03_Neural_Networks.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# **Ouroboros EEG-fMRI NF: Predicting EEG activity, fMRI activity and NF scores**\n",
    "\n",
    "#### Version: 28th October 2022\n",
    "\n",
    "==============================================================================================\n",
    "\n",
    "Project developed by Maël Donoso, Ph.D. in Cognitive and Computational Neuroscience. Affiliations: Ouroboros Neurotechnologies (https://ouroboros-neurotechnologies.com/), Institut Lémanique du Cerveau (https://institut-cerveau.ch/), Policlinique Ostéopathique de Lausanne (https://policlinique-osteopathique-lausanne.ch/). "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "==============================================================================================\n",
    "\n",
    "This project is presented through six Notebooks:\n",
    "\n",
    "*01: Data Analysis*\n",
    "\n",
    "*02: Classification* (all classification models except neural networks)\n",
    "\n",
    "***03: Neural Networks***\n",
    "\n",
    "*04: Regression on fMRI Data*\n",
    "\n",
    "*05: Regression on EEG Data*\n",
    "\n",
    "*06: Results*\n",
    "\n",
    "=============================================================================================="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Notebook 03\n",
    "\n",
    "# **Neural Networks**"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## **1. Introduction to Neural Networks**\n",
    "\n",
    "### 1.1 Objective\n",
    "\n",
    "The objective of this project is to **explore several ways to apply machine learning models to a given EEG-fMRI NF dataset, and to evaluate which ones result in interesting predictions**. In this Notebook, we will focus on neural networks, and apply them to the fMRI data with the original voxel size, and the EEG bandpowers obtained from all channels, for a single subject. Like in the previous Notebook, we will evaluate if our machine learning models are able to predict the **brain state** of the subject, i.e. when he/she is at rest versus when he/she is performing the NF task. This time, we will also take a step further, and see if we can predict the specific experimental block of 20 seconds during which the fMRI image was acquired or the EEG bandpowers computed, and if we can discriminate between the beginning and the end of the rest and task blocks. \n",
    "\n",
    "### 1.2 Models\n",
    "\n",
    "We will use **dense neural networks**, with one or two layers, and store the test score. For the neural networks with two layers, we will add both a dropout and a L2 regularization to the hidden layer. \n",
    "\n",
    "### 1.3 Data import\n",
    "\n",
    "Here we import the **fMRI data with the original voxel size** and the **EEG bandpowers obtained from all channels**, for a single subject. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import pickle\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the raw data path. \n",
    "data_path = '../ouroboros_eeg-fmri_nf_raw_data/'\n",
    "\n",
    "# Define the preprocessed data path. \n",
    "preprocessed_data_path = '../ouroboros_eeg-fmri_nf_preprocessed_data/'\n",
    "\n",
    "# Define the results path. If empty, the results will be saved in the current directory. \n",
    "results_path = ''"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "['sub-xp101', 'sub-xp102', 'sub-xp103', 'sub-xp104', 'sub-xp105', 'sub-xp106', 'sub-xp107', 'sub-xp108', 'sub-xp109', 'sub-xp110']\n"
     ]
    }
   ],
   "source": [
    "# Define the list of subjects. \n",
    "subjects = []\n",
    "\n",
    "for subject_index in range(10):\n",
    "    if subject_index < 9:\n",
    "        subjects.append('sub-xp10' + str(subject_index + 1))\n",
    "    else:\n",
    "        subjects.append('sub-xp1' + str(subject_index + 1))\n",
    "\n",
    "print(subjects)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'sub-xp101'"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Define an example subject. \n",
    "subject_index = subjects[0]\n",
    "subject_index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(106, 106, 32, 200)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Load the fMRI data with the original voxel size for this subject. \n",
    "with np.load(preprocessed_data_path + 'predictors_fMRI.npz', allow_pickle = False) as npz_file:\n",
    "    predictors_fMRI_single_subject = npz_file['sub_' + str(subjects.index(subject_index) + 1)]\n",
    "    \n",
    "# Display the shape of the array. \n",
    "predictors_fMRI_single_subject.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(200, 100674)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Load the data, and retrieve the number and position of non-NaN voxels per scan. \n",
    "image_data = predictors_fMRI_single_subject\n",
    "non_nan_indexes = ~np.isnan(image_data[:, :, :, 0])\n",
    "nb_non_nan = np.sum(non_nan_indexes)\n",
    "\n",
    "# Retrieve the number of scans, then create a NumPy array with one row per scan and one column per non-NaN voxel. \n",
    "nb_scans = image_data.shape[3]\n",
    "predictors_fMRI_single_subject_flatten = np.empty((nb_scans, nb_non_nan))\n",
    "\n",
    "# Fill in the array. \n",
    "for scan in range(nb_scans):\n",
    "    flatten_image = image_data[:, :, :, scan].flatten()\n",
    "    flatten_image = flatten_image[~np.isnan(flatten_image)]\n",
    "    predictors_fMRI_single_subject_flatten[scan, :] = flatten_image\n",
    "    \n",
    "# Display the shape of the array. \n",
    "predictors_fMRI_single_subject_flatten.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(200, 320)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Load the EEG predictors with all channels for this subject. \n",
    "with open(preprocessed_data_path + 'predictors_EEG_single_subject_all_channels_200_samples.p', 'rb') as file:\n",
    "    predictors_EEG_single_subject_all_channels_200_samples = pickle.load(file)\n",
    "\n",
    "# Display the shape of the array. \n",
    "predictors_EEG_single_subject_all_channels_200_samples.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Determine the proportion of the test set for the neural networks models. \n",
    "test_set_proportion = 0.2\n",
    "\n",
    "# Define batch size and validation split. \n",
    "batch_size = 96\n",
    "validation_split = 0.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>onset</th>\n",
       "      <th>duration</th>\n",
       "      <th>trial_type</th>\n",
       "      <th>stim_file</th>\n",
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       "      <td>Rest</td>\n",
       "      <td>Rest_Xp1.png</td>\n",
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       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>22</td>\n",
       "      <td>20</td>\n",
       "      <td>Task-NF</td>\n",
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       "      <td>Rest</td>\n",
       "      <td>Rest_Xp1.png</td>\n",
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       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>102</td>\n",
       "      <td>20</td>\n",
       "      <td>Task-NF</td>\n",
       "      <td>Task-NF_Xp1.png</td>\n",
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       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>122</td>\n",
       "      <td>20</td>\n",
       "      <td>Rest</td>\n",
       "      <td>Rest_Xp1.png</td>\n",
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       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>142</td>\n",
       "      <td>20</td>\n",
       "      <td>Task-NF</td>\n",
       "      <td>Task-NF_Xp1.png</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>162</td>\n",
       "      <td>20</td>\n",
       "      <td>Rest</td>\n",
       "      <td>Rest_Xp1.png</td>\n",
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       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>182</td>\n",
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       "      <td>Task-NF</td>\n",
       "      <td>Task-NF_Xp1.png</td>\n",
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       "      <td>Rest_Xp1.png</td>\n",
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       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>222</td>\n",
       "      <td>20</td>\n",
       "      <td>Task-NF</td>\n",
       "      <td>Task-NF_Xp1.png</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>242</td>\n",
       "      <td>20</td>\n",
       "      <td>Rest</td>\n",
       "      <td>Rest_Xp1.png</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>262</td>\n",
       "      <td>20</td>\n",
       "      <td>Task-NF</td>\n",
       "      <td>Task-NF_Xp1.png</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>282</td>\n",
       "      <td>20</td>\n",
       "      <td>Rest</td>\n",
       "      <td>Rest_Xp1.png</td>\n",
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       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>302</td>\n",
       "      <td>20</td>\n",
       "      <td>Task-NF</td>\n",
       "      <td>Task-NF_Xp1.png</td>\n",
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       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>322</td>\n",
       "      <td>20</td>\n",
       "      <td>Rest</td>\n",
       "      <td>Rest_Xp1.png</td>\n",
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       "      <td>Rest</td>\n",
       "      <td>Rest_Xp1.png</td>\n",
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       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>382</td>\n",
       "      <td>20</td>\n",
       "      <td>Task-NF</td>\n",
       "      <td>Task-NF_Xp1.png</td>\n",
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      ],
      "text/plain": [
       "    onset  duration trial_type        stim_file\n",
       "0       2        20       Rest     Rest_Xp1.png\n",
       "1      22        20    Task-NF  Task-NF_Xp1.png\n",
       "2      42        20       Rest     Rest_Xp1.png\n",
       "3      62        20    Task-NF  Task-NF_Xp1.png\n",
       "4      82        20       Rest     Rest_Xp1.png\n",
       "5     102        20    Task-NF  Task-NF_Xp1.png\n",
       "6     122        20       Rest     Rest_Xp1.png\n",
       "7     142        20    Task-NF  Task-NF_Xp1.png\n",
       "8     162        20       Rest     Rest_Xp1.png\n",
       "9     182        20    Task-NF  Task-NF_Xp1.png\n",
       "10    202        20       Rest     Rest_Xp1.png\n",
       "11    222        20    Task-NF  Task-NF_Xp1.png\n",
       "12    242        20       Rest     Rest_Xp1.png\n",
       "13    262        20    Task-NF  Task-NF_Xp1.png\n",
       "14    282        20       Rest     Rest_Xp1.png\n",
       "15    302        20    Task-NF  Task-NF_Xp1.png\n",
       "16    322        20       Rest     Rest_Xp1.png\n",
       "17    342        20    Task-NF  Task-NF_Xp1.png\n",
       "18    362        20       Rest     Rest_Xp1.png\n",
       "19    382        20    Task-NF  Task-NF_Xp1.png"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Retrieve and display the events file for the eegfmriNF run. \n",
    "events = pd.read_csv(data_path + 'task-eegfmriNF_events.tsv', sep = '\\t')\n",
    "events"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We are interested in the **brain state** variable, i.e. whether the subject is currently in a **rest block** or in a **task block**. Like in the previous Notebook, this target variable is easy to reconstruct. This time, we will also take a step further, and refine our concept of brain state. Specifically, we will try to predict the specific experimental block, and to discriminate between the beginning and the end of the rest and task blocks. The appropriate target variables will be defined in each section. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## **2. Neural networks based on fMRI data**\n",
