-y    right-x    right-y    nose-x    nose-y  \\\n",
       "speaker                                                                   \n",
       "man-1    15.154425  36.328485  18.901917  54.902340  6.654573  5.520045   \n",
       "woman-1  17.573442  26.594521  16.459943  34.667787  3.549392  3.538330   \n",
       "woman-2  15.388711  28.825025  14.890288  39.649111  4.099760  3.416167   \n",
       "\n",
       "           grnd-ry    grnd-rx    grnd-ly    grnd-lx  left-x-mean  \n",
       "speaker                                                           \n",
       "man-1    53.487999  20.269032  36.572749  15.080360          0.0  \n",
       "woman-1  33.972660  16.764706  27.117393  17.328941          0.0  \n",
       "woman-2  39.128572  16.191324  29.320655  15.050938          0.0  "
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/html": [
       "<font color=green>Correct!</font><br/>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from asl_utils import test_std_tryit\n",
    "# TODO Create a dataframe named `df_std` with standard deviations grouped by speaker\n",
    "df_std = asl.df.groupby('speaker').std()\n",
    "\n",
    "# test the code\n",
    "test_std_tryit(df_std)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='part1_submission'></a>\n",
    "### Features Implementation Submission\n",
    "Implement four feature sets and answer the question that follows.\n",
    "- normalized Cartesian coordinates\n",
    "    - use *mean* and *standard deviation* statistics and the [standard score](https://en.wikipedia.org/wiki/Standard_score) equation to account for speakers with different heights and arm length\n",
    "    \n",
    "- polar coordinates\n",
    "    - calculate polar coordinates with [Cartesian to polar equations](https://en.wikipedia.org/wiki/Polar_coordinate_system#Converting_between_polar_and_Cartesian_coordinates)\n",
    "    - use the [np.arctan2](https://docs.scipy.org/doc/numpy-1.10.0/reference/generated/numpy.arctan2.html) function and *swap the x and y axes* to move the $0$ to $2\\pi$ discontinuity to 12 o'clock instead of 3 o'clock;  in other words, the normal break in radians value from $0$ to $2\\pi$ occurs directly to the left of the speaker's nose, which may be in the signing area and interfere with results.  By swapping the x and y axes, that discontinuity move to directly above the speaker's head, an area not generally used in signing.\n",
    "\n",
    "- delta difference\n",
    "    - as described in Thad's lecture, use the difference in values between one frame and the next frames as features\n",
    "    - pandas [diff method](http://pandas.pydata.org/pandas-docs/stable/generated/pandas.DataFrame.diff.html) and [fillna method](http://pandas.pydata.org/pandas-docs/stable/generated/pandas.DataFrame.fillna.html) will be helpful for this one\n",
    "\n",
    "- custom features\n",
    "    - These are your own design; combine techniques used above or come up with something else entirely. We look forward to seeing what you come up with! \n",
    "    Some ideas to get you started:\n",
    "        - normalize using a [feature scaling equation](https://en.wikipedia.org/wiki/Feature_scaling)\n",
    "        - normalize the polar coordinates\n",
    "        - adding additional deltas\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
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       "      <th>norm-rx</th>\n",
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       "      <th>norm-lx</th>\n",
       "      <th>norm-ly</th>\n",
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       "      <th>3</th>\n",
       "      <td>1.153232</td>\n",
       "      <td>1.663433</td>\n",
       "      <td>-0.891199</td>\n",
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       "      <th>4</th>\n",
       "      <td>1.153232</td>\n",
       "      <td>1.663433</td>\n",
       "      <td>-0.891199</td>\n",
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      ],
      "text/plain": [
       "              norm-rx   norm-ry   norm-lx   norm-ly\n",
       "video frame                                        \n",
       "98    0      1.153232  1.663433 -0.891199  0.741835\n",
       "      1      1.153232  1.663433 -0.891199  0.741835\n",
       "      2      1.153232  1.663433 -0.891199  0.741835\n",
       "      3      1.153232  1.663433 -0.891199  0.741835\n",
       "      4      1.153232  1.663433 -0.891199  0.741835"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# TODO add features for normalized by speaker values of left, right, x, y\n",
    "# Name these 'norm-rx', 'norm-ry', 'norm-lx', and 'norm-ly'\n",
    "# using Z-score scaling (X-Xmean)/Xstd\n",
    "\n",
    "features_norm = ['norm-rx', 'norm-ry', 'norm-lx','norm-ly']\n",
    "for feature, x in zip(features_norm, ['right-x', 'right-y', 'left-x', 'left-y']):\n",
    "    asl.df[feature] = (asl.df[x] - asl.df['speaker'].map(df_means[x])) / asl.df['speaker'].map(df_std[x])\n",
    "asl.df[features_norm].head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>polar-rr</th>\n",
       "      <th>polar-rtheta</th>\n",
       "      <th>polar-lr</th>\n",
       "      <th>polar-ltheta</th>\n",
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       "      <td>-0.100501</td>\n",
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       "      <td>113.35784</td>\n",
       "      <td>0.079478</td>\n",
       "      <td>119.603512</td>\n",
       "      <td>-0.100501</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>113.35784</td>\n",
       "      <td>0.079478</td>\n",
       "      <td>119.603512</td>\n",
       "      <td>-0.100501</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>113.35784</td>\n",
       "      <td>0.079478</td>\n",
       "      <td>119.603512</td>\n",
       "      <td>-0.100501</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>113.35784</td>\n",
       "      <td>0.079478</td>\n",
       "      <td>119.603512</td>\n",
       "      <td>-0.100501</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "              polar-rr  polar-rtheta    polar-lr  polar-ltheta\n",
       "video frame                                                   \n",
       "98    0      113.35784      0.079478  119.603512     -0.100501\n",
       "      1      113.35784      0.079478  119.603512     -0.100501\n",
       "      2      113.35784      0.079478  119.603512     -0.100501\n",
       "      3      113.35784      0.079478  119.603512     -0.100501\n",
       "      4      113.35784      0.079478  119.603512     -0.100501"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# TODO add features for polar coordinate values where the nose is the origin\n",
    "# Name these 'polar-rr', 'polar-rtheta', 'polar-lr', and 'polar-ltheta'\n",
    "# Note that 'polar-rr' and 'polar-rtheta' refer to the radius and angle\n",
    "\n",
    "features_polar = ['polar-rr', 'polar-rtheta', 'polar-lr', 'polar-ltheta']\n",
    "\n",
    "for r, t, g in zip(features_polar[::2], features_polar[1::2], [('grnd-rx', 'grnd-ry'), ('grnd-lx', 'grnd-ly')]):\n",
    "    x = asl.df[g[0]]\n",
    "    y = asl.df[g[1]]\n",
    "    asl.df[r] = np.sqrt(x**2 + y**2)\n",
    "    asl.df[t] = np.arctan2(x, y)\n",
    "asl.df[features_polar].head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
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       "      <th>delta-rx</th>\n",
       "      <th>delta-ry</th>\n",
       "      <th>delta-lx</th>\n",
       "      <th>delta-ly</th>\n",
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       "      <th rowspan=\"5\" valign=\"top\">125</th>\n",
       "      <th>52</th>\n",
       "      <td>2.0</td>\n",
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       "      <th>53</th>\n",
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       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>54</th>\n",
       "      <td>3.0</td>\n",
       "      <td>8.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>55</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>56</th>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
       "      <td>0.0</td>\n",
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      "text/plain": [
       "             delta-rx  delta-ry  delta-lx  delta-ly\n",
       "video frame                                        \n",
       "125   52          2.0       9.0       0.0       0.0\n",
       "      53          1.0       9.0       0.0       0.0\n",
       "      54          3.0       8.0       0.0       0.0\n",
       "      55          0.0       0.0       0.0       0.0\n",
       "      56          0.0       0.0       0.0       0.0"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# TODO add features for left, right, x, y differences by one time step, i.e. the \"delta\" values discussed in the lecture\n",
    "# Name these 'delta-rx', 'delta-ry', 'delta-lx', and 'delta-ly'\n",
    "\n",
    "features_delta = ['delta-rx', 'delta-ry', 'delta-lx', 'delta-ly']\n",
    "for feature, x in zip(features_delta, ['right-x', 'right-y', 'left-x', 'left-y']):\n",
    "    asl.df[feature] = asl.df[x].diff().fillna(0, None, 0, False, None, None)\n",
    "asl.df[features_delta].tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
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       "      <th></th>\n",
       "      <th></th>\n",
       "      <th>rescale-rx</th>\n",
       "      <th>rescale-ry</th>\n",
       "      <th>rescale-lx</th>\n",
       "      <th>rescale-ly</th>\n",
       "    </tr>\n",
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       "      <th>video</th>\n",
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       "      <th>1</th>\n",
       "      <td>0.66087</td>\n",
       "      <td>0.971831</td>\n",
       "      <td>0.104167</td>\n",
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       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.66087</td>\n",
       "      <td>0.971831</td>\n",
       "      <td>0.104167</td>\n",
       "      <td>0.906542</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.66087</td>\n",
       "      <td>0.971831</td>\n",
       "      <td>0.104167</td>\n",
       "      <td>0.906542</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.66087</td>\n",
       "      <td>0.971831</td>\n",
       "      <td>0.104167</td>\n",
       "      <td>0.906542</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             rescale-rx  rescale-ry  rescale-lx  rescale-ly\n",
       "video frame                                                \n",
       "98    0         0.66087    0.971831    0.104167    0.906542\n",
       "      1         0.66087    0.971831    0.104167    0.906542\n",
       "      2         0.66087    0.971831    0.104167    0.906542\n",
       "      3         0.66087    0.971831    0.104167    0.906542\n",
       "      4         0.66087    0.971831    0.104167    0.906542"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# TODO add features of your own design, which may be a combination of the above or something else\n",
    "# Name these whatever you would like\n",
    "\n",
    "# TODO define a list named 'features_custom' for building the training set\n",
    "features_custom = ['rescale-rx', 'rescale-ry', 'rescale-lx', 'rescale-ly']\n",
    "\n",
    "df_min = asl.df.groupby('speaker').min()\n",
    "df_max = asl.df.groupby('speaker').max()\n",
    "\n",
    "for feature, x in zip(features_custom, ['right-x', 'right-y', 'left-x', 'left-y']):\n",
    "    min_x = asl.df['speaker'].map(df_min[x])\n",
    "    max_x = asl.df['speaker'].map(df_max[x])\n",
    "    asl.df[feature] = (asl.df[x] - min_x) / (max_x - min_x)\n",
    "asl.df[features_custom].head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 1:**  What custom features did you choose for the features_custom set and why?\n",
    "\n",
    "**Answer 1:**\n",
    "- I used [feature scaling](https://en.wikipedia.org/wiki/Feature_scaling) to rescale the features `right-x`, `right-y`, `left-x`, `left-y` with min-max scaling to the range in [0, 1]. Because feature scaling would help to standardize the range of the features."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='part1_test'></a>\n",
    "### Features Unit Testing\n",
    "Run the following unit tests as a sanity check on the defined \"ground\", \"norm\", \"polar\", and 'delta\"\n",
    "feature sets.  The test simply looks for some valid values but is not exhaustive.  However, the project should not be submitted if these tests don't pass."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "....\n",
      "----------------------------------------------------------------------\n",
      "Ran 4 tests in 0.030s\n",
      "\n",
      "OK\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<unittest.runner.TextTestResult run=4 errors=0 failures=0>"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import unittest\n",
    "# import numpy as np\n",
    "\n",
    "class TestFeatures(unittest.TestCase):\n",
    "\n",
    "    def test_features_ground(self):\n",
    "        sample = (asl.df.ix[98, 1][features_ground]).tolist()\n",
    "        self.assertEqual(sample, [9, 113, -12, 119])\n",
    "\n",
    "    def test_features_norm(self):\n",
    "        sample = (asl.df.ix[98, 1][features_norm]).tolist()\n",
    "        np.testing.assert_almost_equal(sample, [ 1.153,  1.663, -0.891,  0.742], 3)\n",
    "\n",
    "    def test_features_polar(self):\n",
    "        sample = (asl.df.ix[98,1][features_polar]).tolist()\n",
    "        np.testing.assert_almost_equal(sample, [113.3578, 0.0794, 119.603, -0.1005], 3)\n",
    "\n",
    "    def test_features_delta(self):\n",
    "        sample = (asl.df.ix[98, 0][features_delta]).tolist()\n",
    "        self.assertEqual(sample, [0, 0, 0, 0])\n",
    "        sample = (asl.df.ix[98, 18][features_delta]).tolist()\n",
    "        self.assertTrue(sample in [[-16, -5, -2, 4], [-14, -9, 0, 0]], \"Sample value found was {}\".format(sample))\n",
    "                         \n",
    "suite = unittest.TestLoader().loadTestsFromModule(TestFeatures())\n",
    "unittest.TextTestRunner().run(suite)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "<a id='part2_tutorial'></a>\n",
    "## PART 2: Model Selection\n",
    "### Model Selection Tutorial\n",
    "The objective of Model Selection is to tune the number of states for each word HMM prior to testing on unseen data.  In this section you will explore three methods: \n",
    "- Log likelihood using cross-validation folds (CV)\n",
    "- Bayesian Information Criterion (BIC)\n",
    "- Discriminative Information Criterion (DIC) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Train a single word\n",
    "Now that we have built a training set with sequence data, we can \"train\" models for each word.  As a simple starting example, we train a single word using Gaussian hidden Markov models (HMM).   By using the `fit` method during training, the [Baum-Welch Expectation-Maximization](https://en.wikipedia.org/wiki/Baum%E2%80%93Welch_algorithm) (EM) algorithm is invoked iteratively to find the best estimate for the model *for the number of hidden states specified* from a group of sample seequences. For this example, we *assume* the correct number of hidden states is 3, but that is just a guess.  How do we know what the \"best\" number of states for training is?  We will need to find some model selection technique to choose the best parameter."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of states trained in model for BOOK is 3\n",
      "logL = -2331.1138127433187\n"
     ]
    }
   ],
   "source": [
    "import warnings\n",
    "from hmmlearn.hmm import GaussianHMM\n",
    "\n",
    "def train_a_word(word, num_hidden_states, features):\n",
    "    \n",
    "    warnings.filterwarnings(\"ignore\", category=DeprecationWarning)\n",
    "    training = asl.build_training(features)  \n",
    "    X, lengths = training.get_word_Xlengths(word)\n",
    "    model = GaussianHMM(n_components=num_hidden_states, n_iter=1000).fit(X, lengths)\n",
    "    logL = model.score(X, lengths)\n",
    "    return model, logL\n",
    "\n",
    "demoword = 'BOOK'\n",
    "model, logL = train_a_word(demoword, 3, features_ground)\n",
    "print(\"Number of states trained in model for {} is {}\".format(demoword, model.n_components))\n",
    "print(\"logL = {}\".format(logL))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The HMM model has been trained and information can be pulled from the model, including means and variances for each feature and hidden state.  The [log likelihood](http://math.stackexchange.com/questions/892832/why-we-consider-log-likelihood-instead-of-likelihood-in-gaussian-distribution) for any individual sample or group of samples can also be calculated with the `score` method."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of states trained in model for BOOK is 3\n",
      "hidden state #0\n",
      "mean =  [-1.12415027 69.44164191 17.02866283 77.7231196 ]\n",
      "variance =  [19.70434594 16.83041492 30.51552305 11.03678246]\n",
      "\n",
      "hidden state #1\n",
      "mean =  [-11.45300909  94.109178    19.03512475 102.2030162 ]\n",
      "variance =  [ 77.403668   203.35441965  26.68898447 156.12444034]\n",
      "\n",
      "hidden state #2\n",
      "mean =  [-3.46504869 50.66686933 14.02391587 52.04731066]\n",
      "variance =  [49.12346305 43.04799144 39.35109609 47.24195772]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "def show_model_stats(word, model):\n",
    "    print(\"Number of states trained in model for {} is {}\".format(word, model.n_components))    \n",
    "    variance=np.array([np.diag(model.covars_[i]) for i in range(model.n_components)])    \n",
    "    for i in range(model.n_components):  # for each hidden state\n",
    "        print(\"hidden state #{}\".format(i))\n",
    "        print(\"mean = \", model.means_[i])\n",
    "        print(\"variance = \", variance[i])\n",
    "        print()\n",
    "    \n",
    "show_model_stats(demoword, model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Try it!\n",
    "Experiment by changing the feature set, word, and/or num_hidden_states values in the next cell to see changes in values.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of states trained in model for CHOCOLATE is 3\n",
      "hidden state #0\n",
      "mean =  [  0.58333333  87.91666667  12.75       108.5       ]\n",
      "variance =  [ 39.41055556  18.74388889   9.855      144.4175    ]\n",
      "\n",
      "hidden state #1\n",
      "mean =  [-9.30211403 55.32333876  6.92259936 71.24057775]\n",
      "variance =  [16.16920957 46.50917372  3.81388185 15.79446427]\n",
      "\n",
      "hidden state #2\n",
      "mean =  [-5.40587658 60.1652424   2.32479599 91.3095432 ]\n",
      "variance =  [  7.95073876  64.13103127  13.68077479 129.5912395 ]\n",
      "\n",
      "logL = -601.3291470028621\n"
     ]
    }
   ],
   "source": [
    "my_testword = 'CHOCOLATE'\n",
    "model, logL = train_a_word(my_testword, 3, features_ground) # Experiment here with different parameters\n",
    "show_model_stats(my_testword, model)\n",
    "print(\"logL = {}\".format(logL))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Visualize the hidden states\n",
    "We can plot the means and variances for each state and feature.  Try varying the number of states trained for the HMM model and examine the variances.  Are there some models that are \"better\" than others?  How can you tell?  We would like to hear what you think in the classroom online."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x263cb2f85f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x263cb3737f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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n9B2OKLDtc7OmTqshu+l3c7S1CZ1hj0Lr0+DtiXAoN9raOKqDM/oORy1zNN98cdu8E/S8fT3ia2JzHSWhMVyRbfr3/zMeKsqjrZGjqjij73DUIqpmXfzDO4zxTEiJPauZcaLZhOW7BbDg/mhr46gqzug7HLXIiqdh3X/g/Idie2PyvtfCqdfAgvsgZ360tXFUBWf0HY5aYtdq+OA30H0YnHVbtLWpOT95Elp0M908R/ZGWxtHqDij73DUAiWF8MYYaNy87s7HrypJqWZT9SN74J3rcOvzxAj14NFzOOo+//0V7F0Pl/8bkk+Itjbho80Z8OM/mymcSx6PtjaOUHBG3+GIMKtnwKrn4dwp0OVH0dYm/Az4JZw4Aj76LexYEW1tHMFwRt/hiCD7voXZN0HHc2DIvdHWJjKIwIjnISXTdGEVHYy2Ro5AOKPvcESI0qPw+iizmfnlM2p3B6zapmlLMwX1wHcw6wbXv1+XcUbf4YgQ//2l2Wf2slfMblT1nY5nm6mo696EpX+PtjYOfzij73BEgFUvwhfPmX78HsOjrU3tMeh26HkxfHgHbF8abW0cvnBG3+EIM7tWw3s3Q+chMGRqtLWpXSTOTElNbQOvj4bCPdHWyOFNSEZfRIaJyHoR2Sgid/pwTxKRmdZ9iYh0tvc7i8hREVllj6fCq77DUbc4uh9mXmrm49f3fnx/NEmHMW9CwS63/n5dJKjRF5F44ElgONAbGCcivb3EbgDyVbU78DfgTx5um1T1NHtMDpPeDkedo6LcLKR2cJsxeqltoq1R9GjbDy5+Crb8Dz7+QTXREU1CqekPADaq6mZVLQGygZFeMiOBF+35G8D5IrG0dqDDUXP+NwU2fWiWJ+hwVrS1iT6nTYT+v4BFf4HVr0ZbG0clokHmVonIKGCYqt5or68BBqrqLR4yX1uZXHu9CRgIpABrgA3AIeBuVf3URxyTgEkAmZmZWdnZ2WFImm8KCgpISUmJWPjhwOkYHmpTx10fn8A3D/SmzSU76HnbhpD91fd8rCgVvry9LwXrU+n7t1U06304zNp9T33Py2AMHTp0har2CyoYbOd0zL63z3pcXwP83UtmDdDe43oT0BJIAlrae1nANqBZoPiysrLCu0W8F5HcjT5cOB3DQ23pmDNf9Y+NVF8YrFpWXDW/DSEfC3arPtZV9c8nqOZvCYtKPmkIeRkIYLkGseeqGlL3Ti7gOcu4PbDDn4yIJABpwH5VLVbVfbZwWWELg54hxOlwxAR710P2pdC8C1z5lvkQy3E8ya3gqvegvARm/BSKDkRbo4ZNKEZ/GdBDRLqISCNgLDDLS2YWMMGejwL+p6oqIq3sQDAi0hXoAWwOj+oOR3Qp3AMzfmJm6IyfA01aRFujuktGLxjzH9i3AV67AsqKo61RwyWo0VfVMuAW4ANgHfCaqq4RkftEZIQVew5oKSIbgduAyvH684CvRORLzADvZFXdH+5EOBy1TdEBeOUiOLwTxr0LLbpGW6O6T5ehMOI5M6PHTeWMHiHNIlbVOcAcr3v3eJwXYfr+vf29CbxZQx0djjpFSQH8ezjs/toY/PYDo61R7ND3WlNgvn+rWYO/vuwtEEs0wE9HHI7qU3oUXh0B25fB6Neh+0XR1ij2GPgrKD4Mc++GxBSz366b4F17OKPvcIRI8WHIHgk58+Cyl+Gky6KtUexy7h+g5DB89ieoKIWLn4a4+Ghr1TBwRt/hCIEj+0yXzs6VcNlLcOr4aGsU24iYFTnjk8zm6iWHTUHqZj9FHmf0HY4gHMo1g7b5m820zBMvibZG9QMRGDrN7LX70W/NWMmomdCobn9fFfO4IRSHIwC5i+FfA8x6OuPfdwY/Egy6Ay5+Bja+D88NggM50daofuOMvsPhh1XTYfpgSGwCN3wOnQdHW6P6S9bPYPx/4dA2+Fd/+G5BtDWqvzij73B4UXoE3vu5mVLY6Tz42TI44eRoa1X/6XYh3LgEmrSEl86HTx8yK5c6wosz+g6HB9uXwtOnw/KnYNBvTe2zSXq0tWo4tOwJNy6Gky6H//0BXvqR2XfXET6c0Xc4gJJC+GSK6VMuPQrXfgI/fqRhboISbRo3N5usX/oi7PwCnjoVlj7hvuANF87oOxo0qvB1NjzZCxY+CKdeDTd/ZZYMcEQPEfP17uQvod0As8n8M/1g68Joaxb7OKPvaJCowob34PlBZrer5BPguoVw6XRT03TUDVp0gas/hNFvmK0oXzj3+y+iHdXDNV4dDYqyYvjmLfjsEcj7AtI6wSXPml2e3BehdRMR6H0FdB8Gi/8Gi/4Kzw4w12f+Brpe4NbvqQrO6DvqPaqwZw188QJ89RIc2WsGDEe+AKeMh/jEaGvoCIVGyXDe3WbtnmX/MMb/lYvMXgZn3AhFXZOirWJM4Iy+o15SVgwHvkrjoznwzduw/1uIS4ReI+H0G03t0NXsY5OkZnDOnaaW/81bsOIZsz8xnMXWP0Ovy6HHcMjs6/5jX4Rk9EVkGPAYEI/ZOvFhL/ck4CXMloj7gCtVNce63QXcAJQDv1LVD8KmvcOBqckf3Ap5q8zaOFs/hdxFUFZ0OnGJ0OVHcNZtZhpg8gnR1tYRLhKS4OSx5ti/Cd778yZKvuzG3LvNCp5JaeY7iw6DoM0Z0Pp0s4tXQyeo0bc7Xz0J/BizLeIyEZmlqms9xG4A8lW1u4iMBf4EXCkivTE7bfUB2gIfi0hPVXWfXDhCpqLMLHhWuBsOb4dD282Xm/s3mhr8vg0eW/AJtO4LWTdBQcuvufhXJ9M4LarqO2qB9G7QYew2hjzVjcM7IWeuWQ01Zx5sePd7ueRM07WX3sNsfJPWAZq1h5Q2pkBokl7/xwdCqekPADaq6mYAEckGRgKeRn8kMNWevwE8ISJi72erajGwxe6sNQBYFB71v+fIPtj8UXC53WtP4Ou8cMceXmpTR7NnvS8HPzL2fNfaTL7cat30+F+t8DjKzVeVWm6Md0UZlJea5XTLS0w3TFkRlBeZL2FLCqG0EIoOQvFBY8x97qkq5oVN7wF9xkLmqdD6NPPbKNmIzJu31xn8BkhqGzjlKnMAHM3/vhW4Z62pKHw721QivJE4Y/iT0qBxmulKSkw2z1RiU4hvbFoYCY1Nd2F8ovmNS7BHPEi8CefYIbYgEchbb94b7P4BIt+fAzTvBB3PiWz+hGL02wHbPK5zAe+9go7JqGqZiBwEWtr7i738tvOOQEQmAZMAMjMzmTdvXojqf8+hb1L54uasECR7s67Kodc2saDjSXxTE+9xisQrcY0qjh3xjcuJb1xOXFIFCSllNDqhjKYpZSSmlZLYrJTEtFKSWpWQ1KqYRunFxDX6vjQqBDYVwyaPqXwFBQXVepZqE6dj+AiopwBZkJYFaUAXoLw4juI9SRTvSaJkXyNKDyRSeiiRsoOJlBUmUFyYwJH98ZRvj6eiOI7yongqSuOoKDGHlgloVXd/OYn1AVxbDd1N73vWBpCoOaEYfV+p8q4f+pMJxS+q+gzwDEC/fv10yJAhIah1PKUDYVAI3pYuXcqAAQOqHH5tUus6+nluj9vNSI6/v2TJEgaeOfBYTeXYb2XNxqu2E59o7sUl2PO4yirOD9vSu3btYvTo0Xyx6AsmTZrEX/7yl2ola968eVTnWapNJk6cSFlZGa+88opP9z59+vDkk0/6TMe8efO4+uqryc3N9Rt2+/btuf/++2ukYyzkI0RHz4py02qt8GjJerZyPVu+KCxatJiBA840nvWHLe1GKSeQ2ibCA0+qGvAAzgI+8Li+C7jLS+YD4Cx7ngDsxbzRx8l6yvk7srKyNJLMnTs3ouF78+9//1uzsrI0OTlZW7durcOGDdNPP/1UVVXvvfdeHT9+/A/8APrtt98eu16zZo1ecskl2qxZM01JSdEhQ4boZ599dpyf4uJivffee7V79+7atGlT7dSpk1533XW6ZcuWYzLvvvuu9u/fX5s2barp6el61VVX6bZt2465v/DCC3r22WcHTM+ECRM0Pj5eX3/99WP3brrpJk1OTtbk5GRNTEzUhISEY9fDhg3TLVu2KHDsXuWRnZ3tM4777rtPL7vsMq2oqAioSzDmzp2rEyZM0ClTptQonKqwa9cuHTt2rLZp00abNWumgwYN0sWLF/uVnzBhgs9nIBTmzp2r7dq1Cxh2ONJelXfG+9kNxuDBg/Vf//pXNbTyHdaHH36oRUVFmpmZeZzbzJkz9ayzztImTZro4MGDwxJfdYik/QGWaxB7rqqI+u3UNYhIArABOB/YDiwDrlLVNR4yvwBOUdXJdiD3clUdIyJ9gBmYfvy2wCdADw0wkCsie4BILrGUgSmUaoNMoDUmPYcwrZxmQCqmq6stkARs8fKXBXwNFFv3k4A9QJ4NIwPTTbYB07MB0B1ItHEdwcy0Srfye4EWQGfrnm/d21td1mJmV7W0YftrgcYBfW2Yh4DNPmR8pakRcAqwwk+43nQCSoEdIcr7IwNIAUrCEFaoNMLk9X5MGir/q9VAhQ/57pi8934GQiEV01PxlR/3zoQn7VV5Zzyf3VA4ETPjLxzvZF8bdxLm2d7g4ZaKqZA2xryDgXpZIkkk7U8nVQ0+PymUkgH4CSYDNwFT7L37gBH2vDHwOrARWAp09fA7xfpbDwwPJb5IHoRYGoYhnjSgABgdQGYq8IqP+wp0t+cvA3N8yPwTWGDPLwCOAh38xCMYY/87r/txmJfkPns9EVgYQN9rMWM3twJHQ00TxvgokBBCvk3HGMsSm38XWD3vtM/RPuA1IN3Dz+uYAvEgsADoY+/neIX1rnf+esR5vz0fgimQf2/DfNnevxhYBRwAPgdOrcKzcAjI8uO2w6bnJeAwsAbo5+GeA1xgz5tYXfMxBfVvgVwP2dOBlTacmUB2ZbqCpcHGcwemADlo/Tf29c5gCqr5Vm4vMNPeX2DzttDm95WYAnA2ptKSb8/bW/kHMAVekZV/wt7vBXyEKTjXA2NCyOMWQLE9vxl4xI/cjcC82rABfuKvFfsTUIdoK1BfMx0YBpQRwNARmtHPA67zITPUvjBNgYeB+QHi6WXD7OLDbRqwyJ5PJLDR/wR4BNOCUeCMUNJEFYy+lZ/uZax+jZkQ0B5Ti3saeNXD/XpMTS4JeBRYVflfe4flnb/e8WGMfhlm2nESxtCeAezGTGCIByZgjGRSCGk5zRq1ND/uO6z7T2zYDwGLPdxz+N7oPwx8imnBdcAU2LnWrRGmYP8NpsU3ClPgVaYrYBrs+VJMSy0dWAdM9vXOAK9iKnNxmArfOQHytiVwBeY5TcUU0G97uM8DbvS4TsZULK7D1MzPwBQsffzk3/mYQqwA05I6gCnkC+35YC/5Bm/06/mM1KjSEtirqsEWhB0jIgc8Dy/3DGCnD387MS9dCxuXLxnPMPAjs9PD3S8i0hFT0MxQ1V2Y2uuEYP682OuV1pNC9HcTpoWZq2b671RglO16RFWfV9XDHm59RaQmkzUrgHtVtVhVjwI/A55W1SWqWq6qL2K6L84MFIiINMO01Kap6sEAogtVdY6abs+XMd0UvhgDPKCq+1V1G/C4h9uZGGP/qKqWquobmK7YSkJJw+OqukNV9wPvYgosX5RiuuDaqmqRqvpd+1JV96nqm6p6RFUPY2r3g/3JY1ojOar6gqqWqepK4E1MIeYr/E9UtTnwNqa7sR2mAGulqs1VdX6AuBokDdHoP1NL8ewDMioNUwBesw/nscPLfS/Qxoe/NhjjlG/j8iXjGQZ+ZNoQWh/jNcA6VV1lr98ErhKRqqxck+GV1lBnpnYC3vIoFNdhWjmZIhIvIg+LyCYROYR54cEUZNX9r/eoapFX/Ld7FcwdMLVin4hIE4zhXKyqDwWIawWmNVfJEaCxn+emLcdPn/7Oy2272uqkD/dQ0uCtR+UW5d75+DtMl+FSEVkjItf7ThqISFMReVpEvrP/zwKguf3o0xedgIFeeo7HjI35Cj/Xyoyzadltw9ghIn/1p1cUqS3745cGZ/TVTA+tDRZhmu2X1jCcj4HRPu6PwXTLHLEyA0SkvZ8w1mP6qY8LR0TiME3vT0LQ41qgq4jkiUgeMAJjWIeHlIqasQ0zHuRZYDRW1e3AVZiPAC/AjKN0tn7E/tfy4kviAAAgAElEQVS+ZiocwXQ3VOJtULz9bMPUsD3jb6qqr/pS1i5L8jZm4sNNQdIW6uA2mFZZB4/rjl5u7exHkb7cq5QGT7zfGVXNU9WfqWpbTPr+ISLd/Xi/HTNYO1BVmwHn2fuVevrK6/leeqao6s1+dGuP6Ur9WFWbYozqL6y/24KlrbapRfvjlwZn9GsL25y/B3hSRC61NZ5EERkuIo9UIahpwCAReUBE0kUkVUR+iTHCv7dxfYwZ+HpLRLJEJMHKTRaR623t7w7gbhG5SkSaiEhr4FnMTIa/ecQnItLY6zgL6IaZhXWaPU7GzMyqahdPdXgKeEBEOlkFW4nISOuWiumm2Icx5A96+d0FdPW6twrTSom360oF6m4A+BcwWUQGiiFZRH4qIqnegrbl8wZmYP1aVfU1Y6e6vAbcJSItbAH/Sw+3RZixiF/Z//9yzP9V5TQEQ0RGe1Qw8jGGu3JGnnd+p2Ly4oCIpAP3egXnLT8b6Cki19j3JVFE+gfpCszCDGCDGQNY7kPneBFpjBkniLPPdYNcX9UZ/Qiiqn8FbgPuxsxe2AbcgqkFhhrGt8A5mH7eHEyN7grgIlX9zEN0FDAHM+viIGaQrx+mFYCqzsR00fwG052zFjNIebaq7vMIZxDmJfU8bgDeUdXVtpaXp6p5mEX4LrYvcygcEJECjyPUmthjwCzgQxE5jBnUrfwq/CVMN8Z2m6bFXn6fA3rbroLKfL8VuAQz0DeeIP+Hqi7H9Ik/gTFyGzGD3r4YhOmXvpDj03tuaEkNyDRMWrcAH2L6/yt1LAEut3rlY2bO/KeaaQhGf2CJiBRg/pdbVbVyyulU4EWb32MwA+tNMM/cYuB9r7Aew4zP5IvI47bf/0LMml07MF1OlYPq/sgCVtpWTi/MDChvrsE8y/8EzrXn/6pSqusJQefpOxwOh6P+4Gr6DofD0YBwRt/hcDgaEM7oOxwORwPCGX2Hw+FoQNS5PXIzMjK0c+fOEQu/sLCQ5OTkiIUfDpyO4cHpGB5iQUeIDT0jqeOKFSv2argWXPN3YD6KWI+Z/nWnD/fbMNPovsJ8ANQpWJj1bWnl6uB0DA9Ox/AQCzqqxoaedWFp5WrX9CW0vXO/wKwYeEREbsYs1nVldeN0OCJNORXksI/15FFKBSfTli5kEOdvpxmHI8aoSfdO0L1zVXWuh/xi4OoaxOdwRAxFmc+3LGELxZSRSDzxCF+SSyqN6U8nzqYb4oy/I8ap9sdZIjIKGKaqN9rrazDra9ziR/4JIE9Vf7B3mxy/R25WdnZ2tXQKhYKCAlJSUoILRhGnY3gIVUdF2dijhJ3tysjYE09mXgLN8+MRYF/LcvLalJGfXk7b3AS6bWwUVsNfn/Ix2sSCnpHUcejQoStUtV9QwVD6gHwdmMW7nvW4vgb4ux/ZqzE1/aDrj7s+fadjuAhFx3Kt0Hd0lU7T2fqRrtMK/eEWjRVaoR/oGp2ms/V9XeNTJpI6RptY0FE1NvSM6T59TD++54p/7fGxLZuIXIDZcGGwmvXOHY46w3usZhW5DKYH59HDZy1eEH7MSVSgLGELCcRxPr2ioK3DUXNqYvSXAT1EpAtmsauxmGVujyEip2N2ORqmqrtrEJfDEXbWs4sv2MYgujGYngFlBeEielNGBZ+xiY6k04MTaklThyN8VPvjLDU7Qt0CfIDZ1OI1VV0jIveJyAgr9mfMRgyvi8gqEZlVY40djjBwlFLeYzWZpDI0iMGvRBCG0ZsMUniP1RQTbFM0h6PuUaOPs1R1DmY5X89793icX1CT8B2OSPEhaymkhHH0J74KdZ8E4rmEU3iBRcxlPcPoE0EtHY7w45ZhcDQ4vmU3X5LL2XSjDVXfSrcD6fSnE0vJIZf8CGjocEQOZ/QdDYoyypnD17QihfPwt8NfcH5EL5rRmHf5inLCuTmWwxFZnNF3NChWspWDHOUi+pCAv725g5NEAsPpwx4K+JLcMGrocEQWZ/QdDYYSyviUjXQinS60rHF4PcmkHc1ZwLeUHdsi1uGo2zij72gwLCWHQkr4ESeG5ataQRjKiRyiiJVsC4OGDkfkcUbf0SAoopTP2UQPTqADoe7jHpwutKQT6SxkI6Wutu+IAZzRdzQIPmczRZSFPCc/VARhCCdSQDHL+S6sYTsckcAZfUe95yglLGELvWlD62pM0QxGJ9LpSgafscl9sOWo8zij76j3LOM7Sinn3BpM0QzGEHpyhBJWsjVicTgc4cAZfUe9ppRylpJDD04gk2YRi6c9LehEOovZ4ubtO+o0zug76jVfsI0jlHA23SIe1yC6cZgiVrM94nE5HNXFGX1HvaVClEVspgMt6BjGGTv+6E4rMknlczajVG9zIocj0jij76i37GlVzkGOMqgWavlgZvIMoht7KWADbiVxR93EGX1HvURRcjuW0IoUetbiuvd9aENzmvAZG11t31EncUbfUS/ZyB4KU5RBtbyZeRxxnElXcjnAVrcCp6MO4oy+o16yiM00KhZOpm2tx306HWhCIovYVOtxOxzBcEbfUe/YwQFy2Ef7bYlV2iAlXCQST386s4Hd7OFwrcfvcATCGX1HveNzNpNEAq131mhjuBrRn04kEMditkRNB4fDF87oO+oV+RxhHTvJoiMJ5bXXl+9NMkmcRnu+YjuHKYqaHg6HN87oO+oVi9mMIAykS7RV4Uy6UkEFS8mJtioOxzFqZPRFZJiIrBeRjSJypw/380RkpYiUiciomsTlcATjCCWsIpdTaEcqjaOtDukk04vWLOc7txCbo85QbaMvIvHAk8BwoDcwTkR6e4ltBSYCM6obj8MRKovZQinlDKJrtFU5xiC6UUwZK9yyy446Qk1q+gOAjaq6WVVLgGxgpKeAquao6lfgVqByRJYiSllGDifRmlakRludY7SjOV3JYJEtkByOaCOq1ftq0HbXDFPVG+31NcBAVb3Fh+x0YLaqvuEnrEnAJIDMzMys7OzsaukUCgUFBaSkpEQs/HDgdKw6WzuWkNO1lDOWNyalwGx4Xld0PJBWzlenF9Ht20a02554nFtd0TEQsaAjxIaekdRx6NChK1S1XzC5msxp8zU1ololiKo+AzwD0K9fPx0yZEgN1ArMvHnziGT44cDpWDVKKGM5c+lOKy7uN+DY/bqio6Lks4g9PY4ytsd5x307UFd0DEQs6AixoWdd0LEm3Tu5QAeP6/bAjpqp43BUnZV2+eRzIrhJSk0QhHPpwSGK+JLcaKvjaODUxOgvA3qISBcRaQSMBWaFRy2HIzTKKGcRm+lEeq0sn1xdupFBW9L4jE1UuCEuRxSpttFX1TLgFuADYB3wmqquEZH7RGQEgIj0F5FcYDTwtIisCYfSDkcly9nKYYo4lx7RViUgprbfnXyO8JXbZMURRWr0nbqqzgHmeN27x+N8Gabbx+EIO8WUspCNdCGDrmREW52g9CSTNqQxjw2cTFsSiI+2So4GiPsi1xGzfM5mjlDC+fSKtiohIQgX0ItDFLmvdB1Rwxl9R0xSQBGL2UJv2tCWtGirEzJdyKA7rVjIRo5SEm11HA0QZ/QdMckCNlJOBUM5MdqqVJnz6UURZSx06+07ooAz+o6YYy8FrGQrZ9CBliRHW50qk0kz+tKepeRQlORm8jhqF2f0HTGForzHahKJ57w6PmMnEEPoiQCbursuHkft4oy+I6ZYRS7fsZ8fcxIpdWAlzeqSRhMG05N9rcpZx85oq+NoQDij74gZCinmI9bRkXROP+5j8NjkLLqQcjiO/7KGo5RGWx1HA8EZfUfM8AFrKaWcn3Iy4nPpp9gijjh6rm9EISV8zLpoq+NoIDij74gJviGPr9nBOXSrU0sn15SUgnjOoitfsI3N7I22Oo4GgDP6jjrPPgp4my9pSxpn0y3a6oSdwfQgg2Te4gsOcjTa6jjqOc7oO+o0JZTxGitIII7RZNXLpQsSiWcM/SilgtdZ4TZbcUQUZ/QddRZFmcVX7KWAyzmdNJpEW6WIkUEKl3EaOzjIHL5Gq7c1hcMRFGf0HXUSRfkf61nLTn5Er5hYUK2mnEgmg+nBl+TyOZujrY6jnlKjVTYdjkigKB/zDYvYzBl0rFMbnUea8+jBXgr4hG8op4Jz6V4vZio56g7O6DvqFIryIWtZQg796cQw+jQooycIl3Ea8cQxjw2UUs6POLFB5YEjsjij76gzHKWU91jNWnYykC5cyEkN0tjFEcdI+pJIPJ+xiUKKGUYfGrnX1REG3FPkqBNsZT9vsYrDFHE+vRhE1wZp8CsRhJ9wMk1pxKdsZCv7uZTTaE+LaKvmiHGc0XdElcMUsZCNLOc7mtOU6xhEO5pHW606gSAM5US6ksHbfMkLLOJMujCIriSTFG31HDGKM/qOqHCAIyxhC8vZiqKcQUcu4CSS3CP5AzrRkps4lw9ZyyI2s5zvyKIjZ9KVZjG86JwjOtToDRORYcBjQDzwrKo+7OWeBLwEZAH7gCtVNacmcTpiE0XJ5wgb2M0adrCdAwhCX9pxLj1oQdNoq1inaUwiI+jLWXRlIZtYwhYWs4WOpNOb1vQkkzSaNOguMUdoVNvoi0g88CTwYyAXWCYis1R1rYfYDUC+qnYXkbHAn4Ara6Kwo25TSjmFFHOQIvIpJJ8j5HGI7RzgiN0esDXN+BEncjJtae6MfZVoRSqXcRqD6cFqtrOOPN5nLe+zlhSSaEsarUmjBU1pQVPSaEJTGpFYD79kdlSPmtT0BwAbVXUzgIhkAyMBT6M/Ephqz98AnhARUdWwf254gCMsZGNQuR09iyngq3BHH1YiraO/zK/8ClQ9rvXYr1Jhf8tR9px6lBwWUUY5JZRRQjlHKf3BEgICtCSZnpxAO1rQmXRakhKppDUY0klmMD0ZTE/2UsAW9rKdA+zgABvY/QP5ROJpQiKNiCeRBBKJJ4E44okjHkEQ4ogjDo61FsSe7TyxmEN86bcVUVfaFvXh3W5Dc7LoGFEdamL02wHbPK5zgYH+ZFS1TEQOAi3h+OUERWQSMAkgMzOTefPmVVmZgpRyvj6lOKicplewvzi3yuHXJlHVUT1eYo9zUXOgEKeCUs7BAweILxfiy6FJudCsTEgoTSSxREgqEZocjSOpSIhTgHwOk8/qWvzStKCgoFrPUm0STh2b26NCmlLUWClqUkFxklKaqJQlKqUJZZTHl1IcD0fiFRWoiIMKMX+02gO+/wWoaF5BfvH2sOgYSerDu71z704Ofxvhd0RVq3UAozH9+JXX1wB/95JZA7T3uN4EtAwUblZWlkaSuXPnRjT8cNDQdczLy9Nzzz1XU1JS9Lbbbqt2OLGQjxMmTNDx48f7de/du7ffdMydO1fbtWsXMOwpU6bUVMWYyEfV2NAzkjoCyzUE212TtXdy4bjti9oDO/zJiEgCkAbsr0GcMceMGTPo168fKSkptGnThuHDh7Nw4UIApk6dytVXX/0DP0OHDmXjxu+7qtauXcuIESNIS0sjNTWVoUOH8vnnnx/np6SkhKlTp9KjRw+Sk5Pp3Lkz119/PTk5OcdkZs+ezYABA0hOTqZly5aMHz+e3Nzvax3Tp0/nnHPOCZieiRMnkpCQwN693zfWJk+eTEpKCikpKTRq1IjExMRj18OHDycnJwcROXav8pg5c6bPOJ555hkyMjI4dOgQf/nLXwLqE4yJEydy99131yiMqrB7927GjRtH27ZtSUtL4+yzz2bJkiXVDm/NmjUMGTIkfApGGBE57tkNxpAhQ3j22WfDEvfUqVP56KOPKC4upnXr1se53XHHHfTo0YPU1FR69erFSy+9FJY4YxHRanavWyO+ATgf2A4sA65S1TUeMr8ATlHVyXYg93JVHRMk3D3Ad9VSKjQyoNZ2q8gEWmPScwjTXd4MSMUUiG2BJGCLl78s4Gug2LqfBOwB8mwYGZiusw1AofXTHUi0cR3BzKhKt/J7gRZAZ+ueb93bW13WAuWYrrcMYL2f9MQBfW2Yh8BnX42vNDUCTgFW+AnXm05AKT+sRFSVDCAFKAlDWKHSCJPX+zFpqPyvVgMVPuS7Y/Le+xkIhVSgC/jtJO5MeNJelXfG89kNhRMxM/vC8U72tXEnYZ7tDR5ubTH/SRGQDPQAvuX796e2iKT96aSqrYJKhdIc8HcAP8Fk7CZgir13HzDCnjcGXgc2AkuBrjWJLxwHITaBwhBPGlAAjA4gMxV4xcd9Bbrb85eBOT5k/gkssOcXAEeBDn7iEYyx/53X/TjMS3KfvZ4ILAyg77WYMZpbgaOhpgljfBRICCHfpmOMZYnNvwusnnfa52wf8BqQ7uHndUyBeBBYAPSx93O8wnrXO3894rzfng/BFMi/t2G+bO9fDKwCDgCfA6dW4Vk4BGT5cdth0/MScBjTJdrPwz0HuMCeN7G65mMK6t8CuR6ypwMrbTgzgezKdAVLg43nDkwBctD6b+zrncEUVPOt3F5gpr2/wOZtoc3vKzEF4GxMpSXfnre38g9gCrwiK/+Evd8L+AhjpNcDY0LI4xZAsT2/GXgkiPws4PbasAVe8daK/QmoQ7QVqK+ZDgwDyghg6AjN6OcB1/mQGWpfmKbAw8D8APH0smF28eE2DVhkzycS2Oh/AjyCacEocEYoaaIKRt/KT/cyVr8GFmNqb0nA08CrHu7XY2q9ScCjwKrK/9o7LO/89Y4PY/TLMNOLkzCG9gxgN2aiQjwwAWMkk0JIy2nWqKX5cd9h3X9iw34IWOzhnsP3Rv9h4FNMC64DpsDOtW6NMAX7bzAtvlGYAq8yXQHTYM+XYmrE6cA6YLKvdwZ4FZiCKYwbA+cEyNuWwBWY5zQVU0C/7eE+D7jR4zoZU7G4DjPR5AxMwdLHT/6djynECjAtqQOYQr7Qng/24acJsBMYVhu2wCvuqBt9t55+5GgJ7FXVsiByY0TkgOfh5Z6BeUC92Yl56VrYuHzJeIaBH5mdHu5+EZGOmIJmhqruwtReJwTz58Ver7SeFKK/mzAtyVxVLcYULKNsFyOq+ryqHvZw6ysiaVXUzZMK4F5VLVbVo8DPgKdVdYmqlqvqi5juizMDBSIizTAttWmqejCA6EJVnaOq5Va+rx+5McADqrpfVbcBj3u4nYkx9o+qaqmqvoHpcq0klDQ8rqo7VHU/8C6mwPJFKaYLrq2qFqnqQn8JU9V9qvqmqh5R1cOY2v1gf/KY1kiOqr6gqmWquhJ4E1OI+Qr/E1VtDryN6W5shynAWqlqc1Wd78PbU8CXwAcB9Ki3NESj/0wtxbMPyKg0TAF4zT6cxw4v971AGx/+2mCMU76Ny5eMZxj4kWlDaH2M1wDrVHWVvX4TuEpEEkPwW0mGV1rXheivE/CWR6G4DtPKyRSReBF5WEQ2icghzAsPpiCr7n+9R1WLvOK/3atg7oCpFftERJpgDOdiVX0oQFwrMK25So4Ajf08N205fpr0d15u29VWJ324h5IGbz0qP6jwzsffYboMl4rIGhG53nfSQESaisjTIvKd/X8WAM3tx52+6AQM9NJzPGZszFf4uVZmnE3LbhvGDhH5qw/5PwMnY7qMorE9WW3ZH780OKOvqrWV6YswzfZLaxjOx5jpsd6MwXTLHLEyA0SkvZ8w1mP6qY8LR0TiME3vT0LQ41qgq4jkiUgeMAJjWIeHlIqasQ0Y7lVgNFbV7cBVmI8AL8CMo3S2fsT+175e7CNw3KfA3gbF2882TA3bM/6mqvqqL2Xt8iNvYyY43BQkbaEOboNplXnOmOvo5dZORMSPe5XS4In3O6Oqear6M1Vti0nfP0Skux/vt2MGaweqajPgPHu/Uk9feT3fS88UVb3Zj27tMV2pH6tqU4xR/YX1d5unrIhMwzyvF6rqoWDpjgS1aH/80uCMfm1hm/P3AE+KyKW2xpMoIsNF5JEqBDUNGCQiD4hIuoikisgvMUb49zaujzEDX2+JSJaIJFi5ySJyva3R3AHcLSJXiUgTEWkNPIuZTfQ3j/hERBp7HWcB3TBfYZ9mj5OBGVS9i6c6PAU8ICKdrIKtRGSkdUvFdFPswxjyB7387oIfbL21CtNKibfrRwXqbgD4FzBZRAaKIVlEfioiqd6CtuXzBmZg/VpV9TVjp7q8BtwlIi1sAf9LD7dFmLGIX9n//3LM/1XlNARDREZ7VDDyMYa78lNs7/xOxeTFARFJB+71Cs5bfjbQU0Suse9Looj0D9IVmIUZwAYzBrDch853YSoIP1bVfUETWY9xRj+CqOpfgduAuzGzF7YBt2BqgaGG8S1wDqafNwdTo7sCuEhVP/MQHQXMwcy6OIgZ5OuHaQWgqjMxXTS/wXTnrMUMaJ3t9RIMwryknscNwDuqutrW8vJUNQ+z2N7F9mUOhQMiUuBx3BbcC9h4ZgEfishhzKBu5dffL2G6MbbbNC328vsc0Nt2FVTm+63AJZiBvvEE+T9UdTmmT/wJjJHbiBn09sUgTL/0hRyf3nNDS2pApmHSugX4ENP/X6ljCXC51SsfM3PmP9VMQzD6A0tEpADzv9yqqpVTTqcCL9r8HoMZWG+CeeYWA+97hfUYZnwmX0Qet/3+FwJjMYPceXw/qO6PLGClbeX0wsyA8uZBTMvnW4//5A9VTXh9oNrz9B0Oh8MRe7iavsPhcDQgnNF3OByOBoQz+g6Hw9GAcEbf4XA4GhB1bkPSjIwM7dy5c8TCLywsJDk5OWLhhwOnY3hwOoaHWNARYkPPSOq4YsWKvRrpBdcicbj19J2O4cLpGB5iQUfV2NCzLqynX+dq+o56zJ498L//waJFsHgxbNoERUXmSEqCXr3gpJPgtNPgiisggi0+h6Oh4oy+I7KowoIF8NRT8OabUFoKTZpA//7GsDdtCo0bw5Ej8M03MH8+vPIK3HEHDBoEV18NEycaPw6Ho8aEZPTtp+qPYZZkfVZVH/ZyPw/z5d2pwFg1K/xVuk3AfJEKZpnXF8OhuCMG+PRT+PWvYeVKaN4cfv5zGD/e1OQTA6zTlpMD2dkwY4bx88ADcO+9cN11kODqKQ5HTQg6e8euhvckZqGi3sA4EentJbYV80n3DC+/lWttDMSsA3KviLSoudqOOs3WrTB2LJx3HuzeDc8+C9u3w6OPmhp+IIMPplvnzjvhq69g3jzo2BEmTYI+fUyrweFwVJtQpmwOADaq6mY163tkY1Y1PIaq5qjqV/xwO7iLgI/UrP+dj1kUbFgY9HbUVWbOhFNOgXfegXvuMV02N9xgunGqw+DB8NlnMGsWlJfDkCGm66eoKKhXh8PxQ4KuvSMiozA7zNxor6/BLJN6iw/Z6cDsyu4dEbkDs+Xa/fb6/2G22fs/L3+TgEkAmZmZWdnZ2TVNl18KCgpISUkJLhhFYlHHuKIiuj/xBG3fe4+DffqwbsoUitoEWuK/6sQfPUrXp56i3axZFHbuzJpp0zjSsaNf+VjMx7pILOgIsaFnJHUcOnToClXtF1Qw2PQezBrsz3pcXwP83Y/sdGCUx/Vvgbs9rv8fQfaldFM2Y1DHnBzVk09WFVG96y7VkpLIRj5njmqrVqppaarvvx+ajnUUp2P4iAU968KUzVC6d3I5fuOG9pglT0OhJn4dscDy5XDmmbBtG7z/Pjz4YPA++5oyfDgsW2b6/n/yE3jsMTNLyOFwBCUUo78M6CEiXUSkEWad61khhv8BcKHd9KEFZp3sBrkvZb1k9mzT556UBJ9/DhdeWHtxd+oECxfCiBFmhtDttzvD73CEQFCjr2Zj71swxnodZk/XNSJyn4iMALA721Rux/e0iKyxfvcDf8QUHMuA++w9R4xzwiefwKWXmo+pFi+G3t4TumqBlBQz9/9Xv4K//c3M8CkvD+7P4WjAhDTpWVXnYHZl8rx3j8f5MkzXjS+/zwPP10BHR13j5Zc56cEH4Zxz4L33jPGNFnFxZipoaqqZz19QAC+9FPkuJocjRnFfujiqxvPPw403cuD002kxZw7UhQWuROD++43hv/NOU9ufMSO4P4ejAeKMviN0XnnFzLm/6CJW/+Y3nFcXDL4nv/+9+WL3jjvM0g4TJ0ZbI4ejzuGMviM03nnHGNGhQ+Htt6lY7L3/eB3h9tvNOj733EPP/Hyjr0i0tXI46gxuExVHcD75BMaMgX79jPFv3DjaGgXm7rvhrrtoO3s2/O530dbG4ahTuJq+IzDLl8PIkdCzJ8yZY/rN6zoi8MADbF+3jnb/93/QurVpATgcDmf0HQHYtMl8/NSqFXz4IaSnR1uj0BHh21tuoV1lH39mplmm2eFo4Dij7/DN7t1w0UVQUQEffABhXkenVoiPN4PP+/aZZZlbtTJpcjgaMK5P3/FDCgvhpz+FHTvMV7c9e0Zbo+qTlARvvWWWZR41ClatirZGDkdUcUbfcTzl5TBunNn4ZOZMs65OrJOWZj4ia97cFGbbtkVbI4cjajij7/geVbj1Vnj3Xfj73+GSS6KtUfho184MRBcUmHGKgwejrZHDERWc0Xd8z6OPwpNPmoHPn/882tqEn1NOgf/8x2zscsUVZr9eh6OB4Yy+w/DWW2Za4xVXwJ/+FG1tIsf555vtGz/5BCZPditzOhocbvaOA5YsMRuWDxwIL79sFjGrz0yYYKaj/vGP0K0b/OEP0dbI4ag1nNFv6GzZYvruW7c2X9s2aRJtjWqHadNg82aYMgW6dDGD1w5HA8AZ/YZMfr4Z1CwrM4OcJ5wQbY1qDxF47jkzk2fiRGjfHs49N9paORwRp5634x1+KS6Gyy4z3RxvvQW9ekVbo9qncg5/ly5mqYn166OtkcMRcZzRb4hUVJgvVOfPh+nTzZaHDZX0dNPKSUgwe+/u2hVtjRyOiOKMfkPk7rvh1VfhoYfgqquirU306drVfHmcl2fGNwoLo62RwxExQjL6IjJMRNaLyEYRudOHe5KIzLTuS0Sks73fWUSOisgqezwVXvUdVeaf/zTG/qabzKYjDsOAAaYgXLHCLCPt5j9z/BAAAA28SURBVPA76ilBjb6IxANPAsOB3sA4EfHeBfsGIF9VuwN/Azwnem9S1dPsMTlMejuqwxtvwC9+YWqzTzzhNhfxZuRI+Mc/THfPTTe5OfyOekkoNf0BwEZV3ayqJUA2MNJLZiTwoj1/AzhfxFmUOsW8eWYu/llnQXa26cN2/JCbboJ77oEXXjDdYA5HPUM0SG1GREYBw1T1Rnt9DTBQVW/xkPnayuTa603AQCAFWANsAA4Bd6vqpz7imARMAsjMzMzKzs4OQ9J8U1BQQEpKSsTCDwfh1jFl40ZO+/WvKc7I4IvHH6esWbMah1mv81GVnn/5C23fe4+NN99M7pgx4VfOUq/zsZaJBT0jqePQoUNXqGq/oIKqGvAARgPPelxfA/zdS2YN0N7jehPQEkgCWtp7WcA2oFmg+LKysjSSzJ07N6Lhh4Ow6rh2rWqrVqodOqhu3Rq2YOt9PpaVqY4apQqqzz0XNp28qff5WIvEgp6R1BFYrkHsuaqG9HFWLtDh/7d35kFSVVcc/s5sKLsiAqIsJuMyGgUdsFTKjEYUIxUlJTLiH6SkJFhSSllxiyVSWC6JSdTCqMFoCe6YCTJEIhGFEktjGMCwiCC7LLKIyDYwzMzJH+c103Zmphvomfd6+nxVt/r1e/f1/PrO6/PuO/fec+LenwpsbqDORhHJAzoAOwMhB4Oby4LgCeAMoCKFv+scK2vWwJVXWliF2bPhtNOSn+MYsQQse/bArbdC+/YWj99xMpxUfPrzgUIR6S0iBUApUJ5QpxwYEWzfAHyoqioinYOBYETkdKAQWJMe6U6jbNxoBv/AAXj//cxOhBIWrVpBWZmNgwwfDuWJl73jZB5Jjb6qVgNjgFnAcmCqqi4TkQki8oug2otAJxFZBdwFxKZ1XgYsFpH/YgO8o1V1Z7q/hJPA119DSQns2AHvvWchhZ2jo00bS8DSt6/19GfMCFuR4xwTKU3hUNWZwMyEfePitg9gvv/E88qAsmPU6BwJ69fD5ZdbXthZs6Bfv7AVZT4dOlhi+KuustDTZWUtK8GMk1X4ityWxNq1FlLhu+/MpXPxxWErajl06GA30T59zPBPnRq2Isc5KtzotxSWLIEBA2D3bhu07d8/bEUtj44d7WZ60UVQWgovvBC2Isc5YtzotwTmzasLC/zRR3DhheHqacnEevyDBsGoUZZlzFfuOhmEG/1MZ9o0GDjQkqB88gmce27Yilo+rVvDO+9Yb/+++2DMGMtJ4DgZgBv9TEUVHn3U/Mt9+sDHH0PPnmGryh4KCuC11+Ceeyxez+DB8P33YatynKS40c9EKistjs4DD1iavzlz4KSTwlaVfeTkmHsnlmj9kktg5cqwVTlOo7jRzzS++gouvdSCpj32mK0azZa8tlFl5Ejz83/zDRQXWzRTx4kobvQziddfhwsusLn45eXmT/ZgptHgiitg0SIoKoKhQ2HsWEtJ6TgRw41+JrBrlyXvvvlm899//rn5kJ1o0aOHzZ664w54+mlbGLdoUdiqHOcHuNGPOtOnW+/x1VctvvucOR44LcoUFJjBnzEDtm+39RITJngmLicyuNGPKhs2wLBhcP310LkzfPYZPPywJz/JFAYPhqVLzdXz0ENw/vm2aM5xQsaNftTYu5deL70EZ55pfvsJE2D+fF9wlYl06mTjMDNmmH9/4EC7CaxeHbYyJ4txox8V9u+HJ5+EwkJ6vfIKDBkCK1bAgw+ay8DJXAYPhmXL7Ent3XfhrLNsNe+GDWErc7IQN/phs3OnzfXu3RvuugvOPpuFEydaD7FHj7DVOeniuONsTGb1ahg9GiZPhsJCznziCYub5DjNhBv9MFCFigq45Rbo3t2mXvbpYzF0PvyQ3R5KoeXSrRtMnGjrLUaO5OQPPoDzzjPXT1mZT/N0mhwfFWxOVq2CN96wXvyXX1qCjhEj4LbbbKDPyR569IBnn+XTQYMYsHw5PPOMJWk54QSL6VNaait8feDeSTPe029KDhywKZZ3323TLgsLYdw4OPlkeO452LQJnn/eDX4WU92+Pdx7L6xbZ1nOrrkGXn7Z8iJ07Wqdgrfegq1bw5bqtBC8G5EuVO2Hu2iRzbaZN89eq6ogP99+xKNGWYA0n2fvJJKbC1dfbWXPHgvrMH26zfyZMsXqFBVZzoR+/awUFdm15ThHQEpGX0QGAU8DucBfVfXxhOOtgCnAhcC3wDBVXRccux8YCdQAd6jqrLSpb25UbcHN+vVW1qwxN82KFfDFF7ZyFuyRvLgY7rzT4txffjm0bRuudidzaNfOXD033GAhmxcuhLlz7alx6lSYNMnq5efb1N6iIpsRdPrpVnr1sqcEvyE49ZDU6ItILvBnYCCwEZgvIuWq+kVctZHAd6r6YxEpBX4HDBORIqAUOAc4BZgtImeoak26v0i9qNqPprraetxVVRRs324zKA4csLJ/P+zbZ2XPHss8tXu3zar59lt73bYNtmyxgFqJKyu7dLEfXGmpJc/u29di2nsQNCcd5OXZqt7+/S2Ms6qNDc2fD4sXW2ejogLefvuHyVxEzI3Ytast7uvc2SKxduxopUMH64i0bWtjS8cfX1dataor+fnIoUP22R7nqUWQSk+/P7BKVdcAiMibwHVAvNG/DhgfbP8NeEZEJNj/pqoeBNaKyKrg8z5Nj/w4FiyAkhKoqbFSXQ21tf9X7ZJUP69NG1tcc+KJ9oM56yybeXHKKRa3vmdP61F17JjGL+E4SRCxsaHCQhg+vG7/wYM273/tWnMzbt5sZcsWezpduxZ27LAOzRFm+vppbCMnx9xQ8SW2LyfHSuzGINJwiR2P/07JtlPgosrKus5WRG9Q/eM11se118JTTzWphlSMfnfg67j3G4GLGqqjqtUi8j3QKdj/74Rzuyf+AREZBYwC6NKlC3Pnzk1Rfh2ttm7l1EGD0NxcNLgIY9uam0ttXh6an09lTQ357dpRW1Bg5bjjqImV1q2pbt2amjZt0GSzJnbtssBnTcDevXuPqg2aE9eYHtKusaAAzjjDSn3U1pK7fz95+/aRW1l5uOQcPEhOVRW5VVVIVRU5hw6Rc+gQUl3NocpKWuXmIjU1daW2FlRtWxVqaw/viyGq9j7YJ7Fj8TedBm5AchQpKA9VV5Oflxfp9JXV1dXsacS27K6tZVMTX7OpGP36bpmJrdpQnVTORVUnAZMAiouLtaSkJAVZ9TBsWNIqc+fO5ag/v5lwjenBNaaHTNAImaEzmcYuQGETa0hlyuZGIH66yanA5obqiEge0AHYmeK5juM4TjMhmuRRKDDiK4GfAZuA+cBwVV0WV+d24CeqOjoYyP2lqt4oIucAr2N+/FOAD4DCxgZyRWQ7sP7YvlajnATsaMLPTweuMT24xvSQCRohM3Q2pcaeqto5WaWk7p3ARz8GmIVN2XxJVZeJyASgQlXLgReBV4KB2p3YjB2CelOxQd9q4PZkM3dSEX0siEiFqhY35d84VlxjenCN6SETNEJm6IyCxpTm6avqTGBmwr5xcdsHgKENnPsI8MgxaHQcx3HShIdhcBzHySKy0ehPCltACrjG9OAa00MmaITM0Bm6xqQDuY7jOE7LIRt7+o7jOFmLG33HcZwsIiuMvogMFZFlIlIrIsUJx+4XkVUiskJErg5LYyIiMl5ENonI50H5ediaYojIoKC9VonIfWHrqQ8RWSciS4K2qwhbD4CIvCQi20Rkady+E0XkfRH5Kng9IYIaI3UtishpIjJHRJYHv+s7g/2RactGNIbellnh0xeRs4Fa4C/Ab1S1IthfBLxB3eKx2UDzRQFtBBEZD+xV1T+ErSWeIOrqSuKirgI3JURdDR0RWQcUq2pkFuuIyGXAXmCKqp4b7Ps9sFNVHw9uoCeo6r0R0zieCF2LItIN6KaqC0WkHbAAuB74FRFpy0Y03kjIbZkVPX1VXa6qK+o5dDgKqKquBWJRQJ2GORx1VVWrgFjUVScJqvoRtngxnuuAycH2ZMwwhEYDGiOFqm5R1YXB9h5gORbIMTJt2YjG0MkKo98I9UUQjcQ/JmCMiCwOHrlDfeyPI+ptFkOBf4nIgiCKa1TpoqpbwAwFcHLIehoiitciItIL6At8RkTbMkEjhNyWLcboi8hsEVlaT2msF5pSFNCmIonm54AfAX2ALcAfm0tXEkJtsyPgUlW9ALgGuD1wWzhHRySvRRFpC5QBY1V1d9h66qMejaG3ZYvJkauqVx7FaaFGAU1Vs4i8APyjieWkSkZETlXVzcHrNhGZhrmlPgpXVb1sFZFuqrol8ANvC1tQIqp6OCt7VK5FEcnHjOlrqvr3YHek2rI+jVFoyxbT0z9KyoFSEWklIr2xUNb/CVkTcHggKMYQYGlDdZuZ+UChiPQWkQIsuF55yJp+gIi0CQbPEJE2wFVEp/0SKQdGBNsjgOkhaqmXqF2LIiJYkMflqvqnuEORacuGNEahLbNl9s4QYCLQGdgFfK6qVwfHHgBuwaKAjlXVf4YmNA4ReQV7BFRgHfDrmL8ybIJpZk9RF3U1UgH1ROR0YFrwNg94PQoaReQNoAQLr7sVeAh4B5gK9AA2AENVNbSB1AY0lhCha1FEBgDzgCXYrDyA32I+80i0ZSMabyLktswKo+84juMY2e7ecRzHySrc6DuO42QRbvQdx3GyCDf6juM4WYQbfcdxnCzCjb7jOE4W4UbfcRwni/gfAUApRi/enVQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x263cb3d5c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x263cb45a080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import math\n",
    "from matplotlib import (cm, pyplot as plt, mlab)\n",
    "\n",
    "def visualize(word, model):\n",
    "    \"\"\" visualize the input model for a particular word \"\"\"\n",
    "    variance=np.array([np.diag(model.covars_[i]) for i in range(model.n_components)])\n",
    "    figures = []\n",
    "    for parm_idx in range(len(model.means_[0])):\n",
    "        xmin = int(min(model.means_[:,parm_idx]) - max(variance[:,parm_idx]))\n",
    "        xmax = int(max(model.means_[:,parm_idx]) + max(variance[:,parm_idx]))\n",
    "        fig, axs = plt.subplots(model.n_components, sharex=True, sharey=False)\n",
    "        colours = cm.rainbow(np.linspace(0, 1, model.n_components))\n",
    "        for i, (ax, colour) in enumerate(zip(axs, colours)):\n",
    "            x = np.linspace(xmin, xmax, 100)\n",
    "            mu = model.means_[i,parm_idx]\n",
    "            sigma = math.sqrt(np.diag(model.covars_[i])[parm_idx])\n",
    "            ax.plot(x, mlab.normpdf(x, mu, sigma), c=colour)\n",
    "            ax.set_title(\"{} feature {} hidden state #{}\".format(word, parm_idx, i))\n",
    "\n",
    "            ax.grid(True)\n",
    "        figures.append(plt)\n",
    "    for p in figures:\n",
    "        p.show()\n",
    "        \n",
    "visualize(my_testword, model)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#####  ModelSelector class\n",
    "Review the `ModelSelector` class from the codebase found in the `my_model_selectors.py` module.  It is designed to be a strategy pattern for choosing different model selectors.  For the project submission in this section, subclass `SelectorModel` to implement the following model selectors.  In other words, you will write your own classes/functions in the `my_model_selectors.py` module and run them from this notebook:\n",
    "\n",
    "- `SelectorCV `:  Log likelihood with CV\n",
    "- `SelectorBIC`: BIC \n",
    "- `SelectorDIC`: DIC\n",
    "\n",