    "\n",
    "### **2.1 Dense neural network: 1-layer**\n",
    "\n",
    "In the following cells, we **run and compute the predictions from a 1-layer neural network model**. Our target will be the **brain state** variable according to our primary definition, i.e. whether the subject is currently in a rest block or in a task block. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Disable warnings. \n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "import tensorflow as tf\n",
    "import tensorflow.keras as keras\n",
    "from tensorflow.keras import Sequential\n",
    "from tensorflow.keras.layers import Dense\n",
    "from tensorflow.keras import activations\n",
    "from tensorflow.keras import initializers\n",
    "from tensorflow.keras import optimizers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1\n",
      " 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1\n",
      " 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1\n",
      " 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0\n",
      " 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0\n",
      " 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1]\n"
     ]
    }
   ],
   "source": [
    "# Define and display the target variable. \n",
    "y = np.repeat(np.tile([0, 1], 10), 10)\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(200,)"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Display the shape of the target variable. \n",
    "y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the features variables. \n",
    "X = predictors_fMRI_single_subject_flatten\n",
    "\n",
    "# Divide the data into a train set and a test set. \n",
    "X_tr, X_te, y_tr, y_te = train_test_split(X, y, test_size = test_set_proportion)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.425"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a baseline containing only the most frequent value in the train set. \n",
    "most_frequent_value = np.bincount(y_tr.astype(int)).argmax()\n",
    "neural_networks_baseline = np.sum(y_te.astype(int) == most_frequent_value) / y_te.shape[0]\n",
    "neural_networks_baseline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train: (160, 100674)\n",
      "Test: (40, 100674)\n"
     ]
    }
   ],
   "source": [
    "# Rescale features variables. \n",
    "scaler = StandardScaler()\n",
    "X_tr_standardized = scaler.fit_transform(X_tr)\n",
    "X_te_standardized = scaler.transform(X_te)\n",
    "\n",
    "print('Train:', X_tr_standardized.shape)\n",
    "print('Test:', X_te_standardized.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Encode target variable. \n",
    "y_tr_encoded = pd.get_dummies(y_tr)\n",
    "y_te_encoded = pd.get_dummies(y_te)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Get and display the encoding order. \n",
    "encoding_order = np.unique(y_te)\n",
    "encoding_order"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "dense (Dense)                (None, 2)                 201350    \n",
      "=================================================================\n",
      "Total params: 201,350\n",
      "Trainable params: 201,350\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "# Create model. \n",
    "model_dense1 = Sequential()\n",
    "\n",
    "# Output layer. \n",
    "model_dense1.add(Dense(\n",
    "    units = 2, activation = activations.softmax, input_dim = X_tr_standardized.shape[1],\n",
    "    kernel_initializer = initializers.VarianceScaling(scale = 1.0, seed = 0)))\n",
    "\n",
    "# Define loss function, optimizer and metrics to track during training. \n",
    "model_dense1.compile(optimizer = 'sgd', loss = 'categorical_crossentropy', metrics = ['acc'])\n",
    "\n",
    "# Print network summary. \n",
    "model_dense1.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Security check: verify that the number of parameters corresponds to what is expected, \n",
    "# i.e. the number of features multiplied by the number of target classes, plus the biases for each output neuron. \n",
    "model_dense1.count_params() == ((X_tr_standardized.shape[1] * 2) + 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 128 samples, validate on 32 samples\n",
      "Epoch 1/100\n",
      "128/128 [==============================] - 0s 3ms/step - loss: 2.2668 - acc: 0.5078 - val_loss: 1.5004 - val_acc: 0.8125\n",
      "Epoch 2/100\n",
      "128/128 [==============================] - 0s 405us/step - loss: 1.9985 - acc: 0.7891 - val_loss: 6.0290 - val_acc: 0.5312\n",
      "Epoch 3/100\n",
      "128/128 [==============================] - 0s 492us/step - loss: 4.2095 - acc: 0.6875 - val_loss: 0.3816 - val_acc: 0.8750\n",
      "Epoch 4/100\n",
      "128/128 [==============================] - 0s 459us/step - loss: 0.8396 - acc: 0.9141 - val_loss: 0.3765 - val_acc: 0.8750\n",
      "Epoch 5/100\n",
      "128/128 [==============================] - 0s 468us/step - loss: 0.2632 - acc: 0.9766 - val_loss: 0.3036 - val_acc: 0.9375\n",
      "Epoch 6/100\n",
      "128/128 [==============================] - 0s 551us/step - loss: 0.2535 - acc: 0.9844 - val_loss: 0.2947 - val_acc: 0.9375\n",
      "Epoch 7/100\n",
      "128/128 [==============================] - 0s 470us/step - loss: 0.2520 - acc: 0.9844 - val_loss: 0.2953 - val_acc: 0.9375\n",
      "Epoch 8/100\n",
      "128/128 [==============================] - 0s 479us/step - loss: 0.2520 - acc: 0.9844 - val_loss: 0.2951 - val_acc: 0.9375\n",
      "Epoch 9/100\n",
      "128/128 [==============================] - 0s 465us/step - loss: 0.2520 - acc: 0.9844 - val_loss: 0.2953 - val_acc: 0.9375\n",
      "Epoch 10/100\n",
      "128/128 [==============================] - 0s 467us/step - loss: 0.2520 - acc: 0.9844 - val_loss: 0.2951 - val_acc: 0.9375\n",
      "Epoch 11/100\n",
      "128/128 [==============================] - 0s 476us/step - loss: 0.2519 - acc: 0.9844 - val_loss: 0.2953 - val_acc: 0.9375\n",
      "Epoch 12/100\n",
      "128/128 [==============================] - 0s 466us/step - loss: 0.2519 - acc: 0.9844 - val_loss: 0.2951 - val_acc: 0.9375\n"
     ]
    }
   ],
   "source": [
    "# End training when accuracy stops improving. \n",
    "early_stopping = keras.callbacks.EarlyStopping(monitor = 'val_loss', patience = 6)\n",
    "\n",
    "# Fit model. \n",
    "history_dense1 = model_dense1.fit(\n",
    "    x = X_tr_standardized, y = y_tr_encoded,\n",
    "    validation_split = validation_split, batch_size = batch_size, epochs = 100,\n",
    "    shuffle = True, callbacks = [early_stopping]\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define a function to plot the results of the neural network training. \n",
    "def neural_network_graph(history):\n",
    "    \n",
    "    # Display the graph. \n",
    "    fig, axes = plt.subplots(nrows = 1, ncols = 2, figsize = (12, 4))\n",
    "\n",
    "    # Plot loss values. \n",
    "    axes[0].plot(history.history['loss'], label = 'train loss', color = 'blue')\n",
    "    axes[0].plot(history.history['val_loss'], label = 'val loss', color = 'green')\n",
    "    axes[0].set_title('Validation loss {:.3f} (mean last 3)'.format(\n",
    "        np.mean(history.history['val_loss'][-3:]) # Take the mean of the last three values. \n",
    "    ))\n",
    "    axes[0].set_xlabel('Epoch')\n",
    "    axes[0].set_ylabel('Loss value')\n",
    "    axes[0].legend()\n",
    "\n",
    "    # Plot accuracy values. \n",
    "    axes[1].plot(history.history['acc'], label = 'train acc', color = 'blue')\n",
    "    axes[1].plot(history.history['val_acc'], label = 'val acc', color = 'green')\n",
    "    axes[1].set_title('Validation accuracy {:.3f} (mean last 3)'.format(\n",
    "        np.mean(history.history['val_acc'][-3:]) # Take the mean of the last three values. \n",
    "    ))\n",
    "    axes[1].set_xlabel('Epoch')\n",
    "    axes[1].set_ylabel('Accuracy')\n",
    "    axes[1].legend();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Display the results. \n",
    "neural_network_graph(history_dense1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "40/40 [==============================] - 0s 251us/step\n",
      "Test loss: 1.27\n",
      "Test accuracy: 85.00%\n"
     ]
    }
   ],
   "source": [
    "# Evaluate test score. \n",
    "(test_loss, test_score_dense1) = model_dense1.evaluate(X_te_standardized, y_te_encoded, batch_size = batch_size)\n",
    "\n",
    "print('Test loss: {:.2f}'.format(test_loss))\n",
    "print('Test accuracy: {:.2f}%'.format(100 * test_score_dense1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 1,\n",
       "       1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0])"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Compute and display the predictions of the neural network. \n",
    "y_pred_dense1 = encoding_order[model_dense1.predict_classes(X_te_standardized)]\n",
    "y_pred_dense1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.85"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Security check: compute the accuracy from these predictions. \n",
    "test_score_dense1_from_pred = np.sum(y_pred_dense1 == y_te) / len(y_te)\n",
    "test_score_dense1_from_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Verify if the two accuracies are equal. \n",
    "np.round(test_score_dense1_from_pred, 4) == np.round(test_score_dense1, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.425"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Display again the baseline. \n",
    "neural_networks_baseline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Result:** The 1-layer neural network model performs better than the baseline. We can also have a look at the confusion matrix. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.metrics import confusion_matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define a function to generate a Scikit-learn confusion matrix. \n",
    "def scikit_learn_confusion_matrix(y_te, y_pred):\n",
    "    \n",
    "    # Compute the confusion matrix. \n",
    "    labels = ['rest', 'task']\n",
    "    matrix = confusion_matrix(\n",
    "        y_true = y_te,\n",
    "        y_pred = y_pred, \n",
    "        labels = labels\n",
    "    )\n",
    "\n",
    "    # Return confusion matrix as a DataFrame. \n",
    "    matrix_df = pd.DataFrame(data = matrix, columns = labels, index = labels)\n",
    "    matrix_df.columns.name = 'Predictions'\n",
    "    matrix_df.index.name = 'True class'\n",
    "    return matrix_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Predictions</th>\n",
       "      <th>rest</th>\n",
       "      <th>task</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>True class</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>rest</th>\n",
       "      <td>13</td>\n",
       "      <td>4</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>task</th>\n",
       "      <td>2</td>\n",
       "      <td>21</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Predictions  rest  task\n",
       "True class             \n",
       "rest           13     4\n",
       "task            2    21"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Rename the labels. \n",
    "y_te_renamed = np.array(['rest', 'task'])[y_te]\n",
    "y_pred_dense1_renamed = np.array(['rest', 'task'])[y_pred_dense1]\n",
    "\n",
    "# Display a Scikit-learn confusion matrix. \n",
    "confusion_matrix_dense1 = scikit_learn_confusion_matrix(y_te_renamed, y_pred_dense1_renamed)\n",
    "confusion_matrix_dense1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### **2.2 Dense neural network: 2-layer**\n",
    "\n",
    "In the following cells, we **run and compute the predictions from a 2-layer neural network model**. We add both a dropout and a L2 regularization to the hidden layer. The number of units in the hidden layer was defined by trial and error. For the dropout and the regularization parameters, we simply use values that seem widely used by the machine learning community. Our target will be the **brain state** variable according to our primary definition, i.e. whether the subject is currently in a rest block or in a task block. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "from tensorflow.keras.layers import Dropout\n",