    "You will train each word in the training set with a range of values for the number of hidden states, and then score these alternatives with the model selector, choosing the \"best\" according to each strategy. The simple case of training with a constant value for `n_components` can be called using the provided `SelectorConstant` subclass as follow:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of states trained in model for VEGETABLE is 3\n"
     ]
    }
   ],
   "source": [
    "from my_model_selectors import SelectorConstant\n",
    "\n",
    "training = asl.build_training(features_ground)  # Experiment here with different feature sets defined in part 1\n",
    "word = 'VEGETABLE' # Experiment here with different words\n",
    "model = SelectorConstant(training.get_all_sequences(), training.get_all_Xlengths(), word, n_constant=3).select()\n",
    "print(\"Number of states trained in model for {} is {}\".format(word, model.n_components))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Cross-validation folds\n",
    "If we simply score the model with the Log Likelihood calculated from the feature sequences it has been trained on, we should expect that more complex models will have higher likelihoods. However, that doesn't tell us which would have a better likelihood score on unseen data.  The model will likely be overfit as complexity is added.  To estimate which topology model is better using only the training data, we can compare scores using cross-validation.  One technique for cross-validation is to break the training set into \"folds\" and rotate which fold is left out of training.  The \"left out\" fold scored.  This gives us a proxy method of finding the best model to use on \"unseen data\". In the following example, a set of word sequences is broken into three folds using the [scikit-learn Kfold](http://scikit-learn.org/stable/modules/generated/sklearn.model_selection.KFold.html) class object. When you implement `SelectorCV`, you will use this technique."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train fold indices:[2 3 4 5] Test fold indices:[0 1]\n",
      "Train fold indices:[0 1 4 5] Test fold indices:[2 3]\n",
      "Train fold indices:[0 1 2 3] Test fold indices:[4 5]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.model_selection import KFold\n",
    "\n",
    "training = asl.build_training(features_ground) # Experiment here with different feature sets\n",
    "word = 'VEGETABLE' # Experiment here with different words\n",
    "word_sequences = training.get_word_sequences(word)\n",
    "split_method = KFold()\n",
    "for cv_train_idx, cv_test_idx in split_method.split(word_sequences):\n",
    "    print(\"Train fold indices:{} Test fold indices:{}\".format(cv_train_idx, cv_test_idx))  # view indices of the folds"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Tip:** In order to run `hmmlearn` training using the X,lengths tuples on the new folds, subsets must be combined based on the indices given for the folds.  A helper utility has been provided in the `asl_utils` module named `combine_sequences` for this purpose."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Scoring models with other criterion\n",
    "Scoring model topologies with **BIC** balances fit and complexity within the training set for each word.  In the BIC equation, a penalty term penalizes complexity to avoid overfitting, so that it is not necessary to also use cross-validation in the selection process.  There are a number of references on the internet for this criterion.  These [slides](http://www2.imm.dtu.dk/courses/02433/doc/ch6_slides.pdf) include a formula you may find helpful for your implementation.\n",
    "\n",
    "The advantages of scoring model topologies with **DIC** over BIC are presented by Alain Biem in this [reference](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.58.6208&rep=rep1&type=pdf) (also found [here](https://pdfs.semanticscholar.org/ed3d/7c4a5f607201f3848d4c02dd9ba17c791fc2.pdf)).  DIC scores the discriminant ability of a training set for one word against competing words.  Instead of a penalty term for complexity, it provides a penalty if model liklihoods for non-matching words are too similar to model likelihoods for the correct word in the word set."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='part2_submission'></a>\n",
    "### Model Selection Implementation Submission\n",
    "Implement `SelectorCV`, `SelectorBIC`, and `SelectorDIC` classes in the `my_model_selectors.py` module.  Run the selectors on the following five words. Then answer the questions about your results.\n",
    "\n",
    "**Tip:** The `hmmlearn` library may not be able to train or score all models.  Implement try/except contructs as necessary to eliminate non-viable models from consideration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "words_to_train = ['FISH', 'BOOK', 'VEGETABLE', 'FUTURE', 'JOHN']\n",
    "import timeit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "# autoreload for automatically reloading changes made in my_model_selectors and my_recognizer\n",
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training complete for FISH with 5 states with time 0.3870741282266863 seconds\n",
      "Training complete for BOOK with 15 states with time 1.91758969583816 seconds\n",
      "Training complete for VEGETABLE with 15 states with time 0.7501672099424468 seconds\n",
      "Training complete for FUTURE with 15 states with time 2.2583763983707286 seconds\n",
      "Training complete for JOHN with 15 states with time 17.15992579157546 seconds\n"
     ]
    }
   ],
   "source": [
    "# TODO: Implement SelectorCV in my_model_selector.py\n",
    "from my_model_selectors import SelectorCV\n",
    "\n",
    "training = asl.build_training(features_ground)  # Experiment here with different feature sets defined in part 1\n",
    "sequences = training.get_all_sequences()\n",
    "Xlengths = training.get_all_Xlengths()\n",
    "for word in words_to_train:\n",
    "    start = timeit.default_timer()\n",
    "    model = SelectorCV(sequences, Xlengths, word, \n",
    "                    min_n_components=2, max_n_components=15, random_state = 14).select()\n",
    "    end = timeit.default_timer()-start\n",
    "    if model is not None:\n",
    "        print(\"Training complete for {} with {} states with time {} seconds\".format(word, model.n_components, end))\n",
    "    else:\n",
    "        print(\"Training failed for {}\".format(word))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training complete for FISH with 5 states with time 0.3778454826056077 seconds\n",
      "Training complete for BOOK with 8 states with time 1.5909944063191688 seconds\n",
      "Training complete for VEGETABLE with 14 states with time 0.6640634722225514 seconds\n",
      "Training complete for FUTURE with 9 states with time 1.7946740917232091 seconds\n",
      "Training complete for JOHN with 14 states with time 14.843238259057216 seconds\n"
     ]
    }
   ],
   "source": [
    "# TODO: Implement SelectorBIC in module my_model_selectors.py\n",
    "from my_model_selectors import SelectorBIC\n",
    "\n",
    "training = asl.build_training(features_ground)  # Experiment here with different feature sets defined in part 1\n",
    "sequences = training.get_all_sequences()\n",
    "Xlengths = training.get_all_Xlengths()\n",
    "for word in words_to_train:\n",
    "    start = timeit.default_timer()\n",
    "    model = SelectorBIC(sequences, Xlengths, word, \n",
    "                    min_n_components=2, max_n_components=15, random_state = 14).select()\n",
    "    end = timeit.default_timer()-start\n",
    "    if model is not None:\n",
    "        print(\"Training complete for {} with {} states with time {} seconds\".format(word, model.n_components, end))\n",
    "    else:\n",
    "        print(\"Training failed for {}\".format(word))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training complete for FISH with 3 states with time 0.8451321857314724 seconds\n",
      "Training complete for BOOK with 13 states with time 3.3077942944373717 seconds\n",
      "Training complete for VEGETABLE with 14 states with time 2.3605674510881727 seconds\n",
      "Training complete for FUTURE with 13 states with time 3.458363440341145 seconds\n",
      "Training complete for JOHN with 14 states with time 16.464329664920115 seconds\n"
     ]
    }
   ],
   "source": [
    "# TODO: Implement SelectorDIC in module my_model_selectors.py\n",
    "from my_model_selectors import SelectorDIC\n",
    "\n",
    "training = asl.build_training(features_ground)  # Experiment here with different feature sets defined in part 1\n",
    "sequences = training.get_all_sequences()\n",
    "Xlengths = training.get_all_Xlengths()\n",
    "for word in words_to_train:\n",
    "    start = timeit.default_timer()\n",
    "    model = SelectorDIC(sequences, Xlengths, word, \n",
    "                    min_n_components=2, max_n_components=15, random_state = 14).select()\n",
    "    end = timeit.default_timer()-start\n",
    "    if model is not None:\n",
    "        print(\"Training complete for {} with {} states with time {} seconds\".format(word, model.n_components, end))\n",
    "    else:\n",
    "        print(\"Training failed for {}\".format(word))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 2:**  Compare and contrast the possible advantages and disadvantages of the various model selectors implemented.\n",
    "\n",
    "**Answer 2:**\n",
    "\n",
    "**CV**\n",
    "- Cross validation avoid overfitting by divides the dataset into K sets and train on partial data.\n",
    "- Cross validation will be incredibly expensive to compute and the slowest selector since it will require running through the data multiple times, over each folds.\n",
    "\n",
    "**BIC**\n",
    "- BIC deals with overfitting by penalizing models that have high complexity. It has the fastest compute time.\n",
    "- If high model complexity is permissable, then it is not a good measure.\n",
    "\n",
    "**DIC**\n",
    "- As discussed in “[A Model Selection Criterion for Classification: Application to HMM Topology Optimization](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.58.6208&rep=rep1&type=pdf)”, DIC outperforms BIC in realizing and reducing more than 18% of the relative error rate in it’s inaugural study. It replaces BIC's Occam's razor principle with discriminative principle.\n",
    "- DIC still produces relatively complex models with high number of states.It performs slower than BIC."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='part2_test'></a>\n",
    "### Model Selector Unit Testing\n",
    "Run the following unit tests as a sanity check on the implemented model selectors.  The test simply looks for valid interfaces  but is not exhaustive. However, the project should not be submitted if these tests don't pass."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "....\n",
      "----------------------------------------------------------------------\n",
      "Ran 4 tests in 44.489s\n",
      "\n",
      "OK\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<unittest.runner.TextTestResult run=4 errors=0 failures=0>"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from asl_test_model_selectors import TestSelectors\n",
    "suite = unittest.TestLoader().loadTestsFromModule(TestSelectors())\n",
    "unittest.TextTestRunner().run(suite)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='part3_tutorial'></a>\n",
    "## PART 3: Recognizer\n",
    "The objective of this section is to \"put it all together\".  Using the four feature sets created and the three model selectors, you will experiment with the models and present your results.  Instead of training only five specific words as in the previous section, train the entire set with a feature set and model selector strategy.  \n",
    "### Recognizer Tutorial\n",
    "##### Train the full training set\n",
    "The following example trains the entire set with the example `features_ground` and `SelectorConstant` features and model selector.  Use this pattern for you experimentation and final submission cells.\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of word models returned = 112\n"
     ]
    }
   ],
   "source": [
    "from my_model_selectors import SelectorConstant\n",
    "\n",
    "def train_all_words(features, model_selector):\n",
    "    training = asl.build_training(features)  # Experiment here with different feature sets defined in part 1\n",
    "    sequences = training.get_all_sequences()\n",
    "    Xlengths = training.get_all_Xlengths()\n",
    "    model_dict = {}\n",
    "    for word in training.words:\n",
    "        model = model_selector(sequences, Xlengths, word, \n",
    "                        n_constant=3).select()\n",
    "        model_dict[word]=model\n",
    "    return model_dict\n",
    "\n",
    "models = train_all_words(features_ground, SelectorConstant)\n",
    "print(\"Number of word models returned = {}\".format(len(models)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### Load the test set\n",
    "The `build_test` method in `ASLdb` is similar to the `build_training` method already presented, but there are a few differences:\n",
    "- the object is type `SinglesData` \n",
    "- the internal dictionary keys are the index of the test word rather than the word itself\n",
    "- the getter methods are `get_all_sequences`, `get_all_Xlengths`, `get_item_sequences` and `get_item_Xlengths`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Number of test set items: 178\n",
      "Number of test set sentences: 40\n"
     ]
    }
   ],
   "source": [
    "test_set = asl.build_test(features_ground)\n",
    "print(\"Number of test set items: {}\".format(test_set.num_items))\n",
    "print(\"Number of test set sentences: {}\".format(len(test_set.sentences_index)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='part3_submission'></a>\n",
    "### Recognizer Implementation Submission\n",
    "For the final project submission, students must implement a recognizer following guidance in the `my_recognizer.py` module.  Experiment with the four feature sets and the three model selection methods (that's 12 possible combinations). You can add and remove cells for experimentation or run the recognizers locally in some other way during your experiments, but retain the results for your discussion.  For submission, you will provide code cells of **only three** interesting combinations for your discussion (see questions below). At least one of these should produce a word error rate of less than 60%, i.e. WER < 0.60 . \n",