    "from tensorflow.keras.regularizers import l2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "dense_1 (Dense)              (None, 128)               12886400  \n",
      "_________________________________________________________________\n",
      "dropout (Dropout)            (None, 128)               0         \n",
      "_________________________________________________________________\n",
      "dense_2 (Dense)              (None, 2)                 258       \n",
      "=================================================================\n",
      "Total params: 12,886,658\n",
      "Trainable params: 12,886,658\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "# Create model. \n",
    "model_dense2 = Sequential()\n",
    "\n",
    "# Hidden layer. \n",
    "model_dense2.add(Dense(\n",
    "    units = 128, activation = activations.relu, input_dim = X_tr_standardized.shape[1],\n",
    "    kernel_initializer = initializers.VarianceScaling(scale = 2.0, seed = 0),\n",
    "    kernel_regularizer = l2(0.01), bias_regularizer = l2(0.01)))\n",
    "model_dense2.add(Dropout(0.5, seed = 0))\n",
    "\n",
    "# Output layer. \n",
    "model_dense2.add(Dense(\n",
    "    units = 2, activation = activations.softmax,\n",
    "    kernel_initializer = initializers.VarianceScaling(scale = 1.0, seed = 0)))\n",
    "\n",
    "# Define loss function, optimizer and metrics to track during training. \n",
    "model_dense2.compile(optimizer = 'sgd', loss = 'categorical_crossentropy', metrics = ['acc'])\n",
    "\n",
    "# Print network summary. \n",
    "model_dense2.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 128 samples, validate on 32 samples\n",
      "Epoch 1/100\n",
      "128/128 [==============================] - 2s 13ms/step - loss: 3.7366 - acc: 0.5391 - val_loss: 6.4193 - val_acc: 0.6875\n",
      "Epoch 2/100\n",
      "128/128 [==============================] - 0s 2ms/step - loss: 6.4421 - acc: 0.6172 - val_loss: 4.7447 - val_acc: 0.7500\n",
      "Epoch 3/100\n",
      "128/128 [==============================] - 0s 2ms/step - loss: 3.9598 - acc: 0.8203 - val_loss: 3.4793 - val_acc: 0.8125\n",
      "Epoch 4/100\n",
      "128/128 [==============================] - 0s 2ms/step - loss: 3.1637 - acc: 0.8828 - val_loss: 3.0286 - val_acc: 0.8438\n",
      "Epoch 5/100\n",
      "128/128 [==============================] - 0s 2ms/step - loss: 3.6164 - acc: 0.8594 - val_loss: 2.9704 - val_acc: 0.8438\n",
      "Epoch 6/100\n",
      "128/128 [==============================] - 0s 2ms/step - loss: 2.8975 - acc: 0.9141 - val_loss: 3.0635 - val_acc: 0.8438\n",
      "Epoch 7/100\n",
      "128/128 [==============================] - 0s 2ms/step - loss: 2.8009 - acc: 0.9453 - val_loss: 2.8806 - val_acc: 0.8750\n",
      "Epoch 8/100\n",
      "128/128 [==============================] - 0s 2ms/step - loss: 2.6000 - acc: 0.9766 - val_loss: 2.8525 - val_acc: 0.8750\n",
      "Epoch 9/100\n",
      "128/128 [==============================] - 0s 2ms/step - loss: 2.5934 - acc: 0.9766 - val_loss: 2.7721 - val_acc: 0.8438\n",
      "Epoch 10/100\n",
      "128/128 [==============================] - 0s 2ms/step - loss: 2.5791 - acc: 0.9922 - val_loss: 2.8369 - val_acc: 0.8438\n",
      "Epoch 11/100\n",
      "128/128 [==============================] - 0s 2ms/step - loss: 2.5578 - acc: 0.9922 - val_loss: 2.8369 - val_acc: 0.8438\n",
      "Epoch 12/100\n",
      "128/128 [==============================] - 0s 2ms/step - loss: 2.5820 - acc: 0.9922 - val_loss: 3.0408 - val_acc: 0.8438\n",
      "Epoch 13/100\n",
      "128/128 [==============================] - 0s 2ms/step - loss: 2.5770 - acc: 0.9922 - val_loss: 2.9308 - val_acc: 0.8438\n",
      "Epoch 14/100\n",
      "128/128 [==============================] - 0s 2ms/step - loss: 2.5490 - acc: 1.0000 - val_loss: 2.8851 - val_acc: 0.8438\n",
      "Epoch 15/100\n",
      "128/128 [==============================] - 0s 2ms/step - loss: 2.5727 - acc: 0.9844 - val_loss: 2.8914 - val_acc: 0.8438\n"
     ]
    }
   ],
   "source": [
    "# End training when accuracy stops improving. \n",
    "early_stopping = keras.callbacks.EarlyStopping(monitor = 'val_loss', patience = 6)\n",
    "\n",
    "# Fit model. \n",
    "history_dense2 = model_dense2.fit(\n",
    "    x = X_tr_standardized, y = y_tr_encoded,\n",
    "    validation_split = validation_split, batch_size = batch_size, epochs = 100,\n",
    "    shuffle = True, callbacks = [early_stopping]\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Display the results. \n",
    "neural_network_graph(history_dense2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "40/40 [==============================] - 0s 562us/step\n",
      "Test loss: 2.85\n",
      "Test accuracy: 87.50%\n"
     ]
    }
   ],
   "source": [
    "# Evaluate test score. \n",
    "(test_loss, test_score_dense2) = model_dense2.evaluate(X_te_standardized, y_te_encoded, batch_size = batch_size)\n",
    "\n",
    "print('Test loss: {:.2f}'.format(test_loss))\n",
    "print('Test accuracy: {:.2f}%'.format(100 * test_score_dense2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1,\n",
       "       1, 1, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 0])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Compute and display the predictions of the neural network. \n",
    "y_pred_dense2 = encoding_order[model_dense2.predict_classes(X_te_standardized)]\n",
    "y_pred_dense2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.875"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Security check: compute the accuracy from these predictions. \n",
    "test_score_dense2_from_pred = np.sum(y_pred_dense2 == y_te) / len(y_te)\n",
    "test_score_dense2_from_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Verify if the two accuracies are equal. \n",
    "np.round(test_score_dense2_from_pred, 4) == np.round(test_score_dense2, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.425"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Display again the baseline. \n",
    "neural_networks_baseline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Result:** The 2-layer neural network model performs better than the baseline. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Predictions</th>\n",
       "      <th>rest</th>\n",
       "      <th>task</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>True class</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>rest</th>\n",
       "      <td>14</td>\n",
       "      <td>3</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>task</th>\n",
       "      <td>2</td>\n",
       "      <td>21</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Predictions  rest  task\n",
       "True class             \n",
       "rest           14     3\n",
       "task            2    21"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Rename the labels. \n",
    "y_te_renamed = np.array(['rest', 'task'])[y_te]\n",
    "y_pred_dense2_renamed = np.array(['rest', 'task'])[y_pred_dense2]\n",
    "\n",
    "# Display a Scikit-learn confusion matrix. \n",
    "confusion_matrix_dense2 = scikit_learn_confusion_matrix(y_te_renamed, y_pred_dense2_renamed)\n",
    "confusion_matrix_dense2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### **2.3 Dense neural network: 2-layer, target: blocks**\n",
    "\n",
    "In the following cells, we **run and compute the predictions from a 2-layer neural network model**. Our target will be the **blocks** of the eegfmriNF run. Here, our objective is to find out if our neural networks can discriminate between the individual blocks of 20 seconds, and not just between the rest condition and the task condition. Since we have a larger number of target values, we will perform a train-test split with stratification. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0  0  0  0  0  0  0  0  0  0  1  1  1  1  1  1  1  1  1  1  2  2  2  2\n",
      "  2  2  2  2  2  2  3  3  3  3  3  3  3  3  3  3  4  4  4  4  4  4  4  4\n",
      "  4  4  5  5  5  5  5  5  5  5  5  5  6  6  6  6  6  6  6  6  6  6  7  7\n",
      "  7  7  7  7  7  7  7  7  8  8  8  8  8  8  8  8  8  8  9  9  9  9  9  9\n",
      "  9  9  9  9 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11\n",
      " 12 12 12 12 12 12 12 12 12 12 13 13 13 13 13 13 13 13 13 13 14 14 14 14\n",
      " 14 14 14 14 14 14 15 15 15 15 15 15 15 15 15 15 16 16 16 16 16 16 16 16\n",
      " 16 16 17 17 17 17 17 17 17 17 17 17 18 18 18 18 18 18 18 18 18 18 19 19\n",
      " 19 19 19 19 19 19 19 19]\n"
     ]
    }
   ],
   "source": [
    "# Define and display the new target variable. \n",
    "y = np.repeat(range(20), 10)\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(200,)"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Display the shape of the target variable. \n",
    "y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Store the number of different target values. \n",
    "nb_target_values = np.unique(y).shape[0]\n",
    "nb_target_values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Divide the data into a train set and a test set. \n",
    "X_tr, X_te, y_tr, y_te = train_test_split(X, y, test_size = test_set_proportion, stratify = y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.05"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a baseline containing only the most frequent value in the train set. \n",
    "most_frequent_value = np.bincount(y_tr.astype(int)).argmax()\n",
    "neural_networks_baseline3 = np.sum(y_te.astype(int) == most_frequent_value) / y_te.shape[0]\n",
    "neural_networks_baseline3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train: (160, 100674)\n",
      "Test: (40, 100674)\n"
     ]
    }
   ],
   "source": [
    "# Rescale features variables. \n",
    "scaler = StandardScaler()\n",
    "X_tr_standardized = scaler.fit_transform(X_tr)\n",
    "X_te_standardized = scaler.transform(X_te)\n",
    "\n",
    "print('Train:', X_tr_standardized.shape)\n",
    "print('Test:', X_te_standardized.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Encode target variable. \n",
    "y_tr_encoded = pd.get_dummies(y_tr)\n",
    "y_te_encoded = pd.get_dummies(y_te)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,\n",
       "       17, 18, 19])"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Get and display the encoding order. \n",
    "encoding_order = np.unique(y_te)\n",
    "encoding_order"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "dense_3 (Dense)              (None, 128)               12886400  \n",
      "_________________________________________________________________\n",
      "dropout_1 (Dropout)          (None, 128)               0         \n",
      "_________________________________________________________________\n",
      "dense_4 (Dense)              (None, 20)                2580      \n",
      "=================================================================\n",
      "Total params: 12,888,980\n",
      "Trainable params: 12,888,980\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "# Create model. \n",
    "model_dense3 = Sequential()\n",
    "\n",
    "# Hidden layer. \n",
    "model_dense3.add(Dense(\n",
    "    units = 128, activation = activations.relu, input_dim = X_tr_standardized.shape[1],\n",
    "    kernel_initializer = initializers.VarianceScaling(scale = 2.0, seed = 0),\n",
    "    kernel_regularizer = l2(0.01), bias_regularizer = l2(0.01)))\n",
    "model_dense3.add(Dropout(0.5, seed = 0))\n",
    "\n",
    "# Output layer. \n",
    "model_dense3.add(Dense(\n",
    "    units = nb_target_values, activation = activations.softmax,\n",
    "    kernel_initializer = initializers.VarianceScaling(scale = 1.0, seed = 0)))\n",
    "\n",
    "# Define loss function, optimizer and metrics to track during training. \n",
    "model_dense3.compile(optimizer = 'sgd', loss = 'categorical_crossentropy', metrics = ['acc'])\n",
    "\n",
    "# Print network summary. \n",
    "model_dense3.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 128 samples, validate on 32 samples\n",
      "Epoch 1/100\n",
      "128/128 [==============================] - 2s 12ms/step - loss: 6.3603 - acc: 0.0859 - val_loss: 6.9727 - val_acc: 0.1562\n",
      "Epoch 2/100\n",
      "128/128 [==============================] - 0s 2ms/step - loss: 5.4589 - acc: 0.3828 - val_loss: 4.6807 - val_acc: 0.5625\n",
      "Epoch 3/100\n",
      "128/128 [==============================] - 0s 2ms/step - loss: 3.7932 - acc: 0.7266 - val_loss: 3.9113 - val_acc: 0.6250\n",
      "Epoch 4/100\n",
      "128/128 [==============================] - 0s 2ms/step - loss: 3.5571 - acc: 0.8125 - val_loss: 4.3562 - val_acc: 0.5625\n",
      "Epoch 5/100\n",
      "128/128 [==============================] - 0s 2ms/step - loss: 2.9862 - acc: 0.8672 - val_loss: 4.4685 - val_acc: 0.4375\n",
      "Epoch 6/100\n",
      "128/128 [==============================] - 0s 2ms/step - loss: 2.9036 - acc: 0.8906 - val_loss: 4.1310 - val_acc: 0.4688\n",
      "Epoch 7/100\n",
      "128/128 [==============================] - 0s 2ms/step - loss: 2.7067 - acc: 0.9453 - val_loss: 4.4807 - val_acc: 0.5625\n",
      "Epoch 8/100\n",
      "128/128 [==============================] - 0s 2ms/step - loss: 2.7810 - acc: 0.9219 - val_loss: 4.0525 - val_acc: 0.5938\n",
      "Epoch 9/100\n",
      "128/128 [==============================] - 0s 2ms/step - loss: 2.7052 - acc: 0.9609 - val_loss: 4.0940 - val_acc: 0.5312\n"
     ]
    }
   ],
   "source": [
    "# End training when accuracy stops improving. \n",
    "early_stopping = keras.callbacks.EarlyStopping(monitor = 'val_loss', patience = 6)\n",
    "\n",
    "# Fit model. \n",
    "history_dense3 = model_dense3.fit(\n",
    "    x = X_tr_standardized, y = y_tr_encoded,\n",
    "    validation_split = validation_split, batch_size = batch_size, epochs = 100,\n",
    "    shuffle = True, callbacks = [early_stopping]\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Display the results. \n",
    "neural_network_graph(history_dense3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "40/40 [==============================] - 0s 591us/step\n",
      "Test loss: 4.03\n",
      "Test accuracy: 67.50%\n"
     ]
    }
   ],
   "source": [
    "# Evaluate test score. \n",
    "(test_loss, test_score_dense3) = model_dense3.evaluate(X_te_standardized, y_te_encoded, batch_size = batch_size)\n",
    "\n",
    "print('Test loss: {:.2f}'.format(test_loss))\n",
    "print('Test accuracy: {:.2f}%'.format(100 * test_score_dense3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4,  5,  1,  9,  7, 11,  3,  3, 18, 15, 15,  2, 16, 15, 17,  1, 15,\n",
       "        2,  9,  4,  8, 18,  2, 16, 16,  7, 13, 13, 11, 13, 18, 11, 16,  6,\n",
       "        5, 18,  0, 19, 19,  9])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Compute and display the predictions of the neural network. \n",
    "y_pred_dense3 = encoding_order[model_dense3.predict_classes(X_te_standardized)]\n",
    "y_pred_dense3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.675"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Security check: compute the accuracy from these predictions. \n",
    "test_score_dense3_from_pred = np.sum(y_pred_dense3 == y_te) / len(y_te)\n",
    "test_score_dense3_from_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Verify if the two accuracies are equal. \n",
    "np.round(test_score_dense3_from_pred, 4) == np.round(test_score_dense3, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.05"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Display again the baseline. \n",
    "neural_networks_baseline3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Result:** The 2-layer neural network model performs better than the baseline. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### **2.4 Dense neural network: 2-layer, target: block positions**\n",
    "\n",
    "In the following cells, we **run and compute the predictions from a 2-layer neural network model**. Our target will be the **block positions** of the eegfmriNF run. Here, our objective is to find out if our neural networks can discriminate not only between the rest and task blocks, but also between the beginning and the end of these blocks. Again, we will perform a train-test split with stratification. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 0 0 0 0 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 0 0 0 0 0 1 1 1 1 1 2 2 2 2 2 3 3\n",
      " 3 3 3 0 0 0 0 0 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 0 0 0 0 0 1 1 1 1 1 2 2 2 2\n",
      " 2 3 3 3 3 3 0 0 0 0 0 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 0 0 0 0 0 1 1 1 1 1 2\n",
      " 2 2 2 2 3 3 3 3 3 0 0 0 0 0 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 0 0 0 0 0 1 1 1\n",
      " 1 1 2 2 2 2 2 3 3 3 3 3 0 0 0 0 0 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 0 0 0 0 0\n",
      " 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3]\n"
     ]
    }
   ],
   "source": [
    "# Define and display the new target variable. \n",
    "y = np.tile(np.repeat([0, 1, 2, 3], 5), 10)\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(200,)"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Display the shape of the target variable. \n",
    "y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Store the number of different target values. \n",
    "nb_target_values = np.unique(y).shape[0]\n",
    "nb_target_values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Divide the data into a train set and a test set. \n",
    "X_tr, X_te, y_tr, y_te = train_test_split(X, y, test_size = test_set_proportion, stratify = y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.25"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a baseline containing only the most frequent value in the train set. \n",
    "most_frequent_value = np.bincount(y_tr.astype(int)).argmax()\n",
    "neural_networks_baseline4 = np.sum(y_te.astype(int) == most_frequent_value) / y_te.shape[0]\n",
    "neural_networks_baseline4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train: (160, 100674)\n",
      "Test: (40, 100674)\n"
     ]
    }
   ],
   "source": [
    "# Rescale features variables. \n",
    "scaler = StandardScaler()\n",
    "X_tr_standardized = scaler.fit_transform(X_tr)\n",
    "X_te_standardized = scaler.transform(X_te)\n",
    "\n",
    "print('Train:', X_tr_standardized.shape)\n",
    "print('Test:', X_te_standardized.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Encode target variable. \n",
    "y_tr_encoded = pd.get_dummies(y_tr)\n",
    "y_te_encoded = pd.get_dummies(y_te)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Get and display the encoding order. \n",
    "encoding_order = np.unique(y_te)\n",
    "encoding_order"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "dense_5 (Dense)              (None, 128)               12886400  \n",
      "_________________________________________________________________\n",
      "dropout_2 (Dropout)          (None, 128)               0         \n",
      "_________________________________________________________________\n",
      "dense_6 (Dense)              (None, 4)                 516       \n",
      "=================================================================\n",
      "Total params: 12,886,916\n",
      "Trainable params: 12,886,916\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "# Create model. \n",
    "model_dense4 = Sequential()\n",
    "\n",
    "# Hidden layer. \n",
    "model_dense4.add(Dense(\n",
    "    units = 128, activation = activations.relu, input_dim = X_tr_standardized.shape[1],\n",
    "    kernel_initializer = initializers.VarianceScaling(scale = 2.0, seed = 0),\n",
    "    kernel_regularizer = l2(0.01), bias_regularizer = l2(0.01)))\n",
    "model_dense4.add(Dropout(0.5, seed = 0))\n",
    "\n",
    "# Output layer. \n",
    "model_dense4.add(Dense(\n",
    "    units = nb_target_values, activation = activations.softmax,\n",
    "    kernel_initializer = initializers.VarianceScaling(scale = 1.0, seed = 0)))\n",
    "\n",
    "# Define loss function, optimizer and metrics to track during training. \n",
    "model_dense4.compile(optimizer = 'sgd', loss = 'categorical_crossentropy', metrics = ['acc'])\n",
    "\n",
    "# Print network summary. \n",
    "model_dense4.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 128 samples, validate on 32 samples\n",
      "Epoch 1/100\n",
      "128/128 [==============================] - 2s 13ms/step - loss: 5.2176 - acc: 0.3047 - val_loss: 8.6960 - val_acc: 0.2812\n",
      "Epoch 2/100\n",
      "128/128 [==============================] - 0s 2ms/step - loss: 7.4301 - acc: 0.4375 - val_loss: 5.5887 - val_acc: 0.5000\n",
      "Epoch 3/100\n",
      "128/128 [==============================] - 0s 2ms/step - loss: 4.3064 - acc: 0.7109 - val_loss: 5.2661 - val_acc: 0.5312\n",
      "Epoch 4/100\n",
      "128/128 [==============================] - 0s 2ms/step - loss: 4.1076 - acc: 0.7891 - val_loss: 4.6164 - val_acc: 0.6562\n",
      "Epoch 5/100\n",
      "128/128 [==============================] - 0s 2ms/step - loss: 4.2164 - acc: 0.8125 - val_loss: 5.1596 - val_acc: 0.5312\n",
      "Epoch 6/100\n",
      "128/128 [==============================] - 0s 2ms/step - loss: 3.0882 - acc: 0.8672 - val_loss: 4.0866 - val_acc: 0.4688\n",
      "Epoch 7/100\n",
      "128/128 [==============================] - 0s 2ms/step - loss: 2.7386 - acc: 0.9453 - val_loss: 3.7466 - val_acc: 0.6250\n",
      "Epoch 8/100\n",
      "128/128 [==============================] - 0s 2ms/step - loss: 2.7313 - acc: 0.9375 - val_loss: 3.8319 - val_acc: 0.5625\n",
      "Epoch 9/100\n",
      "128/128 [==============================] - 0s 2ms/step - loss: 2.6894 - acc: 0.9609 - val_loss: 4.3007 - val_acc: 0.6250\n",
      "Epoch 10/100\n",
      "128/128 [==============================] - 0s 2ms/step - loss: 2.7125 - acc: 0.9375 - val_loss: 3.8736 - val_acc: 0.5625\n",
      "Epoch 11/100\n",
      "128/128 [==============================] - 0s 2ms/step - loss: 2.6070 - acc: 0.9766 - val_loss: 3.6921 - val_acc: 0.5938\n",
      "Epoch 12/100\n",
      "128/128 [==============================] - 0s 2ms/step - loss: 2.6001 - acc: 0.9844 - val_loss: 3.7321 - val_acc: 0.5625\n",
      "Epoch 13/100\n",
      "128/128 [==============================] - 0s 2ms/step - loss: 2.5822 - acc: 0.9844 - val_loss: 3.7962 - val_acc: 0.5312\n",
      "Epoch 14/100\n",
      "128/128 [==============================] - 0s 2ms/step - loss: 2.5641 - acc: 1.0000 - val_loss: 3.7743 - val_acc: 0.5625\n",
      "Epoch 15/100\n",
      "128/128 [==============================] - 0s 2ms/step - loss: 2.5847 - acc: 0.9922 - val_loss: 3.8016 - val_acc: 0.5938\n",
      "Epoch 16/100\n",
      "128/128 [==============================] - 0s 2ms/step - loss: 2.5624 - acc: 0.9844 - val_loss: 3.7591 - val_acc: 0.5938\n",
      "Epoch 17/100\n",
      "128/128 [==============================] - 0s 2ms/step - loss: 2.5548 - acc: 1.0000 - val_loss: 3.7543 - val_acc: 0.5938\n"
     ]
    }
   ],
   "source": [
    "# End training when accuracy stops improving. \n",
    "early_stopping = keras.callbacks.EarlyStopping(monitor = 'val_loss', patience = 6)\n",
    "\n",
    "# Fit model. \n",
    "history_dense4 = model_dense4.fit(\n",
    "    x = X_tr_standardized, y = y_tr_encoded,\n",
    "    validation_split = validation_split, batch_size = batch_size, epochs = 100,\n",
    "    shuffle = True, callbacks = [early_stopping]\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Display the results. \n",
    "neural_network_graph(history_dense4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "40/40 [==============================] - 0s 595us/step\n",