    "\n",
    "**Tip:** The hmmlearn library may not be able to train or score all models.  Implement try/except contructs as necessary to eliminate non-viable models from consideration."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [],
   "source": [
    "# TODO implement the recognize method in my_recognizer\n",
    "from my_recognizer import recognize\n",
    "from asl_utils import show_errors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Evaluating ['grnd-rx', 'grnd-ry', 'grnd-lx', 'grnd-ly']\n",
      "\n",
      "**** WER = 0.5786516853932584\n",
      "Total correct: 75 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "  100: *IX NEW CAR *ARRIVE                                           POSS NEW CAR BREAK-DOWN\n",
      "    2: JOHN *NEW *GIVE1                                              JOHN WRITE HOMEWORK\n",
      "   67: JOHN *JOHN *MARY BUY HOUSE                                    JOHN FUTURE NOT BUY HOUSE\n",
      "    7: *SOMETHING-ONE *CAR *ARRIVE *WHAT                             JOHN CAN GO CAN\n",
      "  201: JOHN *MARY *LOVE *LOVE *GIVE1 HOUSE                           JOHN TELL MARY IX-1P BUY HOUSE\n",
      "   74: *IX *GO *MARY MARY                                            JOHN NOT VISIT MARY\n",
      "  119: *VISIT *BUY1 IX *BOX *IX                                      SUE BUY IX CAR BLUE\n",
      "   12: *IX *WHAT *WHAT *HOUSE                                        JOHN CAN GO CAN\n",
      "   77: *JOHN *GIVE1 MARY                                             ANN BLAME MARY\n",
      "  142: JOHN BUY YESTERDAY WHAT BOOK                                  JOHN BUY YESTERDAY WHAT BOOK\n",
      "  107: JOHN *IX *HAVE *ARRIVE *JOHN                                  JOHN POSS FRIEND HAVE CANDY\n",
      "   84: *JOHN *GIVE1 *VISIT BOOK                                      IX-1P FIND SOMETHING-ONE BOOK\n",
      "   21: JOHN *GIVE1 *JOHN *FUTURE *CAR *CAR *FUTURE *MARY             JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: JOHN *IX IX *WHO IX                                           JOHN LIKE IX IX IX\n",
      "   89: *MARY IX *IX *IX IX *ARRIVE *BOOK                             JOHN IX GIVE MAN IX NEW COAT\n",
      "   71: JOHN *FUTURE VISIT MARY                                       JOHN WILL VISIT MARY\n",
      "   92: JOHN *IX IX *IX *IX BOOK                                      JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   90: JOHN *SOMETHING-ONE IX *IX *VISIT *ARRIVE                     JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   30: JOHN *MARY *MARY *MARY *MARY                                  JOHN LIKE IX IX IX\n",
      "  193: JOHN *SOMETHING-ONE *VISIT BOX                                JOHN GIVE GIRL BOX\n",
      "   36: *VISIT *VISIT *IX *GO *MARY *IX                               MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "  139: JOHN *BUY1 WHAT *MARY BOOK                                    JOHN BUY WHAT YESTERDAY BOOK\n",
      "  167: JOHN *MARY *GO LOVE MARY                                      JOHN IX SAY LOVE MARY\n",
      "   40: *MARY *GO *GIVE MARY *MARY                                    JOHN IX THINK MARY LOVE\n",
      "   28: JOHN *WHO IX *FUTURE IX                                       JOHN LIKE IX IX IX\n",
      "  171: JOHN MARY BLAME                                               JOHN MARY BLAME\n",
      "   43: JOHN *IX BUY HOUSE                                            JOHN MUST BUY HOUSE\n",
      "  108: *IX ARRIVE                                                    WOMAN ARRIVE\n",
      "  174: *CAR *GIVE1 GIVE1 *YESTERDAY *WHAT                            PEOPLE GROUP GIVE1 JANA TOY\n",
      "  113: IX CAR *IX *MARY *IX                                          IX CAR BLUE SUE BUY\n",
      "   50: *JOHN JOHN *GIVE1 CAR *JOHN                                   FUTURE JOHN BUY CAR SHOULD\n",
      "  199: *JOHN *ARRIVE *GO                                             LIKE CHOCOLATE WHO\n",
      "  158: LOVE JOHN WHO                                                 LOVE JOHN WHO\n",
      "   54: JOHN SHOULD NOT BUY HOUSE                                     JOHN SHOULD NOT BUY HOUSE\n",
      "  105: JOHN *FRANK                                                   JOHN LEG\n",
      "  184: *IX BOY *GIVE1 TEACHER *YESTERDAY                             ALL BOY GIVE TEACHER APPLE\n",
      "   57: *MARY *VISIT VISIT MARY                                       JOHN DECIDE VISIT MARY\n",
      "  122: JOHN *BUY BOOK                                                JOHN READ BOOK\n",
      "  189: JOHN *SOMETHING-ONE *VISIT *WHAT                              JOHN GIVE GIRL BOX\n",
      "  181: JOHN ARRIVE                                                   JOHN ARRIVE\n",
      "Evaluating ['polar-rr', 'polar-rtheta', 'polar-lr', 'polar-ltheta']\n",
      "\n",
      "**** WER = 0.5449438202247191\n",
      "Total correct: 81 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "  100: POSS NEW CAR BREAK-DOWN                                       POSS NEW CAR BREAK-DOWN\n",
      "    2: JOHN *NEW *GIVE1                                              JOHN WRITE HOMEWORK\n",
      "   67: *SHOULD FUTURE *MARY BUY HOUSE                                JOHN FUTURE NOT BUY HOUSE\n",
      "    7: JOHN CAN GO CAN                                               JOHN CAN GO CAN\n",
      "  201: JOHN *GIVE *LOVE *JOHN BUY HOUSE                              JOHN TELL MARY IX-1P BUY HOUSE\n",
      "   74: *IX *GO *GO MARY                                              JOHN NOT VISIT MARY\n",
      "  119: *MARY *BUY1 IX *BLAME *IX                                     SUE BUY IX CAR BLUE\n",
      "   12: JOHN *WHAT *JOHN CAN                                          JOHN CAN GO CAN\n",
      "   77: *JOHN *GIVE1 MARY                                             ANN BLAME MARY\n",
      "  142: JOHN BUY YESTERDAY WHAT BOOK                                  JOHN BUY YESTERDAY WHAT BOOK\n",
      "  107: JOHN POSS *HAVE *GO *MARY                                     JOHN POSS FRIEND HAVE CANDY\n",
      "   84: *JOHN *JOHN *FUTURE *COAT                                     IX-1P FIND SOMETHING-ONE BOOK\n",
      "   21: JOHN *NEW *JOHN *WHO *CAR *WHAT *FUTURE *WHO                  JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: JOHN *IX IX *WHO IX                                           JOHN LIKE IX IX IX\n",
      "   89: *GIVE *GIVE *IX *IX IX *ARRIVE *BOOK                          JOHN IX GIVE MAN IX NEW COAT\n",
      "   71: JOHN *FUTURE *GIVE1 MARY                                      JOHN WILL VISIT MARY\n",
      "   92: JOHN *IX IX *IX *IX BOOK                                      JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   90: JOHN GIVE IX SOMETHING-ONE WOMAN *ARRIVE                      JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   30: JOHN LIKE *MARY *MARY *MARY                                   JOHN LIKE IX IX IX\n",
      "  193: JOHN *GO *YESTERDAY BOX                                       JOHN GIVE GIRL BOX\n",
      "   36: *IX *VISIT *GIVE *GIVE *MARY *MARY                            MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "  139: JOHN *ARRIVE WHAT *MARY *ARRIVE                               JOHN BUY WHAT YESTERDAY BOOK\n",
      "  167: JOHN *MARY *VISIT LOVE MARY                                   JOHN IX SAY LOVE MARY\n",
      "   40: JOHN *GO *GIVE *JOHN *MARY                                    JOHN IX THINK MARY LOVE\n",
      "   28: JOHN *FUTURE IX *FUTURE IX                                    JOHN LIKE IX IX IX\n",
      "  171: *IX MARY BLAME                                                JOHN MARY BLAME\n",
      "   43: JOHN *IX BUY HOUSE                                            JOHN MUST BUY HOUSE\n",
      "  108: *LOVE *LOVE                                                   WOMAN ARRIVE\n",
      "  174: *JOHN *JOHN GIVE1 *YESTERDAY *JOHN                            PEOPLE GROUP GIVE1 JANA TOY\n",
      "  113: IX CAR *IX *MARY *JOHN                                        IX CAR BLUE SUE BUY\n",
      "   50: *JOHN *SEE BUY CAR *JOHN                                      FUTURE JOHN BUY CAR SHOULD\n",
      "  199: *JOHN *STUDENT *GO                                            LIKE CHOCOLATE WHO\n",
      "  158: LOVE JOHN WHO                                                 LOVE JOHN WHO\n",
      "   54: JOHN SHOULD NOT BUY HOUSE                                     JOHN SHOULD NOT BUY HOUSE\n",
      "  105: JOHN *SEE                                                     JOHN LEG\n",
      "  184: *GO BOY *GIVE1 TEACHER *YESTERDAY                             ALL BOY GIVE TEACHER APPLE\n",
      "   57: *MARY *GO *GO MARY                                            JOHN DECIDE VISIT MARY\n",
      "  122: JOHN *GIVE1 BOOK                                              JOHN READ BOOK\n",
      "  189: *MARY *GO *YESTERDAY BOX                                      JOHN GIVE GIRL BOX\n",
      "  181: *EAT ARRIVE                                                   JOHN ARRIVE\n",
      "Evaluating ['delta-rx', 'delta-ry', 'delta-lx', 'delta-ly']\n",
      "\n",
      "**** WER = 0.6348314606741573\n",
      "Total correct: 65 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "  100: *JOHN NEW CAR *BOOK                                           POSS NEW CAR BREAK-DOWN\n",
      "    2: JOHN *GIVE1 *ARRIVE                                           JOHN WRITE HOMEWORK\n",
      "   67: JOHN *JOHN *MARY BUY HOUSE                                    JOHN FUTURE NOT BUY HOUSE\n",
      "    7: JOHN *ARRIVE *GIVE1 *ARRIVE                                   JOHN CAN GO CAN\n",
      "  201: JOHN *IX *JOHN *JOHN BUY HOUSE                                JOHN TELL MARY IX-1P BUY HOUSE\n",
      "   74: JOHN *JOHN *IX MARY                                           JOHN NOT VISIT MARY\n",
      "  119: *JOHN *BUY1 IX CAR *MARY                                      SUE BUY IX CAR BLUE\n",
      "   12: JOHN *BOX *JOHN CAN                                           JOHN CAN GO CAN\n",
      "   77: *JOHN *ARRIVE MARY                                            ANN BLAME MARY\n",
      "  142: JOHN BUY *FUTURE WHAT *WHAT                                   JOHN BUY YESTERDAY WHAT BOOK\n",
      "  107: JOHN *JOHN *CAR *MARY *JOHN                                   JOHN POSS FRIEND HAVE CANDY\n",
      "   84: *GO *CAR *IX BOOK                                             IX-1P FIND SOMETHING-ONE BOOK\n",
      "   21: JOHN *MARY *LOVE *MARY *BUY *FUTURE *FUTURE *MARY             JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: JOHN *IX *JOHN IX IX                                          JOHN LIKE IX IX IX\n",
      "   89: *MARY *JOHN *IX *IX *JOHN *WHAT *ARRIVE                       JOHN IX GIVE MAN IX NEW COAT\n",
      "   71: JOHN *MARY VISIT *CAR                                         JOHN WILL VISIT MARY\n",
      "   92: JOHN *IX *JOHN *IX *IX BOOK                                   JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   90: JOHN *JOHN *JOHN *IX *IX *MARY                                JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   30: JOHN *IX *SHOULD *JOHN IX                                     JOHN LIKE IX IX IX\n",
      "  193: JOHN *IX *IX BOX                                              JOHN GIVE GIRL BOX\n",
      "   36: *JOHN *JOHN *JOHN IX *MARY *MARY                              MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "  139: JOHN *GIVE1 WHAT *JOHN *WHAT                                  JOHN BUY WHAT YESTERDAY BOOK\n",
      "  167: JOHN IX *IX *BOOK MARY                                        JOHN IX SAY LOVE MARY\n",
      "   40: *MARY IX *JOHN MARY *MARY                                     JOHN IX THINK MARY LOVE\n",
      "   28: JOHN *MARY *JOHN IX *SHOULD                                   JOHN LIKE IX IX IX\n",
      "  171: JOHN *JOHN BLAME                                              JOHN MARY BLAME\n",
      "   43: JOHN *IX BUY HOUSE                                            JOHN MUST BUY HOUSE\n",
      "  108: *JOHN *BOOK                                                   WOMAN ARRIVE\n",
      "  174: *GIVE1 *MARY GIVE1 *JOHN *CAR                                 PEOPLE GROUP GIVE1 JANA TOY\n",
      "  113: *JOHN CAR *MARY *MARY *GIVE1                                  IX CAR BLUE SUE BUY\n",
      "   50: *JOHN JOHN BUY CAR *MARY                                      FUTURE JOHN BUY CAR SHOULD\n",
      "  199: *JOHN *WHAT *MARY                                             LIKE CHOCOLATE WHO\n",
      "  158: *ARRIVE JOHN *JOHN                                            LOVE JOHN WHO\n",
      "   54: JOHN *JOHN *JOHN BUY HOUSE                                    JOHN SHOULD NOT BUY HOUSE\n",
      "  105: JOHN *JOHN                                                    JOHN LEG\n",
      "  184: *IX *JOHN *GIVE1 TEACHER *MARY                                ALL BOY GIVE TEACHER APPLE\n",
      "   57: *MARY *JOHN *IX *IX                                           JOHN DECIDE VISIT MARY\n",
      "  122: JOHN *ARRIVE *WHAT                                            JOHN READ BOOK\n",
      "  189: JOHN *JOHN *JOHN *ARRIVE                                      JOHN GIVE GIRL BOX\n",
      "  181: JOHN ARRIVE                                                   JOHN ARRIVE\n",
      "Evaluating ['rescale-rx', 'rescale-ry', 'rescale-lx', 'rescale-ly']\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "**** WER = 0.5786516853932584\n",
      "Total correct: 75 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "  100: POSS NEW CAR BREAK-DOWN                                       POSS NEW CAR BREAK-DOWN\n",
      "    2: *MOTHER WRITE HOMEWORK                                        JOHN WRITE HOMEWORK\n",
      "   67: JOHN FUTURE *SHOULD BUY HOUSE                                 JOHN FUTURE NOT BUY HOUSE\n",
      "    7: JOHN *NEXT-WEEK GO *TOY                                       JOHN CAN GO CAN\n",
      "  201: *FRANK *THINK *WOMAN *LIKE BUY HOUSE                          JOHN TELL MARY IX-1P BUY HOUSE\n",
      "   74: *IX *WHO VISIT MARY                                           JOHN NOT VISIT MARY\n",
      "  119: *VEGETABLE *BUY1 IX *JOHN *POSS                               SUE BUY IX CAR BLUE\n",
      "   12: *BLUE CAN *GO1 CAN                                            JOHN CAN GO CAN\n",
      "   77: ANN BLAME *ANN                                                ANN BLAME MARY\n",
      "  142: JOHN BUY YESTERDAY WHAT BOOK                                  JOHN BUY YESTERDAY WHAT BOOK\n",
      "  107: *MARY POSS FRIEND *MARY *JOHN                                 JOHN POSS FRIEND HAVE CANDY\n",
      "   84: *ANN *STUDENT *FUTURE BOOK                                    IX-1P FIND SOMETHING-ONE BOOK\n",
      "   21: *ANN FISH *HOMEWORK *VEGETABLE *GIVE3 *CAR *CHICKEN *EAT      JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: *ANN LIKE *ANN *LIKE *ANN                                     JOHN LIKE IX IX IX\n",
      "   89: *THINK *POSS *GIVE2 *BILL *OLD *GIVE1 COAT                    JOHN IX GIVE MAN IX NEW COAT\n",
      "   71: *SHOOT WILL VISIT MARY                                        JOHN WILL VISIT MARY\n",
      "   92: *FRANK *WILL *SOMETHING-ONE SOMETHING-ONE WOMAN BOOK          JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   90: *PREFER *IX IX *IX WOMAN BOOK                                 JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   30: *IX LIKE *MARY *LIKE IX                                       JOHN LIKE IX IX IX\n",
      "  193: *IX *SELF *CORN BOX                                           JOHN GIVE GIRL BOX\n",
      "   36: MARY *JOHN *GIVE1 *WOMAN LIKE *IX                             MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "  139: JOHN *BUY1 *TOY YESTERDAY BOOK                                JOHN BUY WHAT YESTERDAY BOOK\n",
      "  167: *MARY *MARY *MARY LOVE *LOVE                                  JOHN IX SAY LOVE MARY\n",
      "   40: JOHN *VISIT *SELF *VEGETABLE *MARY                            JOHN IX THINK MARY LOVE\n",
      "   28: *ANN LIKE *ANN *LIKE *ANN                                     JOHN LIKE IX IX IX\n",
      "  171: *MARY *TOY1 BLAME                                             JOHN MARY BLAME\n",
      "   43: JOHN *JOHN BUY HOUSE                                          JOHN MUST BUY HOUSE\n",
      "  108: *LEAVE *CHOCOLATE                                             WOMAN ARRIVE\n",
      "  174: *STUDENT GROUP GIVE1 *PREFER TOY                              PEOPLE GROUP GIVE1 JANA TOY\n",
      "  113: *SHOOT CAR BLUE *WONT *BUY1                                   IX CAR BLUE SUE BUY\n",
      "   50: *JOHN *SEE *WRITE CAR SHOULD                                  FUTURE JOHN BUY CAR SHOULD\n",
      "  199: *JOHN CHOCOLATE *FRANK                                        LIKE CHOCOLATE WHO\n",
      "  158: LOVE *MARY WHO                                                LOVE JOHN WHO\n",
      "   54: *SHOOT *FUTURE *WILL BUY HOUSE                                JOHN SHOULD NOT BUY HOUSE\n",
      "  105: JOHN *SEE                                                     JOHN LEG\n",
      "  184: *THROW BOY *GIVE1 TEACHER APPLE                               ALL BOY GIVE TEACHER APPLE\n",
      "   57: *IX *MARY VISIT *GIVE2                                        JOHN DECIDE VISIT MARY\n",
      "  122: JOHN *GIVE1 BOOK                                              JOHN READ BOOK\n",
      "  189: *JANA *SELF *CORN *LIVE                                       JOHN GIVE GIRL BOX\n",
      "  181: *SUE *STUDENT                                                 JOHN ARRIVE\n"
     ]
    }
   ],
   "source": [
    "# TODO Choose a feature set and model selector\n",
    "#features = features_ground # change as needed\n",
    "model_selector = SelectorCV # change as needed\n",
    "\n",
    "for features in [features_ground, features_polar, features_delta, features_custom]:\n",
    "    print('Evaluating {}'.format(features))\n",
    "    models = train_all_words(features, model_selector)\n",
    "    test_set = asl.build_test(features)\n",
    "    probabilities, guesses = recognize(models, test_set)\n",
    "    show_errors(guesses, test_set)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Evaluating ['grnd-rx', 'grnd-ry', 'grnd-lx', 'grnd-ly']\n",
      "\n",
      "**** WER = 0.5449438202247191\n",
      "Total correct: 81 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "  100: *IX NEW CAR BREAK-DOWN                                        POSS NEW CAR BREAK-DOWN\n",
      "    2: JOHN *NEW *GIVE1                                              JOHN WRITE HOMEWORK\n",
      "   67: JOHN *YESTERDAY *WOMAN BUY HOUSE                              JOHN FUTURE NOT BUY HOUSE\n",
      "    7: *SOMETHING-ONE CAN GO *WHAT                                   JOHN CAN GO CAN\n",
      "  201: JOHN *GIVE *WOMAN *LOVE BUY HOUSE                             JOHN TELL MARY IX-1P BUY HOUSE\n",
      "   74: *IX *VISIT *GO MARY                                           JOHN NOT VISIT MARY\n",
      "  119: *VISIT *ARRIVE IX *BOX *GO                                    SUE BUY IX CAR BLUE\n",
      "   12: *IX *WHAT *CAN CAN                                            JOHN CAN GO CAN\n",
      "   77: *JOHN *GIVE1 MARY                                             ANN BLAME MARY\n",
      "  142: JOHN BUY YESTERDAY WHAT BOOK                                  JOHN BUY YESTERDAY WHAT BOOK\n",
      "  107: JOHN *GO *BOOK *ARRIVE *JOHN                                  JOHN POSS FRIEND HAVE CANDY\n",
      "   84: *JOHN *ARRIVE *VISIT BOOK                                     IX-1P FIND SOMETHING-ONE BOOK\n",
      "   21: JOHN *GIVE1 *JOHN *FUTURE *GIVE1 *WHAT *VISIT *FUTURE         JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: JOHN *MARY IX *MARY IX                                        JOHN LIKE IX IX IX\n",
      "   89: *MARY IX *IX *IX IX *ARRIVE *BOOK                             JOHN IX GIVE MAN IX NEW COAT\n",
      "   71: JOHN *FUTURE VISIT MARY                                       JOHN WILL VISIT MARY\n",
      "   92: JOHN *IX IX *IX WOMAN BOOK                                    JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   90: *POSS *IX IX *IX *VISIT *ARRIVE                               JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   30: JOHN *MARY *MARY *MARY *MARY                                  JOHN LIKE IX IX IX\n",
      "  193: JOHN *IX *VISIT BOX                                           JOHN GIVE GIRL BOX\n",
      "   36: *VISIT *VISIT *GIVE *GO *MARY *MARY                           MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "  139: JOHN *BUY1 WHAT *MARY BOOK                                    JOHN BUY WHAT YESTERDAY BOOK\n",
      "  167: JOHN *MARY *VISIT LOVE MARY                                   JOHN IX SAY LOVE MARY\n",
      "   40: *MARY *GO *GIVE MARY *MARY                                    JOHN IX THINK MARY LOVE\n",
      "   28: JOHN *MARY IX *MARY IX                                        JOHN LIKE IX IX IX\n",
      "  171: JOHN MARY BLAME                                               JOHN MARY BLAME\n",
      "   43: JOHN *IX BUY HOUSE                                            JOHN MUST BUY HOUSE\n",
      "  108: *MARY *LOVE                                                   WOMAN ARRIVE\n",
      "  174: *CAN *GIVE1 GIVE1 *YESTERDAY *WHAT                            PEOPLE GROUP GIVE1 JANA TOY\n",
      "  113: IX CAR *IX *MARY *IX                                          IX CAR BLUE SUE BUY\n",
      "   50: *JOHN *SEE BUY CAR *JOHN                                      FUTURE JOHN BUY CAR SHOULD\n",
      "  199: *JOHN *ARRIVE WHO                                             LIKE CHOCOLATE WHO\n",
      "  158: LOVE JOHN WHO                                                 LOVE JOHN WHO\n",
      "   54: JOHN SHOULD NOT BUY HOUSE                                     JOHN SHOULD NOT BUY HOUSE\n",
      "  105: JOHN *FRANK                                                   JOHN LEG\n",
      "  184: *IX BOY *GIVE1 TEACHER *YESTERDAY                             ALL BOY GIVE TEACHER APPLE\n",
      "   57: *MARY *VISIT VISIT MARY                                       JOHN DECIDE VISIT MARY\n",
      "  122: JOHN *GIVE1 BOOK                                              JOHN READ BOOK\n",
      "  189: JOHN *IX *VISIT BOX                                           JOHN GIVE GIRL BOX\n",
      "  181: JOHN ARRIVE                                                   JOHN ARRIVE\n",
      "Evaluating ['polar-rr', 'polar-rtheta', 'polar-lr', 'polar-ltheta']\n",
      "\n",
      "**** WER = 0.5168539325842697\n",
      "Total correct: 86 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "  100: POSS NEW CAR BREAK-DOWN                                       POSS NEW CAR BREAK-DOWN\n",
      "    2: *GO *NEW *GIVE1                                               JOHN WRITE HOMEWORK\n",
      "   67: *SHOULD FUTURE *MARY BUY HOUSE                                JOHN FUTURE NOT BUY HOUSE\n",
      "    7: JOHN *BOX GO *ARRIVE                                          JOHN CAN GO CAN\n",
      "  201: JOHN *MARY *LOVE *LOVE BUY HOUSE                              JOHN TELL MARY IX-1P BUY HOUSE\n",
      "   74: *IX *VISIT VISIT MARY                                         JOHN NOT VISIT MARY\n",
      "  119: *VISIT *BUY1 IX *BLAME *GO                                    SUE BUY IX CAR BLUE\n",
      "   12: JOHN *WHAT *JOHN CAN                                          JOHN CAN GO CAN\n",
      "   77: *JOHN BLAME MARY                                              ANN BLAME MARY\n",
      "  142: JOHN BUY YESTERDAY WHAT BOOK                                  JOHN BUY YESTERDAY WHAT BOOK\n",
      "  107: JOHN *IX *HAVE *GO *GO                                        JOHN POSS FRIEND HAVE CANDY\n",
      "   84: *JOHN *GIVE1 *GIVE1 *COAT                                     IX-1P FIND SOMETHING-ONE BOOK\n",
      "   21: JOHN *ARRIVE WONT *WHO *GIVE1 *TEACHER *FUTURE *WHO           JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: JOHN LIKE IX *WHO IX                                          JOHN LIKE IX IX IX\n",
      "   89: JOHN *SHOULD GIVE *IX IX *ARRIVE *BOOK                        JOHN IX GIVE MAN IX NEW COAT\n",
      "   71: JOHN *FUTURE *GIVE1 MARY                                      JOHN WILL VISIT MARY\n",
      "   92: JOHN GIVE IX *IX *IX BOOK                                     JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   90: JOHN *HAVE IX SOMETHING-ONE *GO *ARRIVE                       JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   30: JOHN LIKE *MARY *MARY *MARY                                   JOHN LIKE IX IX IX\n",
      "  193: JOHN *HAVE *YESTERDAY BOX                                     JOHN GIVE GIRL BOX\n",
      "   36: MARY VEGETABLE *GIVE *GIVE *MARY *MARY                        MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "  139: JOHN *BUY1 WHAT *JOHN BOOK                                    JOHN BUY WHAT YESTERDAY BOOK\n",
      "  167: JOHN IX *VISIT LOVE MARY                                      JOHN IX SAY LOVE MARY\n",
      "   40: JOHN *GO *MARY *JOHN *MARY                                    JOHN IX THINK MARY LOVE\n",
      "   28: JOHN *WHO IX *WHO IX                                          JOHN LIKE IX IX IX\n",
      "  171: JOHN *IX BLAME                                                JOHN MARY BLAME\n",
      "   43: JOHN *JOHN BUY HOUSE                                          JOHN MUST BUY HOUSE\n",
      "  108: *JOHN *BOOK                                                   WOMAN ARRIVE\n",
      "  174: *JOHN *JOHN GIVE1 *YESTERDAY *JOHN                            PEOPLE GROUP GIVE1 JANA TOY\n",
      "  113: IX CAR *IX *IX *BUY1                                          IX CAR BLUE SUE BUY\n",
      "   50: *JOHN *SEE BUY CAR *JOHN                                      FUTURE JOHN BUY CAR SHOULD\n",
      "  199: *JOHN *STUDENT *GO                                            LIKE CHOCOLATE WHO\n",
      "  158: LOVE JOHN WHO                                                 LOVE JOHN WHO\n",
      "   54: JOHN SHOULD *WHO BUY HOUSE                                    JOHN SHOULD NOT BUY HOUSE\n",
      "  105: JOHN *SEE                                                     JOHN LEG\n",
      "  184: *IX BOY *GIVE1 TEACHER *YESTERDAY                             ALL BOY GIVE TEACHER APPLE\n",
      "   57: *MARY *VISIT VISIT MARY                                       JOHN DECIDE VISIT MARY\n",
      "  122: JOHN *GIVE1 BOOK                                              JOHN READ BOOK\n",
      "  189: *MARY *MARY *YESTERDAY BOX                                    JOHN GIVE GIRL BOX\n",
      "  181: *GO ARRIVE                                                    JOHN ARRIVE\n",
      "Evaluating ['delta-rx', 'delta-ry', 'delta-lx', 'delta-ly']\n",
      "\n",
      "**** WER = 0.6292134831460674\n",
      "Total correct: 66 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "  100: *JOHN NEW CAR *BOOK                                           POSS NEW CAR BREAK-DOWN\n",
      "    2: JOHN *LOVE *ARRIVE                                            JOHN WRITE HOMEWORK\n",
      "   67: JOHN *JOHN *MARY BUY HOUSE                                    JOHN FUTURE NOT BUY HOUSE\n",
      "    7: JOHN *PEOPLE *GIVE1 *ARRIVE                                   JOHN CAN GO CAN\n",
      "  201: JOHN *IX MARY *IX BUY HOUSE                                   JOHN TELL MARY IX-1P BUY HOUSE\n",
      "   74: JOHN *JOHN *IX MARY                                           JOHN NOT VISIT MARY\n",
      "  119: *JOHN *GIVE1 IX CAR *MARY                                     SUE BUY IX CAR BLUE\n",
      "   12: JOHN *BOX *LOVE CAN                                           JOHN CAN GO CAN\n",
      "   77: *JOHN *CAR MARY                                               ANN BLAME MARY\n",
      "  142: JOHN BUY *FUTURE WHAT *MARY                                   JOHN BUY YESTERDAY WHAT BOOK\n",
      "  107: JOHN *JOHN *CAR *JOHN *MARY                                   JOHN POSS FRIEND HAVE CANDY\n",
      "   84: *JOHN *CAR *IX BOOK                                           IX-1P FIND SOMETHING-ONE BOOK\n",
      "   21: *MARY *MARY *LOVE *MARY *CAR *ARRIVE *FUTURE *MARY            JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: JOHN *IX *MARY IX IX                                          JOHN LIKE IX IX IX\n",
      "   89: *MARY *JOHN *IX *IX *JOHN *WHAT *CAN                          JOHN IX GIVE MAN IX NEW COAT\n",
      "   71: JOHN *MARY VISIT MARY                                         JOHN WILL VISIT MARY\n",
      "   92: JOHN *IX *JOHN *IX WOMAN BOOK                                 JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   90: JOHN *JOHN *JOHN *IX *IX *JOHN                                JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   30: JOHN *IX IX *JOHN IX                                          JOHN LIKE IX IX IX\n",