      "Test loss: 3.56\n",
      "Test accuracy: 72.50%\n"
     ]
    }
   ],
   "source": [
    "# Evaluate test score. \n",
    "(test_loss, test_score_dense4) = model_dense4.evaluate(X_te_standardized, y_te_encoded, batch_size = batch_size)\n",
    "\n",
    "print('Test loss: {:.2f}'.format(test_loss))\n",
    "print('Test accuracy: {:.2f}%'.format(100 * test_score_dense4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([3, 2, 3, 2, 0, 3, 3, 0, 0, 1, 2, 0, 0, 2, 3, 1, 2, 3, 2, 3, 2, 1,\n",
       "       3, 1, 1, 0, 0, 2, 0, 0, 3, 2, 0, 1, 0, 3, 2, 3, 0, 3])"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Compute and display the predictions of the neural network. \n",
    "y_pred_dense4 = encoding_order[model_dense4.predict_classes(X_te_standardized)]\n",
    "y_pred_dense4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.725"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Security check: compute the accuracy from these predictions. \n",
    "test_score_dense4_from_pred = np.sum(y_pred_dense4 == y_te) / len(y_te)\n",
    "test_score_dense4_from_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Verify if the two accuracies are equal. \n",
    "np.round(test_score_dense4_from_pred, 4) == np.round(test_score_dense4, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 73,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.25"
      ]
     },
     "execution_count": 73,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Display again the baseline. \n",
    "neural_networks_baseline4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Result:** The 2-layer neural network model performs better than the baseline. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Save the results into a .npz file. \n",
    "np.savez(results_path + 'neural_networks_with_fMRI_predictors_single_subject.npz', \n",
    "         test_score_dense1 = test_score_dense1, \n",
    "         test_score_dense2 = test_score_dense2, \n",
    "         test_score_dense3 = test_score_dense3, \n",
    "         test_score_dense4 = test_score_dense4, \n",
    "         y_pred_dense1 = y_pred_dense1, \n",
    "         y_pred_dense2 = y_pred_dense2, \n",
    "         y_pred_dense3 = y_pred_dense3,\n",
    "         y_pred_dense4 = y_pred_dense4,\n",
    "         neural_networks_baseline1 = neural_networks_baseline,\n",
    "         neural_networks_baseline2 = neural_networks_baseline,\n",
    "         neural_networks_baseline3 = neural_networks_baseline3,\n",
    "         neural_networks_baseline4 = neural_networks_baseline4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## **3. Neural networks based on EEG data**\n",
    "\n",
    "### **3.1 Dense neural network: 1-layer**\n",
    "\n",
    "In the following cells, we **run and compute the predictions from a 1-layer neural network model**. Our target will be the **brain state** variable according to our primary definition, i.e. whether the subject is currently in a rest block or in a task block. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1\n",
      " 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1\n",
      " 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1\n",
      " 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0\n",
      " 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0\n",
      " 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1]\n"
     ]
    }
   ],
   "source": [
    "# Define and display the target variable. \n",
    "y = np.repeat(np.tile([0, 1], 10), 10)\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(200,)"
      ]
     },
     "execution_count": 76,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Display the shape of the target variable. \n",
    "y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define the features variables. \n",
    "X = predictors_EEG_single_subject_all_channels_200_samples\n",
    "\n",
    "# Divide the data into a train set and a test set. \n",
    "X_tr, X_te, y_tr, y_te = train_test_split(X, y, test_size = test_set_proportion)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4"
      ]
     },
     "execution_count": 78,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a baseline containing only the most frequent value in the train set. \n",
    "most_frequent_value = np.bincount(y_tr.astype(int)).argmax()\n",
    "neural_networks_baseline = np.sum(y_te.astype(int) == most_frequent_value) / y_te.shape[0]\n",
    "neural_networks_baseline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train: (160, 320)\n",
      "Test: (40, 320)\n"
     ]
    }
   ],
   "source": [
    "# Rescale features variables. \n",
    "scaler = StandardScaler()\n",
    "X_tr_standardized = scaler.fit_transform(X_tr)\n",
    "X_te_standardized = scaler.transform(X_te)\n",
    "\n",
    "print('Train:', X_tr_standardized.shape)\n",
    "print('Test:', X_te_standardized.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Encode target variable. \n",
    "y_tr_encoded = pd.get_dummies(y_tr)\n",
    "y_te_encoded = pd.get_dummies(y_te)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1])"
      ]
     },
     "execution_count": 81,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Get and display the encoding order. \n",
    "encoding_order = np.unique(y_te)\n",
    "encoding_order"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 82,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "dense_7 (Dense)              (None, 2)                 642       \n",
      "=================================================================\n",
      "Total params: 642\n",
      "Trainable params: 642\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "# Create model. \n",
    "model_dense1 = Sequential()\n",
    "\n",
    "# Output layer. \n",
    "model_dense1.add(Dense(\n",
    "    units = 2, activation = activations.softmax, input_dim = X_tr_standardized.shape[1],\n",
    "    kernel_initializer = initializers.VarianceScaling(scale = 1.0, seed = 0)))\n",
    "\n",
    "# Define loss function, optimizer and metrics to track during training. \n",
    "model_dense1.compile(optimizer = 'sgd', loss = 'categorical_crossentropy', metrics = ['acc'])\n",
    "\n",
    "# Print network summary. \n",
    "model_dense1.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 83,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 83,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Security check: verify that the number of parameters corresponds to what is expected, \n",
    "# i.e. the number of features multiplied by the number of target classes, plus the biases for each output neuron. \n",
    "model_dense1.count_params() == ((X_tr_standardized.shape[1] * 2) + 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 84,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 128 samples, validate on 32 samples\n",
      "Epoch 1/100\n",
      "128/128 [==============================] - 0s 4ms/step - loss: 0.8461 - acc: 0.4297 - val_loss: 0.7496 - val_acc: 0.5625\n",
      "Epoch 2/100\n",
      "128/128 [==============================] - 0s 45us/step - loss: 0.6815 - acc: 0.6016 - val_loss: 0.6962 - val_acc: 0.5625\n",
      "Epoch 3/100\n",
      "128/128 [==============================] - 0s 45us/step - loss: 0.6541 - acc: 0.6094 - val_loss: 0.6781 - val_acc: 0.5625\n",
      "Epoch 4/100\n",
      "128/128 [==============================] - 0s 39us/step - loss: 0.6389 - acc: 0.6172 - val_loss: 0.6390 - val_acc: 0.5938\n",
      "Epoch 5/100\n",
      "128/128 [==============================] - 0s 30us/step - loss: 0.6251 - acc: 0.6250 - val_loss: 0.6069 - val_acc: 0.5625\n",
      "Epoch 6/100\n",
      "128/128 [==============================] - 0s 30us/step - loss: 0.6207 - acc: 0.6406 - val_loss: 0.6154 - val_acc: 0.5938\n",
      "Epoch 7/100\n",
      "128/128 [==============================] - 0s 37us/step - loss: 0.6181 - acc: 0.6172 - val_loss: 0.6116 - val_acc: 0.5938\n",
      "Epoch 8/100\n",
      "128/128 [==============================] - 0s 36us/step - loss: 0.6163 - acc: 0.6172 - val_loss: 0.6035 - val_acc: 0.5938\n",
      "Epoch 9/100\n",
      "128/128 [==============================] - 0s 33us/step - loss: 0.6208 - acc: 0.6172 - val_loss: 0.5976 - val_acc: 0.5938\n",
      "Epoch 10/100\n",
      "128/128 [==============================] - 0s 38us/step - loss: 0.6241 - acc: 0.6250 - val_loss: 0.5992 - val_acc: 0.5938\n",
      "Epoch 11/100\n",
      "128/128 [==============================] - 0s 34us/step - loss: 0.6214 - acc: 0.6250 - val_loss: 0.5960 - val_acc: 0.6250\n",
      "Epoch 12/100\n",
      "128/128 [==============================] - 0s 29us/step - loss: 0.6202 - acc: 0.6094 - val_loss: 0.5992 - val_acc: 0.5938\n",
      "Epoch 13/100\n",
      "128/128 [==============================] - 0s 30us/step - loss: 0.6166 - acc: 0.6250 - val_loss: 0.6002 - val_acc: 0.6250\n",
      "Epoch 14/100\n",
      "128/128 [==============================] - 0s 30us/step - loss: 0.6150 - acc: 0.6250 - val_loss: 0.5984 - val_acc: 0.6250\n",
      "Epoch 15/100\n",
      "128/128 [==============================] - 0s 28us/step - loss: 0.6143 - acc: 0.6094 - val_loss: 0.5981 - val_acc: 0.6250\n",
      "Epoch 16/100\n",
      "128/128 [==============================] - 0s 28us/step - loss: 0.6154 - acc: 0.6328 - val_loss: 0.5979 - val_acc: 0.6250\n",
      "Epoch 17/100\n",
      "128/128 [==============================] - 0s 33us/step - loss: 0.6163 - acc: 0.6172 - val_loss: 0.6005 - val_acc: 0.6250\n"
     ]
    }
   ],
   "source": [
    "# End training when accuracy stops improving. \n",
    "early_stopping = keras.callbacks.EarlyStopping(monitor = 'val_loss', patience = 6)\n",
    "\n",
    "# Fit model. \n",
    "history_dense1 = model_dense1.fit(\n",
    "    x = X_tr_standardized, y = y_tr_encoded,\n",
    "    validation_split = validation_split, batch_size = batch_size, epochs = 100,\n",
    "    shuffle = True, callbacks = [early_stopping]\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Display the results. \n",
    "neural_network_graph(history_dense1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "40/40 [==============================] - 0s 24us/step\n",
      "Test loss: 0.64\n",
      "Test accuracy: 60.00%\n"
     ]
    }
   ],
   "source": [
    "# Evaluate test score. \n",
    "(test_loss, test_score_dense1) = model_dense1.evaluate(X_te_standardized, y_te_encoded, batch_size = batch_size)\n",
    "\n",
    "print('Test loss: {:.2f}'.format(test_loss))\n",
    "print('Test accuracy: {:.2f}%'.format(100 * test_score_dense1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 1, 0, 0,\n",
       "       1, 0, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1])"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Compute and display the predictions of the neural network. \n",
    "y_pred_dense1 = encoding_order[model_dense1.predict_classes(X_te_standardized)]\n",
    "y_pred_dense1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6"
      ]
     },
     "execution_count": 88,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Security check: compute the accuracy from these predictions. \n",
    "test_score_dense1_from_pred = np.sum(y_pred_dense1 == y_te) / len(y_te)\n",
    "test_score_dense1_from_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 89,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Verify if the two accuracies are equal. \n",
    "np.round(test_score_dense1_from_pred, 4) == np.round(test_score_dense1, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4"
      ]
     },
     "execution_count": 90,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Display again the baseline. \n",
    "neural_networks_baseline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Result:** The 1-layer neural network model performs better than the baseline. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Predictions</th>\n",
       "      <th>rest</th>\n",
       "      <th>task</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>True class</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>rest</th>\n",
       "      <td>19</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>task</th>\n",
       "      <td>11</td>\n",
       "      <td>5</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Predictions  rest  task\n",
       "True class             \n",
       "rest           19     5\n",
       "task           11     5"
      ]
     },
     "execution_count": 91,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Rename the labels. \n",
    "y_te_renamed = np.array(['rest', 'task'])[y_te]\n",
    "y_pred_dense1_renamed = np.array(['rest', 'task'])[y_pred_dense1]\n",
    "\n",
    "# Display a Scikit-learn confusion matrix. \n",
    "confusion_matrix_dense1 = scikit_learn_confusion_matrix(y_te_renamed, y_pred_dense1_renamed)\n",
    "confusion_matrix_dense1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### **3.2 Dense neural network: 2-layer**\n",
    "\n",
    "In the following cells, we **run and compute the predictions from a 2-layer neural network model**. We add both a dropout and a L2 regularization to the hidden layer. The number of units in the hidden layer was defined by trial and error. For the dropout and the regularization parameters, we simply use values that seem widely used by the machine learning community. Our target will be the **brain state** variable according to our primary definition, i.e. whether the subject is currently in a rest block or in a task block. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "dense_8 (Dense)              (None, 128)               41088     \n",
      "_________________________________________________________________\n",
      "dropout_3 (Dropout)          (None, 128)               0         \n",
      "_________________________________________________________________\n",
      "dense_9 (Dense)              (None, 2)                 258       \n",
      "=================================================================\n",
      "Total params: 41,346\n",
      "Trainable params: 41,346\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "# Create model. \n",
    "model_dense2 = Sequential()\n",
    "\n",
    "# Hidden layer. \n",
    "model_dense2.add(Dense(\n",
    "    units = 128, activation = activations.relu, input_dim = X_tr_standardized.shape[1],\n",
    "    kernel_initializer = initializers.VarianceScaling(scale = 2.0, seed = 0),\n",
    "    kernel_regularizer = l2(0.01), bias_regularizer = l2(0.01)))\n",
    "model_dense2.add(Dropout(0.5, seed = 0))\n",
    "\n",
    "# Output layer. \n",
    "model_dense2.add(Dense(\n",
    "    units = 2, activation = activations.softmax,\n",
    "    kernel_initializer = initializers.VarianceScaling(scale = 1.0, seed = 0)))\n",
    "\n",
    "# Define loss function, optimizer and metrics to track during training. \n",
    "model_dense2.compile(optimizer = 'sgd', loss = 'categorical_crossentropy', metrics = ['acc'])\n",
    "\n",
    "# Print network summary. \n",
    "model_dense2.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 128 samples, validate on 32 samples\n",
      "Epoch 1/100\n",
      "128/128 [==============================] - 1s 5ms/step - loss: 3.4062 - acc: 0.4922 - val_loss: 3.2473 - val_acc: 0.6875\n",
      "Epoch 2/100\n",
      "128/128 [==============================] - 0s 81us/step - loss: 3.2838 - acc: 0.5938 - val_loss: 3.2419 - val_acc: 0.6875\n",
      "Epoch 3/100\n",
      "128/128 [==============================] - 0s 88us/step - loss: 3.2383 - acc: 0.5937 - val_loss: 3.2455 - val_acc: 0.5938\n",
      "Epoch 4/100\n",
      "128/128 [==============================] - 0s 75us/step - loss: 3.2353 - acc: 0.5547 - val_loss: 3.2539 - val_acc: 0.5938\n",
      "Epoch 5/100\n",
      "128/128 [==============================] - 0s 101us/step - loss: 3.2758 - acc: 0.5859 - val_loss: 3.2524 - val_acc: 0.6250\n",
      "Epoch 6/100\n",
      "128/128 [==============================] - 0s 103us/step - loss: 3.2296 - acc: 0.5781 - val_loss: 3.2584 - val_acc: 0.6250\n",
      "Epoch 7/100\n",
      "128/128 [==============================] - 0s 75us/step - loss: 3.2628 - acc: 0.5937 - val_loss: 3.2590 - val_acc: 0.6250\n",
      "Epoch 8/100\n",
      "128/128 [==============================] - 0s 66us/step - loss: 3.2800 - acc: 0.5859 - val_loss: 3.2488 - val_acc: 0.6250\n"
     ]
    }
   ],
   "source": [
    "# End training when accuracy stops improving. \n",
    "early_stopping = keras.callbacks.EarlyStopping(monitor = 'val_loss', patience = 6)\n",
    "\n",
    "# Fit model. \n",
    "history_dense2 = model_dense2.fit(\n",
    "    x = X_tr_standardized, y = y_tr_encoded,\n",
    "    validation_split = validation_split, batch_size = batch_size, epochs = 100,\n",
    "    shuffle = True, callbacks = [early_stopping]\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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hFPiMKOGEUI+9mHDacxTwWyt9LuG/EGoby81CjfgZhPrPjwl/k0cJo9MAPyH8jTcQ3hclTtFVTqMIp8c/Axbw/YT4x8Cy6LTlNYTTpWW+vyJHA/MkbSJ8OZtAGMEv8iPgKQu16M6VWw3vd+8iJLHrCBfDJ8a5I9p3B+BTwkVy/aN1fyPUAY8h9Ccv8O3sUjdE2xWVRrxQRgwPEGraVxP6jklJ639MuK5kEeGC1hsTYvyGcFahXWLsySzUu58fxVxImJVkQNF6SQ9Lejhhk2sJyePnhIsixxDuSQDhc6kl8FjC50Hi58UNhL5wLWHqwkFmNrWEuLYCT/LdC0xTFr2XTo2O5XNCaclvCZ9xUPH3b1lK+5uV9hn9b8LZhxWSVlO8cwmlThsI5VEP8d1JFi4mjOhnDCWUrzrnqjGFU9XvAidZDbhhz+6IflfvAcdaCjPbOOeyj6Q7gEPMrEKJbNwU7vg7HehpNeCGPbsjOiv6OuF3tbms9tWFJ+HOOeecyypRKcS7wI/NbFrc8ThXHC9Hcc4551zWkDSIcGHiRE/AXXXmI+HOOeecc85VMR8Jd84555xzropVdM7hjNKiRQtr27Zt3GE451y5zZ49e7WZtYw7jqrkfbZzLlOVp8+uEUl427ZtmTVrVtxhOOdcuUnKmDlvK4v32c65TFWePtvLUZxzzjnnnKtinoQ755xzzjlXxTwJd84555xzrorViJpw51x6bdu2jYKCAjZvzpgblVU79evXp02bNtStWzfuUJxzNYj33xVTGX22J+HOud1WUFBA48aNadu2LZLiDifjmBlr1qyhoKCAdu3axR2Oc64G8f67/Cqrz/ZyFOfcbtu8eTPNmzf3DryCJNG8eXMfiXLOVTnvv8uvsvpsT8Kdc5XCO/Dd478/51xcvP8pv8r4nXk5SjHWrIHhw+Hss6FHj7ijcc45V5YHZjzAV998FXcYJWpSvwnXH3E9dWr5x65zLvDeoBi1asFdd8G2bZ6EO5cJ1q5dy5gxYxgyZEi5t83Pz2fMmDE0adIkpfZ33nknjRo14ic/+Um5X8ulz4iZI1j81eK4wyiWYQC0atyKAV0HxByNc9VLVfbf1Y0n4cVo2hSOOgomTIBf/CLuaJxzZVm7di0jRowothPfvn07deqU3NVNmDAhnaG5KvLhdR/GHUKJdtpOOj7UkREzR3gS7lySmtx/e014CfLz4Z134Isv4o7EOVeWYcOGsWTJEnJycrj55puZOnUqP/zhDznrrLPo3LkzAOeccw6HH344Xbp0YeTIkbu2bdu2LatXr2bZsmV06tSJQYMG0aVLF0499VS++eabUl93zpw59O7dm+7du3PuuedSWFgIwIMPPkjnzp3p3r07AwaEpOv1118nJyeHnJwcevbsyYYNG9L023DVTS3VYnDuYKZ/Op15K+fFHY5z1UpV9t8vv/wyRxxxBD179uTkk09m5cqVAGzcuJErrriCbt260b17d8aNGwfApEmTOOyww+jRowcnnXRSpR+7j4SXID8ffvpTmDQJrrgi7micyxw33ghz5lTuPnNy4IEHSl5/zz338P777zMneuGpU6fyzjvv8P777++aPurxxx+nWbNmfPPNN+Tl5XH++efTvHnz7+zno48+4q9//SuPPPII/fr1Y9y4cVxyySUlvu6ll17KQw89xHHHHccdd9zBXXfdxQMPPMA999zDxx9/TL169Vi7di0A9913H8OHD+foo49m48aN1K9ffzd/Ky6TXJFzBbdPuZ3hM4fz8BkPxx2Oc8XK9v77mGOOYcaMGUji0Ucf5d577+X3v/89v/jFL9h7772ZNy98SS4sLGTVqlUMGjSIadOm0a5dO776qvKvOUnbSLik+pLelvSepPmS7iql7fmSTFJuwrJbJS2W9IGk0xKW94mWLZY0LF3xd+8OrVrBxInpegXnXDr16tXrO/O3Pvjgg/To0YPevXuzfPlyPvroo+9t065dO3JycgA4/PDDWbZsWYn7X7duHWvXruW4444D4LLLLmPatGkAdO/enYsvvpinn35616nUo48+mptuuokHH3yQtWvXlnqK1WWf5g2bM6DrAJ6e+zTrNq+LOxznqrV09d8FBQWcdtppdOvWjd/97nfMnz8fgNdee42hQ4fuate0aVNmzJjBscceuyuOZs2aVeYhAukdCd8CnGhmGyXVBd6QNNHMZiQ2ktQYuAF4K2FZZ2AA0AVoBbwm6ZBo9XDgFKAAmCnpJTNbUNnBS2E0/G9/Cxdo+k3snEtNaSMeVWnPPffc9fPUqVN57bXXePPNN2nYsCHHH398sfO71qtXb9fPtWvXLrMcpSSvvPIK06ZN4+WXX+ZXv/oV8+bNY9iwYZx++ulMmDCBo48+msmTJ3PooYdWaP8uMw3NG8qTc55k1HujuO6I6+IOx7nvyfb++7rrruOmm27irLPOYurUqdx5551piT9VaRsJt2Bj9LRu9LBimv4C+C2Q+Bs9GxhrZlvM7GNgMdAreiw2s6VmthUYG7VNi759Yd06ePPNdL2Cc64yNG7cuNQa63Xr1tG0aVMaNmzIokWLmDFjRoltU7X33nvTtGlTpk+fDsDo0aM57rjj2LlzJ8uXL+eEE07gt7/9LevWrWPjxo0sWbKEbt26ccstt5CXl8eiRYt2OwaXWXJb5dKrdS9GzBqBWXEfh87VPFXZf69bt47WrVsD8NRTT+1afsoppzB8+PBdzwsLC+nduzfTpk3j448/BsischQASbUlzQG+BF41s7eS1h8GHGBmryRt2hpYnvC8IFpW0vLiXvtqSbMkzVq1alWF4j/5ZKhTJ8yS4pyrvpo3b87RRx9N165dufnmm7+3vk+fPmzfvp1OnToxbNgwevfuXSmv+9RTT3HzzTfTvXt35syZwx133MGOHTu45JJL6NatGz179uT666+nSZMmPPDAA3Tt2pXu3btTt25d+vbtWykxuMwyJHcIi1YvYsqyKXGH4ly1UJX995133smFF17I4YcfTosWLXYtv+222ygsLKRr16706NGDKVOm0LJlS0aOHMl5551Hjx496N+/f4VftySqim/jkpoA44HrzOz9aFkt4N/A5Wa2TNJU4CdmNkvSn4AZZvZ01PYxoKg6u4+ZXRUt/zFwhJldW9rr5+bm2qxZsyoU+4knwurVMHduhTZ3rkZYuHAhnTp1ijuMjFfc71HSbDPLLWGTrLQ7fXZ1t3n7Ztr8oQ3HtT2Ocf3GxR2Oc95/74bd7bOrZIpCM1sLTAH6JCxuDHQFpkpaBvQGXoouzvwMOCChbZtoWUnL0yY/H+bNg+XLy27rnHPOlaZ+nfpc2fNKXlz0IgXrC+IOxzkXo3TOjtIyGgFHUgPCxZS7iiDNbJ2ZtTCztmbWFpgBnGVms4CXgAGS6klqB3QE3gZmAh0ltZO0B+HizZfSdQwQknAIUxU651w2S2X2KUn9JC2IZr0aEy07QdKchMdmSedE656U9HHCupyqPKbq6Jrca9hpOxk5e2TZjZ1zWSudI+H7A1MkzSUkz6+a2T8k3S3prNI2NLP5wHPAAmASMNTMdpjZduBaYDKwEHguaps2nTrBQQd5XbhzLrtJqk2Yfaov0Bm4KJqpKrFNR+BW4Ggz6wLcCGBmU8wsx8xygBOBr4F/Jmx6c9F6M6vkWYgzT7um7cjvmM/I2SPZumNr3OE452KStikKzWwu0LOY5XeU0P74pOe/An5VTLsJQJWlxFKYJeXpp2HLFkiYAcc557LJrtmnACQVzT6VOAXsIGC4mRUCmNmXxeznAmCimX2d5ngz2pC8IZw+5nT+vvDvfit752oov219CvLzYeNGeOONuCNxzrm0SWX2qUOAQyT9R9IMSX34vgHAX5OW/UrSXEn3Syp2KKMyZrTKJH069KF90/aMmDki7lCcczHxJDwFJ54Ie+zhJSnOuRqvDuEaneOBi4BHiq79AZC0P9CNUDJY5FbgUCAPaAbcUtyOzWykmeWaWW7Lli3TE301Uku1GJw7mOmfTmfeynlxh+Oci4En4SnYc084/nhPwp3LJo0aNSrX8hogldmnCoCXzGxbdCO1DwlJeZF+wHgz21a0wMy+iG7etgV4glD24oArcq6gfp36DJ85vOzGzrldsqWf9iQ8Rfn5sGgRRDdOcs65bJPK7FMvEEbBkdSCUJ6yNGH9RSSVokSj40gScA7wfjqCz0TNGzZnQNcBPD33adZtXhd3OM65KuZJeIqKpiqcOLH0ds65qjds2LDv3HL4zjvv5L777mPjxo2cdNJJHHbYYXTr1o0XX3wx5X2aGTfffDNdu3alW7duPPvsswB88cUXHHvsseTk5NC1a1emT5/Ojh07uPzyy3e1vf/++yv9GNOtpNmnkma0mgyskbSAcO+Hm81sDYCktoSR9NeTdv2MpHnAPKAF8Mt0H0smGZo3lE3bNjHqvVFxh+JcLCqz/z7nnHM4/PDD6dKlCyNHfjsF6KRJkzjssMPo0aMHJ510EgAbN27kiiuuoFu3bnTv3p1x46r+5llVcsfMuFXW3dc6doQf/AD+8Y9KCMq5LJJ417AbJ93InBWVOwtdzn45PNDngRLXv/vuu9x44428/nrI/zp37szkyZPZf//9+frrr9lrr71YvXo1vXv35qOPPkISjRo1YuPGjd/bV9HycePG8fDDDzNp0iRWr15NXl4eb731FmPGjGHz5s387Gc/Y8eOHXz99dd8+OGHDBs2jFdffRWAtWvX0qRJk+/tuyx+x8wgm++YWZxej/Riw9YNLBiygHDCwLmqk03991dffUWzZs345ptvyMvL4/XXX2fnzp0cdthhTJs2jXbt2u1qc8stt7BlyxYeeCDEVlhYSNOmTct1bLvbZ6dtisJs1LcvPPoofPMNNGgQdzTOuSI9e/bkyy+/5PPPP2fVqlU0bdqUAw44gG3btvHTn/6UadOmUatWLT777DNWrlzJfvvtV+Y+33jjDS666CJq167Nvvvuy3HHHcfMmTPJy8tj4MCBbNu2jXPOOYecnBzat2/P0qVLue666zj99NM59dRTq+CoXbYYmjeUy1+8nCnLpnBiuxPjDse5KlWZ/feDDz7I+PHjAVi+fDkfffQRq1at4thjj6Vdu3YANGvWDIDXXnuNsWPH7tq2vAl4ZfAkvBzy8+Ghh+D116FPcRNzOedKHfFIpwsvvJDnn3+eFStW0L9/fwCeeeYZVq1axezZs6lbty5t27Zl8+bNu/U6xx57LNOmTeOVV17h8ssv56abbuLSSy/lvffeY/LkyTz88MM899xzPP7445VxWK4G6N+1Pzf98yaGzxzuSbiLVSb331OnTuW1117jzTffpGHDhhx//PG73d+nm9eEl8Nxx4URcJ8lxbnqp3///owdO5bnn3+eCy+8EIB169axzz77ULduXaZMmcInn3yS8v5++MMf8uyzz7Jjxw5WrVrFtGnT6NWrF5988gn77rsvgwYN4qqrruKdd95h9erV7Ny5k/PPP59f/vKXvPPOO+k6TJeF6tepz5U9r+TFRS9SsL4g7nCcq3KV0X+vW7eOpk2b0rBhQxYtWsSMGTMA6N27N9OmTePjaGaNr776CoBTTjnlO7XohYWF6Ti0UnkSXg4NGoQ5w195BWpAKb1zGaVLly5s2LCB1q1bs//++wNw8cUXM2vWLLp168aoUaM49NBDU97fueeeS/fu3enRowcnnngi9957L/vttx9Tp06lR48e9OzZk2effZYbbriBzz77jOOPP56cnBwuueQSfvOb36TrMF2WGpw7mJ22k5GzR5bd2LksUxn9d58+fdi+fTudOnVi2LBh9O7dG4CWLVsycuRIzjvvPHr06LFrpP22226jsLCQrl270qNHD6ZMmZLegyyGX5hZTiNGwNCh8MEHcMghlbJL5zJecRenuPLzCzODmnZhZpEzxpzBrM9n8en/fsoetfeIOxxXQ3j/XXG722f7SHg59e0b/vWpCp1zzlWmIXlDWLlpJeMXjo87FOdcFfAkvJzatYNOnbwu3DnnXOXq06EP7Zu29ztoOldDeBJeAX37wtSpsGlT3JE4V33UhNK2dPLfn6ulWgzOHcz0T6czb+W8uMNxNYj3P+VXGb8zT8IrID8ftm6Ff//7b5OTAAAgAElEQVQ77kicqx7q16/PmjVrvCOvIDNjzZo11K9fP+5QXMyuyLmC+nXqM2LmiLhDcTWE99/lV1l9ts8TXgHHHAONGoWSlDPPjDsa5+LXpk0bCgoKWLVqVdyhZKz69evTpk2buMNwMWvesDkDug5g9NzR3HPyPexdf++4Q3JZzvvviqmMPtuT8AqoVw9OPjkk4Wbgdxl2NV3dunV33Y3MObd7huYN5ck5TzLqvVFcd8R1cYfjspz33/HxcpQKys+HTz+FhQvjjsQ551w2yW2VS16rPEbMGuElAs5lMU/CK6hoqkKfJcU551xlG5o3lEWrFzFlWdXfQMQ5VzXSloRLqi/pbUnvSZov6a5i2lwjaZ6kOZLekNQ5Wn5xtKzosVNSTrRuqqQPEtbtk65jKE2bNtC9uyfhzjnnKl+/Lv1o1qCZT1foXBZL50j4FuBEM+sB5AB9JPVOajPGzLqZWQ5wL/AHADN7xsxyouU/Bj42szkJ211ctN7MvkzjMZSqb1+YPh3Wr48rAuecc9moQd0GXNnzSl5c9CIF6wviDsc5lwZpS8It2Bg9rRs9LKlNYvq6Z/L6yEXA2LQEuZvy82H7dnjttbgjcc45l22uyb2GnbaTkbNHxh2Kcy4N0loTLqm2pDnAl8CrZvZWMW2GSlpCGAm/vpjd9Af+mrTsiagU5Xap+LlJJF0taZakWemadufII2Hvvb0kxTmXHST1icr9FksaVkKbfpIWRGWGYxKW70goE3wpYXk7SW9F+3xW0h5VcSzZoH3T9vTt2JeRs0eydcfWuMNxzlWytCbhZrYjKilpA/SS1LWYNsPN7GDgFuC2xHWSjgC+NrP3ExZfbGbdgB9Gjx+X