      "  193: JOHN *IX *WOMAN BOX                                           JOHN GIVE GIRL BOX\n",
      "   36: *JOHN *JOHN *JOHN IX *MARY *MARY                              MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "  139: JOHN *GIVE1 WHAT *JOHN *MARY                                  JOHN BUY WHAT YESTERDAY BOOK\n",
      "  167: JOHN IX *IX *BOOK MARY                                        JOHN IX SAY LOVE MARY\n",
      "   40: *MARY IX *JOHN MARY *MARY                                     JOHN IX THINK MARY LOVE\n",
      "   28: JOHN *MARY *JOHN IX *SHOULD                                   JOHN LIKE IX IX IX\n",
      "  171: JOHN *JOHN BLAME                                              JOHN MARY BLAME\n",
      "   43: JOHN *IX *FINISH HOUSE                                        JOHN MUST BUY HOUSE\n",
      "  108: *JOHN *BOOK                                                   WOMAN ARRIVE\n",
      "  174: *GIVE1 *MARY GIVE1 *MARY *FINISH                              PEOPLE GROUP GIVE1 JANA TOY\n",
      "  113: *JOHN CAR *MARY *MARY *GIVE1                                  IX CAR BLUE SUE BUY\n",
      "   50: *JOHN JOHN BUY CAR *MARY                                      FUTURE JOHN BUY CAR SHOULD\n",
      "  199: *JOHN *BOOK *MARY                                             LIKE CHOCOLATE WHO\n",
      "  158: *GIVE1 JOHN *JOHN                                             LOVE JOHN WHO\n",
      "   54: JOHN *JOHN *JOHN BUY HOUSE                                    JOHN SHOULD NOT BUY HOUSE\n",
      "  105: JOHN *JOHN                                                    JOHN LEG\n",
      "  184: *IX *JOHN *GIVE1 *WHO *MARY                                   ALL BOY GIVE TEACHER APPLE\n",
      "   57: *MARY *JOHN *IX *IX                                           JOHN DECIDE VISIT MARY\n",
      "  122: JOHN *ARRIVE *MARY                                            JOHN READ BOOK\n",
      "  189: JOHN *JOHN *JOHN *ARRIVE                                      JOHN GIVE GIRL BOX\n",
      "  181: JOHN ARRIVE                                                   JOHN ARRIVE\n",
      "Evaluating ['rescale-rx', 'rescale-ry', 'rescale-lx', 'rescale-ly']\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "**** WER = 0.5955056179775281\n",
      "Total correct: 72 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "  100: POSS NEW *HOUSE BREAK-DOWN                                    POSS NEW CAR BREAK-DOWN\n",
      "    2: *FIND WRITE HOMEWORK                                          JOHN WRITE HOMEWORK\n",
      "   67: *SHOULD FUTURE *SHOULD *STUDENT HOUSE                         JOHN FUTURE NOT BUY HOUSE\n",
      "    7: JOHN *PEOPLE GO *TOY                                          JOHN CAN GO CAN\n",
      "  201: JOHN *THINK *OLD *LIKE BUY HOUSE                              JOHN TELL MARY IX-1P BUY HOUSE\n",
      "   74: *IX *WHO *MARY MARY                                           JOHN NOT VISIT MARY\n",
      "  119: *VEGETABLE *BUY1 IX *JOHN *POSS                               SUE BUY IX CAR BLUE\n",
      "   12: *CAR *ARRIVE *GO1 CAN                                         JOHN CAN GO CAN\n",
      "   77: ANN BLAME *ANN                                                ANN BLAME MARY\n",
      "  142: JOHN *ARRIVE YESTERDAY WHAT BOOK                              JOHN BUY YESTERDAY WHAT BOOK\n",
      "  107: *MARY POSS FRIEND *MARY *JOHN                                 JOHN POSS FRIEND HAVE CANDY\n",
      "   84: *ANN *STUDENT *FUTURE BOOK                                    IX-1P FIND SOMETHING-ONE BOOK\n",
      "   21: *ANN FISH *HOMEWORK *VEGETABLE *GIVE3 *BLAME *CHICKEN *EAT    JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: *ANN LIKE *ANN *LIKE *ANN                                     JOHN LIKE IX IX IX\n",
      "   89: *THINK *WILL *GIVE2 *BILL *OLD *BLAME COAT                    JOHN IX GIVE MAN IX NEW COAT\n",
      "   71: *SHOOT WILL VISIT MARY                                        JOHN WILL VISIT MARY\n",
      "   92: *SOMETHING-ONE *WILL *SOMETHING-ONE SOMETHING-ONE WOMAN BOOK  JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   90: JOHN *IX IX *IX *CORN BOOK                                    JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   30: *IX LIKE *MARY *LIKE IX                                       JOHN LIKE IX IX IX\n",
      "  193: *IX *SELF *CORN BOX                                           JOHN GIVE GIRL BOX\n",
      "   36: MARY *JOHN *GIVE1 *WOMAN LIKE *IX                             MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "  139: JOHN *BUY1 *TOY YESTERDAY BOOK                                JOHN BUY WHAT YESTERDAY BOOK\n",
      "  167: *MARY *MARY *MARY LOVE *PUTASIDE                              JOHN IX SAY LOVE MARY\n",
      "   40: JOHN *VISIT *SELF *VEGETABLE *MARY                            JOHN IX THINK MARY LOVE\n",
      "   28: *ANN LIKE *ANN *LIKE *ANN                                     JOHN LIKE IX IX IX\n",
      "  171: *MARY *TOY1 BLAME                                             JOHN MARY BLAME\n",
      "   43: JOHN *FUTURE BUY HOUSE                                        JOHN MUST BUY HOUSE\n",
      "  108: *OLD *BUY1                                                    WOMAN ARRIVE\n",
      "  174: *BUY GROUP GIVE1 *CORN TOY                                    PEOPLE GROUP GIVE1 JANA TOY\n",
      "  113: *SHOOT CAR BLUE SUE *BUY1                                     IX CAR BLUE SUE BUY\n",
      "   50: *POSS *FRANK *WRITE CAR SHOULD                                FUTURE JOHN BUY CAR SHOULD\n",
      "  199: *JOHN CHOCOLATE *FRANK                                        LIKE CHOCOLATE WHO\n",
      "  158: LOVE *MARY WHO                                                LOVE JOHN WHO\n",
      "   54: *SHOOT SHOULD *FUTURE BUY HOUSE                               JOHN SHOULD NOT BUY HOUSE\n",
      "  105: JOHN *SEE                                                     JOHN LEG\n",
      "  184: *THROW BOY *GIVE1 TEACHER APPLE                               ALL BOY GIVE TEACHER APPLE\n",
      "   57: *IX *MARY *WOMAN *GIVE2                                       JOHN DECIDE VISIT MARY\n",
      "  122: JOHN *GIVE1 BOOK                                              JOHN READ BOOK\n",
      "  189: *JANA *SELF *CORN *LIVE                                       JOHN GIVE GIRL BOX\n",
      "  181: *SUE ARRIVE                                                   JOHN ARRIVE\n"
     ]
    }
   ],
   "source": [
    "#features = features_polar # change as needed\n",
    "model_selector = SelectorBIC # change as needed\n",
    "\n",
    "for features in [features_ground, features_polar, features_delta, features_custom]:\n",
    "    print('Evaluating {}'.format(features))\n",
    "    models = train_all_words(features, model_selector)\n",
    "    test_set = asl.build_test(features)\n",
    "    probabilities, guesses = recognize(models, test_set)\n",
    "    show_errors(guesses, test_set)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Evaluating ['grnd-rx', 'grnd-ry', 'grnd-lx', 'grnd-ly']\n",
      "\n",
      "**** WER = 0.5674157303370787\n",
      "Total correct: 77 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "  100: *IX NEW CAR BREAK-DOWN                                        POSS NEW CAR BREAK-DOWN\n",
      "    2: JOHN *NEW *GIVE1                                              JOHN WRITE HOMEWORK\n",
      "   67: JOHN *YESTERDAY *MARY BUY HOUSE                               JOHN FUTURE NOT BUY HOUSE\n",
      "    7: *SOMETHING-ONE CAN GO *ARRIVE                                 JOHN CAN GO CAN\n",
      "  201: JOHN *GIVE *WOMAN *JOHN *ARRIVE HOUSE                         JOHN TELL MARY IX-1P BUY HOUSE\n",
      "   74: *IX *VISIT *GO MARY                                           JOHN NOT VISIT MARY\n",
      "  119: *VISIT *ARRIVE IX *BOX *GO                                    SUE BUY IX CAR BLUE\n",
      "   12: *IX *WHAT *CAR CAN                                            JOHN CAN GO CAN\n",
      "   77: *JOHN *GIVE1 *LOVE                                            ANN BLAME MARY\n",
      "  142: JOHN BUY YESTERDAY WHAT BOOK                                  JOHN BUY YESTERDAY WHAT BOOK\n",
      "  107: JOHN *IX *BOOK *ARRIVE *JOHN                                  JOHN POSS FRIEND HAVE CANDY\n",
      "   84: *JOHN *ARRIVE *VISIT BOOK                                     IX-1P FIND SOMETHING-ONE BOOK\n",
      "   21: JOHN *GIVE1 *JOHN *FUTURE *GIVE1 *CAR *VISIT *FUTURE          JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: JOHN *MARY IX *MARY IX                                        JOHN LIKE IX IX IX\n",
      "   89: *MARY IX *IX *IX IX *ARRIVE *BOOK                             JOHN IX GIVE MAN IX NEW COAT\n",
      "   71: JOHN *FUTURE VISIT MARY                                       JOHN WILL VISIT MARY\n",
      "   92: JOHN *WOMAN IX *IX *IX BOOK                                   JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   90: *POSS *IX IX *IX *VISIT *ARRIVE                               JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   30: JOHN *MARY *MARY *MARY *MARY                                  JOHN LIKE IX IX IX\n",
      "  193: JOHN *IX *VISIT BOX                                           JOHN GIVE GIRL BOX\n",
      "   36: *VISIT *VISIT *GIVE *JOHN *MARY *MARY                         MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "  139: JOHN *BUY1 WHAT *MARY BOOK                                    JOHN BUY WHAT YESTERDAY BOOK\n",
      "  167: JOHN *MARY *VISIT LOVE MARY                                   JOHN IX SAY LOVE MARY\n",
      "   40: *MARY *GO *GIVE MARY *MARY                                    JOHN IX THINK MARY LOVE\n",
      "   28: JOHN *MARY IX *MARY *LOVE                                     JOHN LIKE IX IX IX\n",
      "  171: JOHN MARY BLAME                                               JOHN MARY BLAME\n",
      "   43: JOHN *IX BUY HOUSE                                            JOHN MUST BUY HOUSE\n",
      "  108: *MARY *LOVE                                                   WOMAN ARRIVE\n",
      "  174: *CAN *GIVE1 GIVE1 *YESTERDAY *WHAT                            PEOPLE GROUP GIVE1 JANA TOY\n",
      "  113: IX CAR *IX *MARY *IX                                          IX CAR BLUE SUE BUY\n",
      "   50: *JOHN JOHN *GIVE1 CAR *JOHN                                   FUTURE JOHN BUY CAR SHOULD\n",
      "  199: *JOHN *ARRIVE WHO                                             LIKE CHOCOLATE WHO\n",
      "  158: LOVE JOHN WHO                                                 LOVE JOHN WHO\n",
      "   54: JOHN SHOULD NOT BUY HOUSE                                     JOHN SHOULD NOT BUY HOUSE\n",
      "  105: JOHN *FRANK                                                   JOHN LEG\n",
      "  184: *IX BOY *GIVE1 TEACHER *YESTERDAY                             ALL BOY GIVE TEACHER APPLE\n",
      "   57: *MARY *VISIT VISIT MARY                                       JOHN DECIDE VISIT MARY\n",
      "  122: JOHN *GIVE1 BOOK                                              JOHN READ BOOK\n",
      "  189: JOHN *IX *VISIT BOX                                           JOHN GIVE GIRL BOX\n",
      "  181: JOHN ARRIVE                                                   JOHN ARRIVE\n",
      "Evaluating ['polar-rr', 'polar-rtheta', 'polar-lr', 'polar-ltheta']\n",
      "\n",
      "**** WER = 0.5280898876404494\n",
      "Total correct: 84 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "  100: POSS NEW CAR BREAK-DOWN                                       POSS NEW CAR BREAK-DOWN\n",
      "    2: *GO *NEW *GIVE1                                               JOHN WRITE HOMEWORK\n",
      "   67: *SHOULD FUTURE *MARY BUY HOUSE                                JOHN FUTURE NOT BUY HOUSE\n",
      "    7: JOHN CAN GO CAN                                               JOHN CAN GO CAN\n",
      "  201: JOHN *MAN *WOMAN *LOVE BUY HOUSE                              JOHN TELL MARY IX-1P BUY HOUSE\n",
      "   74: *IX *VISIT VISIT MARY                                         JOHN NOT VISIT MARY\n",
      "  119: *VISIT *BUY1 IX *BLAME *GO                                    SUE BUY IX CAR BLUE\n",
      "   12: JOHN *WHAT *JOHN CAN                                          JOHN CAN GO CAN\n",
      "   77: *JOHN *GIVE1 *LOVE                                            ANN BLAME MARY\n",
      "  142: JOHN BUY YESTERDAY WHAT BOOK                                  JOHN BUY YESTERDAY WHAT BOOK\n",
      "  107: JOHN *IX *HAVE *GO *GO                                        JOHN POSS FRIEND HAVE CANDY\n",
      "   84: *JOHN *GIVE1 *GIVE1 *COAT                                     IX-1P FIND SOMETHING-ONE BOOK\n",
      "   21: JOHN *NEW *FUTURE *WHO *GIVE1 *CAR *FUTURE *WHO               JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: JOHN *IX IX *WHO IX                                           JOHN LIKE IX IX IX\n",
      "   89: JOHN *GIVE GIVE *IX IX *ARRIVE *BOOK                          JOHN IX GIVE MAN IX NEW COAT\n",
      "   71: JOHN *FUTURE *GIVE1 MARY                                      JOHN WILL VISIT MARY\n",
      "   92: JOHN GIVE IX *IX *IX BOOK                                     JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   90: JOHN *IX IX SOMETHING-ONE *GO *ARRIVE                         JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   30: JOHN LIKE *MARY *MARY *MARY                                   JOHN LIKE IX IX IX\n",
      "  193: JOHN *IX *YESTERDAY BOX                                       JOHN GIVE GIRL BOX\n",
      "   36: MARY VEGETABLE *GIVE *GIVE *MARY *MARY                        MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "  139: JOHN *ARRIVE WHAT *JOHN *ARRIVE                               JOHN BUY WHAT YESTERDAY BOOK\n",
      "  167: JOHN IX *VISIT LOVE MARY                                      JOHN IX SAY LOVE MARY\n",
      "   40: JOHN *GO *MARY *JOHN *MARY                                    JOHN IX THINK MARY LOVE\n",
      "   28: JOHN *WHO IX *WHO IX                                          JOHN LIKE IX IX IX\n",
      "  171: JOHN *IX BLAME                                                JOHN MARY BLAME\n",
      "   43: JOHN *JOHN BUY HOUSE                                          JOHN MUST BUY HOUSE\n",
      "  108: *JOHN *BOOK                                                   WOMAN ARRIVE\n",
      "  174: *JOHN *JOHN GIVE1 *YESTERDAY *JOHN                            PEOPLE GROUP GIVE1 JANA TOY\n",
      "  113: IX CAR *IX *IX *BOX                                           IX CAR BLUE SUE BUY\n",
      "   50: *JOHN *SEE BUY CAR *JOHN                                      FUTURE JOHN BUY CAR SHOULD\n",
      "  199: *JOHN *STUDENT *GO                                            LIKE CHOCOLATE WHO\n",
      "  158: LOVE JOHN WHO                                                 LOVE JOHN WHO\n",
      "   54: JOHN SHOULD NOT BUY HOUSE                                     JOHN SHOULD NOT BUY HOUSE\n",
      "  105: JOHN *SEE                                                     JOHN LEG\n",
      "  184: *IX BOY *GIVE1 TEACHER *YESTERDAY                             ALL BOY GIVE TEACHER APPLE\n",
      "   57: *MARY *VISIT VISIT MARY                                       JOHN DECIDE VISIT MARY\n",
      "  122: JOHN *GIVE1 BOOK                                              JOHN READ BOOK\n",
      "  189: *MARY *MARY *YESTERDAY BOX                                    JOHN GIVE GIRL BOX\n",
      "  181: *GO ARRIVE                                                    JOHN ARRIVE\n",
      "Evaluating ['delta-rx', 'delta-ry', 'delta-lx', 'delta-ly']\n",
      "\n",
      "**** WER = 0.6460674157303371\n",
      "Total correct: 63 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "  100: *JOHN *ARRIVE CAR *BOOK                                       POSS NEW CAR BREAK-DOWN\n",
      "    2: JOHN *GIVE1 *ARRIVE                                           JOHN WRITE HOMEWORK\n",
      "   67: JOHN *JOHN *MARY BUY HOUSE                                    JOHN FUTURE NOT BUY HOUSE\n",
      "    7: JOHN *GIVE1 *GIVE1 *ARRIVE                                    JOHN CAN GO CAN\n",
      "  201: JOHN *IX *JOHN *JOHN BUY HOUSE                                JOHN TELL MARY IX-1P BUY HOUSE\n",
      "   74: JOHN *JOHN *IX MARY                                           JOHN NOT VISIT MARY\n",
      "  119: *JOHN *BUY1 IX CAR *MARY                                      SUE BUY IX CAR BLUE\n",
      "   12: JOHN *BOX *LOVE CAN                                           JOHN CAN GO CAN\n",
      "   77: *JOHN *ARRIVE *JOHN                                           ANN BLAME MARY\n",
      "  142: JOHN BUY YESTERDAY WHAT *MARY                                 JOHN BUY YESTERDAY WHAT BOOK\n",
      "  107: JOHN *JOHN *ARRIVE *IX *JOHN                                  JOHN POSS FRIEND HAVE CANDY\n",
      "   84: *JOHN *CAR *IX BOOK                                           IX-1P FIND SOMETHING-ONE BOOK\n",
      "   21: JOHN *MARY *FUTURE *MARY *HOUSE *FUTURE *FUTURE *MARY         JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: JOHN *IX *JOHN IX IX                                          JOHN LIKE IX IX IX\n",
      "   89: *MARY *JOHN *IX *IX *JOHN *WHAT *ARRIVE                       JOHN IX GIVE MAN IX NEW COAT\n",
      "   71: JOHN *MARY VISIT *CAR                                         JOHN WILL VISIT MARY\n",
      "   92: JOHN *IX *JOHN *IX *IX BOOK                                   JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   90: JOHN *JOHN *JOHN *IX *IX *WHAT                                JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   30: JOHN *IX *SHOULD *JOHN IX                                     JOHN LIKE IX IX IX\n",
      "  193: JOHN *IX *IX BOX                                              JOHN GIVE GIRL BOX\n",
      "   36: *JOHN *JOHN *JOHN *GIVE *JOHN *MARY                           MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "  139: JOHN *GIVE1 WHAT *JOHN *MARY                                  JOHN BUY WHAT YESTERDAY BOOK\n",
      "  167: JOHN IX *IX *BOOK MARY                                        JOHN IX SAY LOVE MARY\n",
      "   40: *MARY IX *JOHN MARY *MARY                                     JOHN IX THINK MARY LOVE\n",
      "   28: JOHN *MARY *JOHN IX *SHOULD                                   JOHN LIKE IX IX IX\n",
      "  171: JOHN *JOHN BLAME                                              JOHN MARY BLAME\n",
      "   43: JOHN *IX *BOOK HOUSE                                          JOHN MUST BUY HOUSE\n",
      "  108: *JOHN *BOOK                                                   WOMAN ARRIVE\n",
      "  174: *GIVE1 *MARY GIVE1 *JOHN *CAR                                 PEOPLE GROUP GIVE1 JANA TOY\n",
      "  113: *JOHN CAR *MARY *MARY *GIVE1                                  IX CAR BLUE SUE BUY\n",
      "   50: *JOHN JOHN BUY CAR *MARY                                      FUTURE JOHN BUY CAR SHOULD\n",
      "  199: *JOHN *BOOK *MARY                                             LIKE CHOCOLATE WHO\n",
      "  158: *ARRIVE JOHN *JOHN                                            LOVE JOHN WHO\n",
      "   54: JOHN *JOHN *JOHN BUY HOUSE                                    JOHN SHOULD NOT BUY HOUSE\n",
      "  105: JOHN *JOHN                                                    JOHN LEG\n",
      "  184: *IX *JOHN *GIVE1 TEACHER *MARY                                ALL BOY GIVE TEACHER APPLE\n",
      "   57: *MARY *JOHN *IX *IX                                           JOHN DECIDE VISIT MARY\n",
      "  122: JOHN *GIVE1 BOOK                                              JOHN READ BOOK\n",
      "  189: JOHN *JOHN *JOHN *ARRIVE                                      JOHN GIVE GIRL BOX\n",
      "  181: JOHN ARRIVE                                                   JOHN ARRIVE\n",
      "Evaluating ['rescale-rx', 'rescale-ry', 'rescale-lx', 'rescale-ly']\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "**** WER = 0.550561797752809\n",
      "Total correct: 80 out of 178\n",
      "Video  Recognized                                                    Correct\n",
      "=====================================================================================================\n",
      "  100: POSS NEW *HOUSE BREAK-DOWN                                    POSS NEW CAR BREAK-DOWN\n",
      "    2: *FUTURE *ARRIVE HOMEWORK                                      JOHN WRITE HOMEWORK\n",
      "   67: JOHN FUTURE *FUTURE BUY HOUSE                                 JOHN FUTURE NOT BUY HOUSE\n",
      "    7: JOHN *BUY GO *TOY                                             JOHN CAN GO CAN\n",
      "  201: JOHN *THINK *OLD *LIKE BUY HOUSE                              JOHN TELL MARY IX-1P BUY HOUSE\n",
      "   74: *IX *WHO VISIT MARY                                           JOHN NOT VISIT MARY\n",
      "  119: *VEGETABLE *BUY1 IX *JOHN *POSS                               SUE BUY IX CAR BLUE\n",
      "   12: *CAR CAN *GO1 CAN                                             JOHN CAN GO CAN\n",
      "   77: ANN BLAME MARY                                                ANN BLAME MARY\n",
      "  142: JOHN *ARRIVE YESTERDAY WHAT BOOK                              JOHN BUY YESTERDAY WHAT BOOK\n",
      "  107: *MARY POSS FRIEND *MARY *JOHN                                 JOHN POSS FRIEND HAVE CANDY\n",
      "   84: *JOHN *STUDENT *BLAME BOOK                                    IX-1P FIND SOMETHING-ONE BOOK\n",
      "   21: *ANN FISH *HOMEWORK *VEGETABLE BUT *GIVE3 *CHICKEN *EAT       JOHN FISH WONT EAT BUT CAN EAT CHICKEN\n",
      "   25: *ANN LIKE *ANN *LIKE *ANN                                     JOHN LIKE IX IX IX\n",
      "   89: *THINK *THROW *THROW *THROW *OLD NEW COAT                     JOHN IX GIVE MAN IX NEW COAT\n",
      "   71: JOHN WILL VISIT MARY                                          JOHN WILL VISIT MARY\n",
      "   92: JOHN *THROW *SOMETHING-ONE SOMETHING-ONE *OLD BOOK            JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   90: JOHN *IX IX *IX *CORN BOOK                                    JOHN GIVE IX SOMETHING-ONE WOMAN BOOK\n",
      "   30: *IX LIKE *MARY *LIKE IX                                       JOHN LIKE IX IX IX\n",
      "  193: *IX *SELF *CORN BOX                                           JOHN GIVE GIRL BOX\n",
      "   36: MARY *JOHN *GIVE1 *VISIT *FRANK *IX                           MARY VEGETABLE KNOW IX LIKE CORN1\n",
      "  139: JOHN *BUY1 *TOY YESTERDAY BOOK                                JOHN BUY WHAT YESTERDAY BOOK\n",
      "  167: *MARY *MARY *MARY LOVE MARY                                   JOHN IX SAY LOVE MARY\n",
      "   40: JOHN *FRANK *SELF *VEGETABLE *MARY                            JOHN IX THINK MARY LOVE\n",
      "   28: *ANN LIKE *ANN *LIKE *ANN                                     JOHN LIKE IX IX IX\n",
      "  171: *MARY *TOY1 BLAME                                             JOHN MARY BLAME\n",
      "   43: JOHN *FUTURE BUY HOUSE                                        JOHN MUST BUY HOUSE\n",
      "  108: *OLD *BUY1                                                    WOMAN ARRIVE\n",
      "  174: *GROUP GROUP GIVE1 *CORN TOY                                  PEOPLE GROUP GIVE1 JANA TOY\n",
      "  113: *SHOOT CAR BLUE *WONT *BUY1                                   IX CAR BLUE SUE BUY\n",
      "   50: *POSS *SEE *FRIEND CAR SHOULD                                 FUTURE JOHN BUY CAR SHOULD\n",
      "  199: *JOHN CHOCOLATE *TELL                                         LIKE CHOCOLATE WHO\n",
      "  158: LOVE *MARY WHO                                                LOVE JOHN WHO\n",
      "   54: JOHN *FUTURE *WILL BUY HOUSE                                  JOHN SHOULD NOT BUY HOUSE\n",
      "  105: JOHN *SEE                                                     JOHN LEG\n",
      "  184: ALL BOY *GIVE1 TEACHER APPLE                                  ALL BOY GIVE TEACHER APPLE\n",
      "   57: *IX *MARY VISIT *FRANK                                        JOHN DECIDE VISIT MARY\n",
      "  122: JOHN *GIVE1 BOOK                                              JOHN READ BOOK\n",
      "  189: *JANA *SELF *CORN *LIVE                                       JOHN GIVE GIRL BOX\n",
      "  181: *SUE ARRIVE                                                   JOHN ARRIVE\n"
     ]
    }
   ],
   "source": [
    "#features = features_norm + features_polar + features_delta # change as needed\n",
    "model_selector = SelectorDIC # change as needed\n",
    "\n",
    "for features in [features_ground, features_polar, features_delta, features_custom]:\n",
    "    print('Evaluating {}'.format(features))\n",
    "    models = train_all_words(features, model_selector)\n",
    "    test_set = asl.build_test(features)\n",
    "    probabilities, guesses = recognize(models, test_set)\n",
    "    show_errors(guesses, test_set)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Question 3:**  Summarize the error results from three combinations of features and model selectors.  What was the \"best\" combination and why?  What additional information might we use to improve our WER?  For more insight on improving WER, take a look at the introduction to Part 4.\n",
    "\n",
    "**Answer 3:** Summarize of the error results show below:\n",
    "\n",
    "|     | features_ground | features_polar | features_delta | features_custom |\n",
    "|-----|:---------------:|:---------------|:--------------:|:---------------:|\n",
    "|  CV | 0.5786          | 0.5449         | 0.6348         | 0.5786          |\n",
    "| BIC | 0.5449          | **0.5168**     | 0.6292         | 0.5955          |\n",
    "| DIC | 0.5674          | 0.5280         | 0.6460         | 0.5505          |\n",
    "\n",
    "Best WER is obtained when using `features_polar` and `SelectorBIC` compared with other selectors in the table above. To improve our WER, I suggest to train the model with more data, or combine some more features together. But to significant improve WER, more techniques introduced in part 4 would be consider.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='part3_test'></a>\n",
    "### Recognizer Unit Tests\n",
    "Run the following unit tests as a sanity check on the defined recognizer.  The test simply looks for some valid values but is not exhaustive. However, the project should not be submitted if these tests don't pass."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "..\n",
      "----------------------------------------------------------------------\n",
      "Ran 2 tests in 36.292s\n",
      "\n",
      "OK\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<unittest.runner.TextTestResult run=2 errors=0 failures=0>"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from asl_test_recognizer import TestRecognize\n",
    "suite = unittest.TestLoader().loadTestsFromModule(TestRecognize())\n",
    "unittest.TextTestRunner().run(suite)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id='part4_info'></a>\n",
    "## PART 4: (OPTIONAL)  Improve the WER with Language Models\n",
    "We've squeezed just about as much as we can out of the model and still only get about 50% of the words right! Surely we can do better than that.  Probability to the rescue again in the form of [statistical language models (SLM)](https://en.wikipedia.org/wiki/Language_model).  The basic idea is that each word has some probability of occurrence within the set, and some probability that it is adjacent to specific other words. We can use that additional information to make better choices.\n",
    "\n",
    "##### Additional reading and resources\n",
    "- [Introduction to N-grams (Stanford Jurafsky slides)](https://web.stanford.edu/class/cs124/lec/languagemodeling.pdf)\n",
    "- [Speech Recognition Techniques for a Sign Language Recognition System, Philippe Dreuw et al](https://www-i6.informatik.rwth-aachen.de/publications/download/154/Dreuw--2007.pdf) see the improved results of applying LM on *this* data!\n",
    "- [SLM data for *this* ASL dataset](ftp://wasserstoff.informatik.rwth-aachen.de/pub/rwth-boston-104/lm/)\n",
    "\n",
    "##### Optional challenge\n",
    "The recognizer you implemented in Part 3 is equivalent to a \"0-gram\" SLM.  Improve the WER with the SLM data provided with the data set in the link above using \"1-gram\", \"2-gram\", and/or \"3-gram\" statistics. The `probabilities` data you've already calculated will be useful and can be turned into a pandas DataFrame if desired (see next cell).  \n",
    "Good luck!  Share your results with the class!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# create a DataFrame of log likelihoods for the test word items\n",
    "df_probs = pd.DataFrame(data=probabilities)\n",
    "df_probs.head()"
   ]
  }
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