8NojzSzXzHJbtmxZSUf0XXXrwqmnwsSJYapC55zLVJJqA8OBvkBn4KKi63QS2nQEbgWONrMuwI0Jq79JKBM8K2H5b4H7zawDUAhcmc7jyDZD84ayctNKxi8cH3cozrlKViWzo5jZWmAK0KeUZmOBc5KWDSBpFNzMPov+3QCMAXpVXqTll58Pn38Oc+fGGYVzzu22XsBiM1tqZlsJffLZSW0GAcPNrBCgrGtyojOVJwLPR4ue4vv9vCtFnw59aNeknV+g6VwWSufsKC0lNYl+bgCcAixKatMx4enpwEcJ62oB/UioB5dUR1KL6Oe6wBlA4ih5lesTfa3wkhTnXIZrDSxPeF4QLUt0CHCIpP9ImiEpcWClflQCOENSUaLdHFhrZttL2SdQNSWEmaiWajE4dzDTP53OvJXz4g7HOVeJ0jkSvj8wRdJcYCahJvwfku6WVHSq8tqornAOcBNwWcL2xwLLzWxpwrJ6wORon3OAz4BH0ngMZdpvPzj8cE/CnXM1Qh2gI3A84aL5R4oGW4CDzCwX+BHwgKSDy7PjqighzFQDew6kfp36jJg5Iu5QnHOVKG23rTezuUDPYpbfkfDzDaVsPxXonbRsE3B45UVZOfr2hV//GgoLoWnTuKNxzrkK+Qw4IOF5m2hZogLgLTPbBnws6UNCUj4zoVRwqaSphP5/HNBEUp1oNLy4fboyNG/YnAFdBzB67mjuOfke9q6/d9whOecqgd8xsxLk58POnfDPf8YdiXPOVdhMoGM0m8kehGtyXkpq8wJhFJyoNPAQYKmkppLqJSw/Glhg4Z7rU4ALou0vA15M94FkoyG5Q9i0bROj3hsVdyjOuUriSXgl6NULmjXzkhTnXOaKRqqvBSYDC4HnzGx+UgnhZGCNpAWE5PpmM1sDdAJmSXovWn6PmS2ItrkFuEnSYkKN+GNVd1TZI691Hnmt8hgxawTm03E5lxXSVo5Sk9SuHS7QnDQpjIjX8q82zrkMZGYTgAlJyxJLCI1w/c5NSW3+C3QrYZ9LiXkWq2wxNG8ol794OVOWTeHEdifGHY5zbjd5ulhJ8vPhyy/hnXfijsQ551w26telH80aNPMLNJ3LEp6EV5LTTgPJS1Kcc86lR4O6Dbiy55W8sOgFCtYXxB2Oc243eRJeSVq0gCOO8CTcOedc+lyTew07bScjZ4+MOxTn3G7yJLwS9e0Lb78Nfp8J55xz6dC+aXv6duzLI+88wtYdW+MOxzm3GzwJr0T5+WAGkyfHHYlzzrlsNTRvKCs2rmD8wvFxh+Kc2w2ehFeiww6DffbxkhTnnHPpc9rBp9GuSTuGzxwedyjOud3gSXglqlUrlKRMngw7dsQdjXPOuWxUu1ZtBucOZvqn05m3cl7c4TjnKsiT8EqWnw9ffRVqw51zzrl0GNhzIPVq1/PpCp3LYJ6EV7JTTgk37/GSFOecc+nSvGFzBnQdwOi5o1m3eV3c4TjnKsCT8ErWtCkceaQn4c4559JraN5QNm3bxOi5o+MOxTlXAZ6Ep0F+frhz5hdfxB2Jc865bJXXOo+8VnmMmDkCM4s7HOdcOXkSngb5+eHfSZPijcM551x2G5I3hIWrFzJl2ZS4Q3HOlZMn4WnQvTu0auUlKc4559Krf5f+NGvQzC/QdC4DeRKeBlIYDX/1Vdi2Le5onHPOZasGdRtwZc8reWHRCxSsL4g7HOdcOXgSnib5+bBuHbz5ZtyROOecy2bX5F7DTtvJyNkj4w7FOVcOnoSnyUknQd26XpLinHMuvdo3bU/fjn155J1H2Lpja9zhOOdSlLYkXFJ9SW9Lek/SfEl3FdPmGknzJM2R9IakztHytpK+iZbPkfRwwjaHR9sslvSgJKXrGHbHXnvBMcd4Eu6cyxyS+kj6IOpfh5XQpp+kBVG/PiZaliPpzWjZXEn9E9o/KenjhP48p6qOpyYZmjeUFRtXMH7h+LhDcc6lKJ0j4VuAE82sB5AD9JHUO6nNGDPrZmY5wL3AHxLWLTGznOhxTcLyPwODgI7Ro0/6DmH35OfDvHmwfHnckTjnXOkk1QaGA32BzsBFRQMjCW06ArcCR5tZF+DGaNXXwKXRsj7AA5KaJGx6c0J/Pifdx1ITnXbwabRr0o7hM4fHHYpzLkV10rVjC5OWboye1o0eltRmfcLTPZPXJ5O0P7CXmc2Ino8CzgEmVlLYlSo/H26+GSZOhKuvjjsa55wrVS9gsZktBZA0FjgbWJDQZhAw3MwKAczsy+jfD4samNnnkr4EWgJrqyj2Gq92rdoMzh3M/732f8xbOY9u+3aLO6Qa4ctNX7Jg1YKyG7qM1LllZ/bZc5+07T9tSTjsGlmZDXQgdNxvFdNmKHATsAdwYsKqdpLeBdYDt5nZdKA1kHj5d0G0rLjXvhq4GuDAAw/c/YOpgE6d4KCDPAl3zmWE1kDiebsC4IikNocASPoPUBu408y+c0cESb0I/fmShMW/knQH8C9gmJltSX7x6tBnZ7qBPQdy+5TbGTFzBH8+489xh5P1Xl3yKv2f70/h5sK4Q3FpMvb8sfTv2r/shhWU1iTczHYAOdFpyfGSuprZ+0lthgPDJf0IuA24DPgCONDM1kg6HHhBUpdyvvZIYCRAbm5uLLcSK5qqcPRo2LIF6tWLIwrnnKs0dQhlgMcDbYBpkrqZ2VrYdbZyNHCZme2MtrkVWEFIzEcCtwB3J++4OvTZma55w+YM6DqA0XNHc8/J97B3/b3jDikrmRm/++/vuPVft9K5ZWfGnD+G+nXqxx2WS4POLTuX3Wg3pDUJL2JmayVNIdQKvl9Cs7GEem+iUZIt0c+zJS0hjMB8Ruj4i7SJllVb+fnw5z/DG2+EGVOcc66a+gw4IOF5cf1rAfCWmW0DPpb0ISEpnylpL+AV4GdFJYMAZvZF9OMWSU8AP0nXAbhwgeZT7z3F6LmjubbXtXGHk3U2bd3ElS9dybPzn+XCzhfy+NmP02iPRnGH5TJUOmdHaVl0YY6kBsApwKKkNh0Tnp4OfJSwbe3o5/aETn5p1Jmvl9Q7mhXlUuDFdB1DZTjhhDAC7rOkOOequZlAR0ntJO0BDABeSmrzAmEUHEktCIMjS6P244FRZvZ84gbR6DhRn30OJQ/EuEqQ1zqPvFZ5jJg5gnBplqssSwuXctTjR/Hc/Oe456R7ePaCZz0Bd7slnbOj7A9MkTSX0Lm/amb/kHS3pLOiNtdGU1rNIdSFXxYtPxaYGy1/HrjGzL6K1g0BHgUWE2oOq+VFmUX23BOOO86TcOdc9WZm24FrgcnAQuA5M5uf1GdPBtZIWgBMIcx6sgboR+i3Ly9mKsJnJM0D5gEtgF9W4WHVSEPyhrBw9UKmLJsSdyhZ49Ulr5I7MpdP133KxIsncssxt1BNZ0h2GUQ14Ztybm6uzZo1K7bX/+Mf4cYbYckSaN8+tjCccxlI0mwzy407jqoUd5+d6b7Z9g1t7m/DCW1P4Pl+z5e9gStRcv33C/1f4OBmB8cdlqvGytNn+x0zq0B+fvh3YrUes3fOOZcNGtRtwMCcgbyw6AUK1heUvYEr1qatm7ho3EXc8totnN/pfN688k1PwF2l8iS8CnTsCB06eBLunHOuagzOG8xO28kjsx+JO5SM5PXfrip4El5F8vPh3/+Gb76JOxLnnHPZrn3T9vTt2JeR74xk646tcYeTUbz+21UVT8KrSH5+SMBffz3uSJxzztUEQ3KHsGLjCsYvHB93KBnBzLj3P/fS55k+tN6rNbMGzeK0DqfFHZbLYp6EV5HjjoMGDXyWFOecc1WjT4c+tGvSjhGzRsQdSrXn9d8uDp6EV5H69eHEE+GVV6AGTEjjnHMuZrVr1WZw7mCmfTKNeSvnxR1OteX13y4uZSbhkg6R9C9J70fPu0u6Lf2hZZ/8fFi6FD76KO5InHPO1QRX9LyCerXrMWKmj4YXx+u/XZxSGQl/BLgV2AZgZnMJd1Jz5dS3b/jXZ0lxzjlXFVo0bMGArgMYPXc067esjzucasPrv111kEoS3tDM3k5atj0dwWS7du2gUyevC3fOOVd1huYNZdO2TYx6b1TcoVQLXv/tqotUkvDVkg4GDEDSBcAXaY0qi+Xnw9SpsGlT3JE455yrCfJa55HbKpcRM0dQE+6SXRqv/3bVSSpJ+FDgL8Chkj4DbgQGpzWqLJafD1u3hjnDnXMuHSRdJ6lp3HG46mNo3lAWrl7I1GVT4w4lNl7/7aqbMpNwM1tqZicDLYFDzewYM1uW9siy1DHHQKNGXpLinEurfYGZkp6T1EeeadR4/bv0p1mDZgyfOTzuUKqc13+76qpOWQ0k3ZH0HAAzuztNMWW1PfaAk08OSbgZ+Eejc66ymdltkm4HTgWuAP4k6TngMTNbEm90Lg4N6jZgYM5A7p9xPwXrC2izV5u4Q6oSm7Zu4sqXruTZ+c9yYecLefzsx738xFUbqZSjbEp47AD6Am3TGFPWy8+HTz+FBQvijsQ5l60sFP+uiB7bgabA85LujTUwF5vBeYPZaTt5ZPYjcYdSJbz+21V3ZY6Em9nvE59Lug+YnLaIaoDEqQq7dIk3Fudc9pF0A3ApsBp4FLjZzLZJqgV8BPxfnPG5eLRv2p6+Hfsy8p2R/OzYn7FH7T3iDiltXl3yKv2f749hTLx4opefuGqpInfMbAjUjPNYadKmDXTv7nXhzrm0aQacZ2anmdnfzKzoPg87gTPiDc3FaUjuEFZsXMH4hePjDiUtvP7bZZJU7pg5T9Lc6DEf+AB4IP2hZbf8fJg+Hdb7vROcc5VvIvBV0RNJe0k6AsDMFsYWlYtdnw59aNekHSNmZd8dNBPn/z6v03k+/7er9lIZCT8DODN6nAq0MrM/pTWqGiA/H7Zvh9deizsS51wW+jOwMeH5xmhZqaKZVD6QtFjSsBLa9JO0QNJ8SWMSll8m6aPocVnC8sOjwZzFkh70mVriVbtWba7JvYZpn0xj3sp5cYdTaRLrv39z0m947oLnvP7bVXslJuGSmklqBmxIeHwD7BUtd7vhyCNh7729JMU5lxayhLuyRGUopV4DJKk2MJxw8X1n4CJJnZPadARuBY42sy6E+0YQfSb8HDgC6AX8PGGe8j8Dg4CO0aPPbh+d2y0Dew6kXu16jJiZHaPhifN/T7h4AsOOGebzf7uMUNpI+GxgVvRv8mNWWTuWVF/S25Lei0ZM7iqmzTXRCMkcSW8UdfiSTpE0O1o3W9KJCdtMjUZq5kSPfcp3yNVDnTpw6qnfTlXonHOVaKmk6yXVjR43AEvL2KYXsDi6N8RWYCxwdlKbQcBwMysEMLMvo+WnAa+a2VfRuleBPpL2B/YysxnRl4JRwDmVc4iuolo0bMGArgMYPXc067dkbk1kcv33zEEz6dPBv+O5zFFiEm5m7cysffRv8qN9CvveApxoZj2AHEKH3DupzRgz62ZmOcC9wB+i5auBM82sG3AZMDppu4vNLCd6fEmGys+HL76A996LOxLnXJa5BjgK+AwoIIxQX13GNq2B5QnPC6JliQ4BDpH0H0kzJPUpY9vW0c+l7RMASVdLmiVp1qpVq8oI1e2uIXlD2LRtE6PeGxV3KBVSXP13h2Yd4g7LuXIpc4pCgOi0YkegftEyM5tW2jbRqEdRTWLd6GFJbRK/gu9ZtN7M3k1YPh9oIKmemW1JJd5M0Sf6+Jo4EXJy4o3FOZc9osGJAWnYdR3CZ8HxhFmypknqVhk7NrORwEiA3NxcPz+YZr1a9yK3VS4jZo5gaN7QjCrfWFq4lHOfPZd5K+fxm5N+wy1H++3nXWZKZXaUq4BphLnB74r+vTOVnUuqLWkO8CXhVOVbxbQZKmkJYST8+mJ2cz7wTlIC/kRUinJ7SRf5ZMKoyn77weGHe124c65yReWAQyWNkPR40aOMzT4DDkh43iZalqgAeMnMtpnZx8CHhKS8pG0/47tT2ha3TxeToXlDWbh6IVOXTY07lJR5/bfLJqnMjnIDkAd8YmYnAD2Btans3Mx2RKUmbYBekroW02a4mR0M3ALclrhOUhfgt8D/JCy+OCpT+WH0+HEJrz3SzHLNLLdly5aphBuL/Hz473+hsDDuSJxzWWQ0sB+hVvt1Qh+8oYxtZgIdJbWTtAdhJP2lpDYvEEbBkdSCUJ6ylDA4c6qkptGZ01OByWb2BbBeUu9owORS4MVKOD5XCfp36U+zBs0YPnN43KGUyeu/XTZKJQnfbGabAaKSkEXAD8rzIma2FphC6VfFjyXhgh1JbYDxwKVmtiRhX59F/24AxhAuJspY+fmwcyf8859xR+KcyyIdzOx2YJOZPQWcTqgLL5GZbQeuJSTUC4HnzGy+pLslnRU1mwyskbSA0KffbGZrzOwr4BeERH4mcHe0DGAI4a6di4ElhDnMXTXQoG4DBuYM5IVFL1CwvqDsDWLi9d8uW6VSE14gqQlhBORVSYXAJ2VtJKklsM3M1kpqAJxCGNVObNPRzD6Knp5OuJ0y0eu9Agwzs/8ktK8DNDGz1ZLqEuYwz+iZtvPyoHnzUJLSv3/c0TjnssS26N+10RnIFUCZM0mZ2QRgQtKyOxJ+NuCm6JG87ePA90pezGwW8L2zoDXJihXw85/Dlmp4VdP6Otewo83vOeUvAziiY/VMbN/+7G0WrV7k9d9Z5MsvYdSo8H+jZ89QmnvIIVCrIvdxz2BlJuFmdm70452SpgB7A5NS2Pf+wFPR3LO1CKMq/5B0NzDLzF4CrpV0MuEDo5AwEwqE0ZgOwB2Sij4ATgU2AZOjBLw2IQF/JIVYqq3ateG008LFmTt31rw3oHMuLUZGZSG3EUpKGgG3xxtSzfXHP8Ijj8CBB8YdSXEOpn7uYBYd8AqrthTQqBre36bRHo2YcPEELz/JcDt3wtSp8Je/wPjxsG0b7LEHbN0a1jdu/G1CfvjhkJsLHTtmd14kK2OSakkPAmPN7L9VE1Lly83NtVmzypzaPDbPPAOXXAIzZ4Y3nXPOFZE028xS7hkk1QIuMLPn0hhWWlX3Prs8tm8PyXduLryUXGFfTWzeDOedFwaDHn0Urrwy7ohcNvnyS3jqKRg5EhYvhqZN4bLLYNCgMPq9YAHMnh0es2aFaZs3bw7bZmJiXp4+O5VylNnAbZJ+QKjRHhudXnSV5LTTQAolKZ6EO+d2h5ntlPR/QMYm4dlk0qRwP4iBA+OOpGT168Pf/x4S8auuCss8EXe7o7hR7x/+MJRlXXBBeM8V6d49PK64Ijzfvv37ifmf/5zZiXlJyhwJ39Uw3Jb4fMIV8weaWcd0BlaZMmFU5cgjw50zZ8yIOxLnXHVS3pHwaJt7CDc9e5ZQxgdAwsWS1Vom9NmpOu88+M9/oKAA6taNO5rS+Yi4212ljXp37lzx/RaXmJc0Yp6bG/6NKzGv7JHwIh2AQ4GDCFfOu0qUnx++Ia5aBdV4RkXnXGYousx7aMIyA1K527GrJCtXwssvw403Vv8EHHxE3FVMeUa9K6pOnbJHzGfPLnnEPO7EvCRlJuGS7gXOJUwtNRb4RTTloKtE+flwxx0weXKoD3fOuYoys3Zxx+Dg6adDolCdS1GSeSLuUlXcqPfQobs/6p2q3UnMi5LyuBPzVEbClwBHmtnqdAdTk/XsCfvsE+rCPQl3zu0OSZcWt9zMRlV1LDWVGTz2WCg17NQp7mjKxxNxV5KqGPXeHakm5iNGVI/EPJUpCv+S/jBcrVrQt284dbljR5i60DnnKigv4ef6wEnAO4An4VXkrbdg4cIwNWEm8kS8bDt2wH33wfz5cNhhIXnr2ZNqOc3j7op71Ht37E5ifuedcMIJaYwtfbt25ZWfH97kb78dRk+cc64izOy6xOfRDdDGxhROjfTYY9CwYWbfhM0T8ZIVFsKPfhRmv2nRAkaPDsslOPTQ787ckZOTmYl5dR/13h2pJubpHg33JLwaOeWUMAI+YYIn4c65SrUJ8DrxKrJpE4wdC/36hRG1TOaJ+Pe9/z6ccw58+mlIUK++OkxDmZi8/fvf4ZoAyLzEPJNHvXdHcYl52l+zrAaSDgYKzGyLpOOB7sAovziz8jVtCkcdFZLwX/wi7micc5lK0suE2VAg3LG4Mz5veJX5299g48bsSVY9Ef/W88/D5ZfDXnvB669/O2C2//5wxhnhUSSTEnMzmDIlJN5//3t2jXpXZ6mMhI8DciV1AEYCLwJjgPx0BlZT5efDrbeG/7z77x93NM65DHVfws/bgU/MrCCuYGqaxx8PdwI8+ui4I6k8NT0R37EDbr8dfvObkHg//zy0alX6Nqkk5v/6V7yJeU0d9a4uUknCd5rZdknnAg+Z2UOS3k13YDVVURI+aVLVnQ5xzmWdT4EvzGwzgKQGktqa2bJ4w8p+H34I06fDPfeEpCqb1NREPLH+++qr4cEHoV69iu2rOiTmxY16H3NMGPU+/3xo0KDi+3blk0oSvk3SRcBlwJnRsgy47UBm6tYNWrcOJSmehDvnKuhvwFEJz3dEy/KKb+4qyxNPhGt7Li12ksjMV9MS8eLqvytbWYn5rFmVk5j7qHf1k0oSfgVwDfArM/tYUjtgdHrDqrmkMFXhc8+Fb6eZcJc151y1U8fMthY9MbOtkvaIM6CaYPv2kOT07Zvd5YQ1JREfNy7ccj25/rsqVFZivueePupdnaUyT/gC4HoASU2Bxmb223QHVpPl58Ojj8Kbb8Kxx8YdjXMuA62SdJaZvQQg6WzAb7iWZpMmhUQpGxPSZNmciFek/rsqlJaYz5pVfClL8+awerWPeldXqcyOMhU4K2o7G/hS0n/M7KY0x1ZjnXRSGAGfMMGTcOdchVwDPCPpT9HzAqDMAglJfYA/ArWBR83snqT1lwO/Az6LFv3JzB6VdAJwf0LTQ4EBZvaCpCeB44B10brLzWxOhY6qmnv88XDn49NPjzuSqpGNiXhhIVx8MUycGBLWhx6qeP13VSgrMV+8GPr08VHv6iqVcpS9zWy9pKsIUxP+XNLcdAdWk+21V5gaaMKEcHGPc86Vh5ktAXpLahQ931jWNpJqA8OBUwhJ+0xJL0VnQxM9a2bXJr3eFCAn2k8zYDHwz4QmN5vZ8xU9nkywcmW44/GNN9asMsJsSsSrov67KhSXmLvqKZV7AdWRtD/QD/hHmuNxkfx8mDcPli+POxLnXKaR9GtJTcxso5ltlNRU0i/L2KwXsNjMlkb15GOBsyvw8hcAE83s6wpsm7GefjrUhA8cGHckVa8oEe/bNyTijz0Wd0TlN24c9O4dbrQ0dWrmJuAus6SShN8NTAaWmNlMSe2Bj9IblsuPZmGfODHeOJxzGalv4g3VzKyQsu/t0BpI/NpfEC1Ldr6kuZKel3RAMesHAH9NWvaraJv7JRV7cl/S1ZJmSZq1atWqMkKtXsxC4nnkkdCpU9zRxCNTE/EdO+CnPw03pOnWLZRxHHVU2ds5VxnKTMLN7G9m1t3MBkfPl5rZ+ekPrWY79FA46KBQkuKcc+VUOzHZldQAqIzK1peBtmbWHXgVeCpxZXTWtBth4KbIrYQa8TygGXBLcTs2s5FmlmtmuS1btqyEUKvOW2/BwoU1cxQ8UVEi3qdPZiTihYVw5pnhAsxBg8IIeHW4ANPVHGUm4ZLaSBov6cvoMU5SmxS2qy/pbUnvSZov6a5i2lwjaZ6kOZLekNQ5Yd2tkhZL+kDSaQnL+0TLFksaVp6DzSRSGA3/179gy5a4o3HOZZhngH9JujK6nud7CXMxPgMSR7bb8O0FmACY2RozK+qRHgUOT9pHP2C8mW1L2OYLC7YATxDKXrLK449Dw4bQv3/ckcSvfn0YP776J+Lvvw95efDaa6H+e+TI6n0BpstOqZSjPAG8BLSKHi9Hy8qyBTjRzHoQLtjpI6l3UpsxZtbNzHKAe4E/AETJ+ACgC9AHGCGpdsKFQ32BzsBFiYl7tsnPh40b4Y034o7EOZdJomlkfwl0An5AGJk+qIzNZgIdJbWL5hQfQOj7d4lGuoucBSxM2sdFJJWiFG0jScA5wPvlOphqbtMmGDsW+vWDxo3jjqZ6qO6JuNd/u+oilSS8pZk9YWbbo8eTQJnnCqORj6Ir8utGD0tqsz7h6Z4J61Dr+dEAACAASURBVM8GxprZFjP7mHClfS8q78KhjHDCCeGbuZekOOcqYCWhT70QOJHvJ8zfYWbbgWsJCftC4Dkzmy/pbklnRc2uj85svke4f8TlRdtLaksYSX89adfPSJoHzANaEL4cZI3nn4cNG7wUJVl1TMS9/ttVN6lMUbhG0iV8O7pxEbAmlZ1HI9ezgQ7AcDN7q5g2Q4GbgD0IHxQQLgaakdAs8QKh5AuHjijhta8GrgY48MADUwm32tlzTzj++JCE//73cUfjnKvuJB1C6KMvItyc51lAZnZCKtub2QRgQtKyOxJ+vpVQ413ctsso5kJOMzvx+62zx2OPQceO4S6E7ruKEvFzz41/+sJMm//b1QypjIQPJNT5rQC+IEw/dXkqOzezHVGpSRugl6SuxbQZbmYHEy7WuS3FuFN57Yy9yCdRfj4sWgRLl8YdiXMuAywiDGacYWbHmNlDwI6YY8paH34I06eHUXAp7miqp+owIu713666SmV2lE/M7Cwza2lm+5jZOUC5ZkeJpsqaQqjvLslYQr0glHyBUJkXDmUbn6rQOVcO5xEGS6ZIekTSSYCnh2nyxBNQuzZcdlnckVRvcSbiXv/tqrNURsKLU+Yt6yW1lNQk+rkB4S5si5LadEx4ejrfzj/+EjBAUj1J7YCOwNukcOFQtunQITy8Ltw5VxYze8HMBhCmBJwC3Pj/27vz+KjK6/Hjn5MQ9gACQUlYFWRVsEZEAXcQouJaFRektWKxLt/6q7VWq61LrdpWa7VWyuqKFKtFRREVBVSgKAgEhCDKjgnIloQly/n98dyEIQkBkrlz7yTn/XrNKzN37sycSfThzDPnOQ/QSkSeE5FBwUZXsxQWwsSJri9269aHPr+2i3UibvXfJh4cTk14RQ5nZqU1MNGrC0/ALfJ5W0QeBBao6lTgVhE5DygAtgE3AHiLgSYDy4BC4BeqWgQgIiULhxKBcaqaWcX3EDcyMuBf/4Ldu6FBg6CjMcaEnarmAa8Ar4jIUbjFmXdz4Fbyphreew82bYrfLdqDEKsacav/NvFCVPXQZ5V9kMhaVY2b1Y7p6em6YMGCoMOosunT3ezBu++6n8aY2kNEvlDV9KDjiKV4GLMvuww+/RTWr4ekpKCjiS979rhE/L33YMyY6CbiS5fCJZfA2rUu+b755ug9tzGH40jG7IOWo4jILhHZWcFlF65fuImRM890M+BWkmKMMcHLzoa33oLrr7cEvCr8Kk2JrP+eOdMScBN+B03CVTVZVZtUcElW1aqWsZgqqF8fzj0X3nkHqvDFhTHGmCh68UVXE269wasumol4RfXf/fpFL1Zj/FLVhZkmxjIyXJvCrKxDn2uMMcYfqm6b+r59oXuN3a85NqKRiG/bBhddBI8+6p7j448h1b6rN3HCkvA4MWSI+2klKcYYE5x582DZMluQGS3VScQj+3//85+ugYEtwDTxxJLwONGhA3TrZv3CjTEmSOPGQcOGcOWVQUdSc1QlEbf6b1MTWBIeRzIy3FdteXlBR2KMMbVPXh5MmuQS8CZNgo6mZjncRNzqv01NYkl4HMnIgH374KOPgo7EGGNqnylTYNcuW5Dpl0Ml4lb/bWoaS8LjSP/+0Lix1YUbY0wQxo6Fzp3dWGz8cbBE3Oq/TU1krQbjSN26MHCgS8JVQQ5n31JjjDHVtnIlzJ7tZmFt7PVX2Z01Fy2C8eMhOdnVf1v5iakpbCY8zmRkuJ3Ali0LOhJjjKk9JkyAhAQYPjzoSGqHyBnxZ56x+m9TM1kSHmdKtq23khRjjImNwkKXhGdkWA1yLJUk4v/5j9V/m5rJkvA406YNnHiiJeHGmOgTkcEiskJEVonIbyq4f4SI5IjIIu/ys4j7iiKOT4043lFE5nnP+ZqI1I3V+4mW6dNh0yZbkBmE+vVdWYrVf5uayJLwOHTFFW5W4D//CToSY0xNISKJwLPAEKA7MExEKtoT8jVV7e1dxkQc3x1xfGjE8ceAJ1W1E7ANiLttbsaOhVat4MILg47EGFOTWBIeh379a+jTB0aMgBUrgo7GGFND9AFWqepqVd0HTAIurs4TiogA5wBTvEMTgUuqFWWMZWfDW2/B9ddDUlLQ0RhjahJLwuNQvXrw73+7bimXX26b9xhjoiINWBdxe713rKzLRWSxiEwRkbYRx+uLyAIRmSsiJYl2C2C7qhYe4jkRkZHe4xfk5ORU861Ez4svuppwK0UxxkSbJeFxql07ePVV1yXlpptcy0JjTDjt3g1vvhl0FFHxFtBBVU8EZuBmtku0V9V04BrgKRE57kieWFVHq2q6qqanpKREL+JqUHXb1PftC90rKswxxphqsCQ8jg0cCA895JLxZ54JOhpjTFm5ufDnP0PHjm5x2fLlQUdUqQ1A5Mx2G+9YKVXdqqp7vZtjgJMj7tvg/VwNfAycBGwFmolIyZ4U5Z4zzObNcxMdNgtujPGDJeFx7p573Da+d94Jn30WdDTGGIAdO+CPf4QOHeCuu1yP408+gW7dgo6sUv8DOnvdTOoCVwNTI08QkdYRN4cCy73jR4lIPe96S6AfsExVFZgJXOE95gbgv76+iygaNw4aNoSrrgo6EmNMTWRJeJxLSIAXXnDlKT/+MXz/fdARGVN7/fADPPCAS77vvRdOPdV9OJ4xA844I+joKufVbd8KTMcl15NVNVNEHhSRkm4nt4tIpoh8BdwOjPCOdwMWeMdnAn9S1ZItxe4G7hSRVbga8bGxeUfVk5cHkya5cbVJk6CjMcbURL5tWy8i9YFZQD3vdaao6gNlzrkT+BlQCOQAP1XVNSJyNvBkxKldgatV9U0RmQCcCezw7huhqov8eh/xoFkzeP11OO00uPpq9w9+Hd/+ssaYsrKz4cknXVlYbq4rPbnvPvjRj4KO7Mio6jRgWplj90dcvwe4p4LHfQaccJDnXI3rvBJXpkyBXbvgxrhrqGiMiRd+zoTvBc5R1V5Ab2CwiPQtc85CIN1b5DMFeBxAVWeW9JvFtbfKB96PeNxdEf1oa3UCXqJ3b/jnP13/8HvvDToaUxWq7m+4bNmhzzXhsGmTKwXr0AEeewwuuAAWL3Y9/OMtATcHGjcOOneG/v2DjsQYU1P5loSrk+vdTPIuWuacmaqa792ci1u0U9YVwLsR55mDuOEGuPlmePxxt9WviS9/+AOMGgWDB8OWLUFHYyqzdi3ceqtbcPn0065kYflyV75wQoXzwSaeZGXBrFluQaZI0NEYY2oqX2vCRSRRRBYB2cAMVZ1Xyek3Au9WcPxq4NUyxx7x+tQ+WbIYqILXDmXPWb/97W9wyikuIV+5MuhozOEaP94l4Rdc4Or6r7sOiouDjsqUtXq1awnaqROMHu02cFmxAiZOhC5dgo7ORMv48W69zfDhQUdijKnJfE3CVbXIKylpA/QRkZ4VnSci1wHpwBNljrfG1RlOjzh8D65G/BSgOW7RT0WvHbqes7FQr56rZbSNfOLHBx/AyJEwaJD7BuNvf4Pp0113DRMOK1a4D7bHH+82bxk5Elatgn/9C447om7YJuwKC2HCBBgyBFJTg47GGFOTxaQ7iqpux62YH1z2PhE5D7gXGBrRf7bElcAbqloQ8VybvFKXvcB44nDBj9/atYNXXoHMTJcs2EY+4bVkifuw1L272wU1KcmVFF17Ldx/P3z4YdAR1m5LlrjFzt26ub/P7be72fBnnnH/n5maZ/p0V+tvCzKNMX7zLQkXkRQRaeZdbwAMBL4uc85JwPO4BDy7gqcZRplSlJI+tSIiwCXA0uhHH/8GDYIHH3TJ+LPPBh2NqciGDZCRAcnJ8M47+9ugibgFml27wjXXuPNMbH35petwcuKJ7m9z993w3Xfw17/a7GhNN24cpKS40jBjjPGTnzPhrYGZIrIYtwnEDFV9u0zP2SeAxsC/RWSRiJRuDCEiHXC7t31S5nlfFpElwBKgJfCwj+8hrv32t3Dhha57w+efBx2NibRzp/tHfscOl+S1KbMkuXFj13YyL8/NxBYUVPw8JrrmznV/l5NPhpkz3bcRa9bAo49Cq1ZBR2f8lp0NU6e6WvC6dYOOxhhT0/nWTVpVF+O2LS57PLLn7HmVPP47IK2C4+dEKcQaLyHB1a+efLLr3vDll5ZIhEFBAVx5JSxdCtOmQa9eFZ/XrZtb/Hftte4D1RNPVHyeqb5PPoGHHnLlPy1awCOPwC9+AU2bBh2ZiaWXXnI14bZNvTEmFmzHzBquZCOfrVvdjGphYdAR1W6qcMstru509GhXNlSZa65xbQv//Gd4883YxFhbqO7fyfKss9yHoieecGUnv/2tJeC1jSqMHQt9+7o1GsYY4zdLwmuBko18Zs50u/iZ4Dz6KIwZ4/4Ohzvb9uSTkJ4OI0a4RYGmelTh7bfdDrODBrnf6d/+Bt9+C7/6lSsFMrXP/PluoyybBTfGxIol4bVEyUY+jz1mM6pBefllt5vp9de7RbOHq149mDzZLdi84grYs8e/GGuy4mK3k+XJJ8NFF8Hmze7D6TffuK4nDRoEHaEJ0tix0LAhXHVV0JEYY2oLS8JrkciNfLKygo6mdvn4Y/jJT+Dss91M+JHuwtexI7zwAixcCHfc4UuINVZREbz6qut0cvnlsGuX64CRleU+mNarcLsvU5vk5bndTn/84/1diowxxm+WhNciJRv5JCXBZZfZRj6xsny5a3fXubObia1q14WLLnKt8kaPdgtuTeUKCtxOlt27u9p6VfdtxPLl7gNRUlLQEZqwmDLFfTizUhRjTCxZEl7LRG7kc/PNtpGP3zZvdjvv1a/vOqE0a1a953v4YbeQ8Oc/dwsJTXl797oPKl26uDr6Bg3cRjtLlrhkvI5vPaFMvBo3Djp1ggEDgo7EGFObWBJeC5Vs5PPyy/CPfwQdTc2Vm+v6tOfkuIWA7dtX/znr1HFfmycnu/rwXbuq/5w1xe7dbifLTp3cB8yWLV3P54UL3e8qwUY7U4GsLJg1y82CH2mZmDHGVIf9s1RLlWzk88tfug1KTHQVFsKwYS4BnDzZLQaMltatXSKelQUjR9q3GQCrVkHPnnDbbe7Dznvvwbx5roTHEitTmfHj3Qe0G24IOhJjTG1jSXgtlZDgFvq1betmCbOzg46o5lB1iyfffhuefdaf7a/POsuVpkyaZN9mLFniygh27HB9v2fPhvPPt+TbHFphoVs3MGQIpKYGHY0xpraxJLwWO+qo/Rv5DBtmG/lEy1/+4hLjX//a1W775e67ISPDfZsxf75/rxNm8+fDmWe6D5WzZsF551nyXR0iMlhEVojIKhH5TQX3jxCRHBFZ5F1+5h3vLSKfi0imiCwWkasiHjNBRL6NeEzvWL6nykyfDhs3wo03Bh2JMaY2siS8luvdG557Dj76CH73u6CjiX+TJ8Ndd7lew48+6u9rJSS4Limpqa612tat/r5e2MycCeee6z5MzpljuxxWl4gkAs8CQ4DuwDARqei3+pqq9vYuY7xj+cBwVe0BDAaeEpHIZch3RTxmkZ/v40iMGwcpKf58W2WMMYdifQIMI0bA55/Dn/7ktmy++OKgI4pPn34Kw4dD//4wYUJsFgI2b+46f/Tr5177rbf8e92CogI27tpIQXEBhcWFpZeCogNvlx4vLn+8onOrct66DYXMX1BIg2sLSEsv5KezCin8uJCuLbqS0TmD8449j+R6yf78ImquPsAqVV0NICKTgIuBZYd6oKqujLi+UUSygRRgu0+xVlt2tlu4e/vtVW8baowx1WFJuAHcRj5ffukSuQULXE9rc/hWroShQ92iwDffdC0JY+WUU9zW9rfe6nZEveee6j1fYXEh3/zwDZk5mWRmZ5KZk8nS7KWs3LqSguKC6AR9EImSSJ2EOiQlJlEnoc4Bl6QEdyw/tw4b1tWhYUoSXbrUoSihDqJ1SJREJi+bzJiFY0hKSGJA+wFkdMpgSOchdGvZDbE6lUNJA9ZF3F4PnFrBeZeLyBnASuCXqhr5GESkD1AX+Cbi8CMicj/wIfAbVd1b9klFZCQwEqBdu3bVeR+H5aWXXAme9QY3xgRFtBa0VkhPT9cFCxYEHUborVkDP/oRpKW5mfFGjYKOKD5kZ8Npp7l2gXPnwrHHxj4GVdcDe/Jk+OADtzPnoRQVF/Ht9m9LE+2SpPvrLV+zt2h/jtSxWUd6tOpBz5SeHNf8OOol1jtkolx6+wjOSZTEQybKzz8Po0a5XulTp5bf3bCgqIDP1n3GtKxpTFs1jaXZrpl6+6btyeicQUbnDM7ucDaN6sbPf9wi8oWqpsfgda4ABqtqSZ339cCpqnprxDktgFxV3SsiNwNXqeo5Efe3Bj4GblDVuRHHNuMS89HAN6r6YGWx+D1mq7puOsnJ1h3KGBNdRzJmWxJuDvD++zB4MFx7reueYpOHlcvPh3POgcWLXY3yqRXNG8bIrl3Qpw9s2+ZaI7Zu7Y4XazFrd6wlM9vNaJck3MtzlrO7cHfp49s1bUePlB70SOlBz1Y96dGqB91adgtNwvr4424x6gUXuBKcBg0O/Zh1O9bx7qp3mZY1jQ9Wf0BeQR71EutxVoezSpPyTs07+R98NcQwCT8N+L2qnu/dvgdAVStc3eDVkP+gqk29201wCfgfVXXKQR5zFvArVb2wslj8HrPnzXOld6NHw003+fYyxphayJLwMiwJPzIPPQT33+/a691yS9DRhFdRkVsQ+eabbjv6Sy4JNh5V5cMF67nwJ5mk9c6k/+VLWb4lk2U5y8gryCs9Ly05jR6tehyQcHdP6R7aGmpVuO8++OMf3YLXF16oWg3v3sK9zF47282SZ01jxdYVAHRu3pkhnYaQ0TmDMzucSf06MawlOgwxTMLr4EpMzgU2AP8DrlHVzIhzWqvqJu/6pcDdqtpXROoC7wJvqepTZZ63tapuEvc1x5PAHlUt13klkt9j9s03u3KUTZvKf5tijDHVYUl4GZaEH5niYlff/P77ru1b375BRxQ9qkp+QT7169QnMSGxWs/1y1/CU0+5evrbb49SgIdBVdmUu2l/GUlEOcnOvTtLz2ukR3Pqsa6MpDTpbtWDZvWbVfLs4VJc7H63zz7rZiyfew4Sq/dnK7V622rezXqXaaum8dG3H7GncA8NkxpyTsdzSmvJOzTrEJ0Xq4ZYJeHea2UATwGJwDhVfUREHgQWqOpUEXkUGAoUAj8Ao1T1axG5DhgPZEY83QhVXSQiH+EWaQqwCPi5quZWFoefY3ZenvuW6LLL3AJqY4yJJkvCy7Ak/Mht2+Z2eSwocAs2U1KCjqhqioqLWPz9Ymavnc3stbOZs3YOm3M3A1C/Tn0aJjWkYVJDGiU1cj/rNjrwtvez7H2zPmrIS+MacemFDfl/t1V8Tt3EutVeDJidl12ujCQzO5Nte7aVntOyYctyZSRjH+3BC8+3YOpUt2tkPCpZNPfii/CrX7lyFL/Ko3YX7Obj7z5mWtY03sl6h2+3fwtA95TuZHRyZSv92vWjbmLs22jEMgkPCz/H7BdecLtjfvKJW1tgjDHRZEl4GZaEV83ChXD66a793fTp0ZuB9NOewj3M3zCf2Wtc0v3Zus/YtW8X4BbnDWg/gB4pPdhXtI+8fXnkF+STX5BPXkHegT/3lb9dpEVHFEuCJJRL7g+V8NevU591O9eVJt1b8reUPt9R9Y8qV0bSo1UPWjVqVf73sMf97b791n2I6tixer/XWNu7F66+2pX6PPQQ3Htv7NYnqCort64sXdw5a80s9hXto3Hdxgw8diAZnTMY0mkIaU3SYhKPJeHRdeaZboOelSttzYsxJvpCkYSLSH1gFlAP1wpxiqo+UOacO4Gf4b7azAF+qqprvPuKgCXeqWtVdah3vCMwCWgBfAFcr6r7KovFkvCqGz/ezUbec4+ryQ2b7Xu28+naT0tnuhdsXMC+IvefQ89WPRnQbgD92/VnQLsBtG3atsqvo6oUFBcw6/N8Lrw0j64n5PPc2Dy0TvmEvcIk/iDJfeSxkkWSyXWTXYLtlY+U/GzduPURzayvXu263XTq5DaziWXbxOrIy3P19R98AE8/DbfdFmw8ufty+ejbj0prydftdB35eh3dq3RxZ982famT4E/HV0vCoycrC44/3o1l1W3laYwxFQlLEi5AI1XNFZEkYA5wR0nbKu+cs4F5qpovIqOAs1T1Ku++XFVtXMHzTgb+o6qTROSfwFeq+lxlsVgSXj0jR8K//uVmJYPeyGfDzg0u4fZmupdmL0VRkhKSSE9NL026+7XrR/MGzaP62t9841oRNmniWjhGu0SnWIvZXbCbhkkNo9bT+r//dQntqFHwj39E5Sl9tX07ZGS47hXjxrmygTBRVTJzMksT8jlr51CkRTSr34zzjzufjM4ZDO40uMJvJ6rKkvDo+e1vXS/9tWtdK1ZjjIm2UCThB7yISENcEj5KVecd5JyTgGdUtZ93u1wS7iX2OcAxqlpYtqXWwVgSXj179rhdILOy4Isv3MxqLKgqK7auKE24Z6+dzXfbvwOgcd3GnN72dPq37c+A9gPok9aHhkkNfYtl61ZX3rFli0vAjz/et5eKul//Gp54Al5+2fUSD6vvv4fzz4dly2DSJLdwLux27NnBjNUzShd4lqw3SE9NL60lT09Nr9YiYEvCo6Ow0G2mddJJ8PbbUX1qY4wpFZok3Osj+wXQCXhWVe+u5NxngM2q+rB3uxC3kr4Q+JOqvikiLYG5qtrJO6ct8K6q9qzg+SJ3Xzt5zZo10X1ztUzJRj5t2rgktKEP+W5BUQELNy9kzto5pYsoS2qiWzVqdUBpSa9jevn29X9Ze/bAeee5nUQ//NDVyMeTggLXy3zhQpg/H7p3Dzqi8tauhYEDYd06943LoEFBR3TkirWYrzZ/VVpLPnf9XIq1mJYNWzK402AyOmVwUZeLaFy33Bd8lbIkPDreeQcuvBBefz0+PuAZY+JTaJLw0hcRaQa8AdymqksruP864FbgzJLtjEUkTVU3iMixwEe43rU7OMwkPJLNhEfH9OkwZAhcdx1MnFj9RU15+/KYu35uadI9d/3c0n7Wxx11HAPaDyid6e7cvHMg244XF8OwYW4nysmTXV/weLRxo5sBbNHCJeKNjywP9NXKle5Dzs6dLlGKtw85B7M1fyvvf/M+01ZN471V77Elfwvrf7n+iBd0WhIeHZdfDrNnw/r1Veszb4wxh+NIxuyYTCWq6nYRmQkMBg5IwkXkPOBeIhJw7zEbvJ+rReRj4CTgdaCZiNRR1UKgDW5TiajaW7iXS167hOObH0+Xll3o2rIrXVp0ITU5NZBEMCzOPx9+/3t44AFXGz1q1JE9fkv+FuasnVOadH+56UsKiwsRhF7H9OKnJ/2U/u36079df1KTU315D0fqnntc8v344/GbgAOkpsIrr7gZ5pKNSsLwn/LixW4GXNXtOHrSSUFHFD0tGrZg2AnDGHbCMIqKi1iSvSRmHVXMgXJyYOpU13PeEnBjTFj4loSLSApQ4CXgDYCBwGNlzjkJeB4YrKrZEcePAvJVda9XgtIPeFxV1Uvmr8B1SLkB+G+0Y9+Sv4XsvGxmr5l9wE6Djes2pkuLLnRp2YUuLfYn551bdPa1HjlM7rvPLZq74w5XnnKwbdpVlTU71jB7zezSpHv5luUA1EusR5+0Ptx1+l0MaDeA09ueTtP6TWP4Lg7Pc8+55PuWW1yf6nh37rnwhz/A734HAwbAz38ebDyff+4WYTZuDDNmQNeuwcbjp8SERHof0zvoMGqtF1/c33feGGPCws/uKCcCE3E7ryUAk1X1wTK7r30AnABs8h62VlWHisjpuOS82HvsU6o61nveY3EJeHNgIXBd5Ax6Rar61aaqsmHXBlZsWcHXW75mxdYV7rJlBWt2HFhj3r5p+3LJeZeWXUhLTqtxs+c//OA28tlHHq+/v4E9SRvZuGsjG3ZuYOOujazbuY55G+axfud6AJrWa0q/dv1KS0vSU9NDtzV4WW+/7TrBZGTAG29AndiUn/uuuNjVxX74IXz6KaQHVOTwwQeua0vr1u56+/bBxBEPrBylelShZ09IToa5cw99vjHGVEfoasKD5kd9YX5BPllbs1ixNSJB3+KS9Nx9+3dkbly3Mce3OL5ccn58i+NDO3u+r2gfm3M3lybVG3dtZMOuA6+v276RvMKd5R7bKKkRaU3S6H1Mbwa0G8CAdgPo2apntbeIj6UvvnA76XXr5nbVa9Qo6Iiia+tWV/aRmOg28jnqqNi+/n//C1deCV26wPvvwzHHxPb1440l4dUzbx707QvPP+/arRpjjJ9CVxNeEzVMakivY3rR65heBxxXVTbu2lialJck6J+v/5xJSyeh7P/Q065pO5eUlyToXv25X7PnxVpMTl5O+aR65wY25u6/npOfU+6xSQlJpCankpqcSo+UHgw6dhAbVqTy+vhUhl2Uyv3/l0ZqcirJdZPjeuZ/zRo3U5yS4mbDa1oCDm5x5uTJ7oPG8OEuKU5IiM1rv/QSjBjhZuCnTYPm0W3lbkw548ZBgwZuB1ZjjAkTS8KjTERIa5JGWpM0zul4zgH37S7YTdYPWeXKWyZ8NeGA2fNGSY3c7HnLLnRt0bW0zOX4FsfTqG75rFBV2bF3x4FJdQUz2JtyN1FYXHhgvAitGrUirUkabZq0oU9qH9KapJUm3GnJ7nqLhi1IkDKZ2hC4KRPGPAJX94GuQ6P3ewzCtm2u+8uePa5coybP0PbtC3/5i1uo9sQTcPdBm4dGzz/+Ab/4hWuX+OabrjzAGD/l5cGrr7pF1U2aBB2NMcYcyJLwGGqQ1IATjz6RE48+8YDjqsqm3E3lkvO56+fy2tLXDpg9b9ukLV1adqFFgxZsyt1UmmDnF+SXe71m9ZuVJtElM+ylybWXaB/d6GiSEpOq/J7+/nfXf3r4cNdHO1Yb+UTb3r2ud/CqVW6RYBh7aUfbrbe6lm33DCuCpAAADolJREFU3uuS8jPP9O+1Hn3U7VZ40UVuFr5+uJcEmBri9ddh1y648cagIzHGmPKsJjzkdhfsZtUPq8rVnm/bs600oU5tnFpu9rp1cuuY1Zx/951bqOnnRj5+UnUfIl56yV2uvTboiGJn50445RT3c+HC6M/+q7o2j4895n6v48dDUtU/89VKVhNedWee6Xrkr1wZjpacxpiaz2rCa5AGSQ044egTOOHoE4IO5aA6dHBbomdkuN7hEybE1z9499/vku+HH65dCTi4r+inTHGtJq+5xi2UjFYnmOJiV37yz3+6dojPPhu72nNjsrJg1iz44x/jazwyxtQe9k+iiYrBg90mPi+84LoQxIuxY13y/bOfuXKJ2uiEE1xP9Jkz3d8wGgoK4PrrXQJ+992uHtwScBNLEya4/+aGDw86EmOMqZjNhJuo+d3vXDuw22+HpUtdaUOrVuUvycnhmJmaPt3tHnn++S5JDENMQbnhBpgzx80ann46XHBB1Z9rzx646iq3Q+Gjj8JvfhO9OI2/RGQw8Dfc/g5jVPVPZe4fATzB/p2Kn1HVMd59NwD3eccfVtWJ3vGTgQlAA2AacIf6XAdZWOiS8MGDIc02KTXGhJQl4SZqEhJcWcdll7nylO3bKz6vXr2Kk/OKLikp7vxo++oruOIKt4nHv/9tdcoATz/tFtdef72rD6/KBjq7drlNjmbOdOUnt9wS/TiNP0QkEXgWt7vxeuB/IjJVVZeVOfU1Vb21zGObAw8A6YACX3iP3QY8B9wEzMMl4YOBd/18L++/72rB//53P1/FGGOqx5JwE1XNm8PHH7vre/fCli2QnV35JTMTvv/enV+Rpk3LJ+YHS9qbN3eb0FRm/Xo309usGbzzjrXKK9GggftAcvLJrqXb7NlH9gHohx/cuoAFC9w24ddd51+sxhd9gFWquhpARCYBFwNlk/CKnA/MUNUfvMfOAAaLyMdAE1Wd6x1/AbgEn5PwsWPdOHHhhX6+ijHGVI8l4cY39eq5r4IP5+tgVcjNPXTCnpXltlvfssUt/CsrIQFatqx8Zv2BB1w3kDlz7Kvqsjp1cl/jX3YZ/OpXhz+TuHkzDBoEK1a4tnAXX+xrmMYfacC6iNvrgVMrOO9yETkDWAn8UlXXHeSxad5lfQXHyxGRkcBIgHbt2lXxLUBOjiuFuv12qFu3yk9jjDG+syTchIKIm5FOTobjjjv0+UVFbub1UEn7ggXu586d+x9bp47brfHEEw/+/LXZpZfCnXfCX/8K/fu7+u7KrFkD550Hmza53+u558YmThOIt4BXVXWviNwMTATOOcRjDouqjgZGg2tRWNXnefFFVxP+059GIypjjPGPJeEmLiUmulntlBTo0ePQ5+/Z42bIsrNdyUrHjv7HGM/+9CeYO9d1jenVC7p2rfi8r7+GgQPdtxgzZsBpp8U2ThNVG4C2EbfbsH8BJgCqujXi5hjg8YjHnlXmsR97x9tU9pzRpOpKUU499fDGBWOMCZI1DTO1Qv360Latq3e2BPzQkpLgtdfc7+2KK9z232UtXAhnnOHaEX7yiSXgNcD/gM4i0lFE6gJXA1MjTxCR1hE3hwLLvevTgUEicpSIHAUMAqar6iZgp4j0FREBhgP/9esNzJ8Py5bZLLgxJj5YEm6MqVCbNvDKKy6pGTXKzTKW+PRTOPtst5hz9mwr7akJVLUQuBWXUC8HJqtqpog8KCJDvdNuF5FMEfkKuB0Y4T32B+AhXCL/P+DBkkWawC24WfNVwDf4uChz3Dj33+ShSqiMMSYMbNt6Y0ylHnzQLWYdPRpuusm1f7v0Upekz5gB1VhDZw6DbVt/ePLz3d4El14KEyf6FJgxxhyCbVtvjIma++5zM9+33ebq6n//e+je3W12dPTRQUdnjDNliutTb6Uoxph4YeUoxphKlWzClJIC994Lp5ziesFbAm7CZNw412LzjDOCjsQYYw6PzYQbYw4pJQXeegtefRXuvx8aNQo6ImP2KyqC3r3dImKRoKMxxpjDY0m4Meaw9O7tLsaETWIiPPVU0FEYY8yR8a0cRUTqi8h8EfnKW03/hwrOuVNElonIYhH5UETae8d7i8jn3uMWi8hVEY+ZICLfisgi72JpgTHGGGOMiSt+zoTvBc5R1VwRSQLmiMi7qjo34pyFQLqq5ovIKNzGD1cB+cBwVc0SkVTgCxGZrqrbvcfdpapTfIzdGGOMMcYY3/g2E65OrnczybtomXNmqmq+d3Mu3s5qqrpSVbO86xuBbCDFr1iNMcYYY4yJJV+7o4hIoogswiXRM1R1XiWn30gFmziISB+gLm6ThxKPeGUqT4pIvYO89kgRWSAiC3JycqrxLowxxhhjjIkuX5NwVS1S1d64Ge4+ItKzovNE5DogHXiizPHWwIvAT1S12Dt8D9AVOAVoDtx9kNcerarpqpqekmKT6MYYY4wxJjxi0ifcq+WeCQwue5+InAfcCwxV1b0Rx5sA7wD3RtaRq+omr9RlLzAe6ON3/MYYY4wxxkSTn91RUkSkmXe9ATAQ+LrMOScBz+MS8OyI43WBN4AXyi7A9GbHEREBLgGW+vUejDHGGGOM8YOf3VFaAxNFJBGX7E9W1bdF5EFggapOxZWfNAb+7XJq1qrqUOBK4AyghYiM8J5vhKouAl4WkRRAgEXAz318D8YYY4wxxkSdqOqhz4pzIpIDrKnCQ1sCW6IcTrSEOTYId3xhjg3CHV+YY4Nwx1fV2Nqraq1a2GJjdiDCHF+YYwOLrzrCHBtULb7DHrNrRRJeVSKyQFXTg46jImGODcIdX5hjg3DHF+bYINzxhTm2miLMv+Mwxwbhji/MsYHFVx1hjg38jy8mCzONMcYYY4wx+1kSbowxxhhjTIxZEl650UEHUIkwxwbhji/MsUG44wtzbBDu+MIcW00R5t9xmGODcMcX5tjA4quOMMcGPsdnNeHGGGOMMcbEmM2EG2OMMcYYE2OWhBtjjDHGGBNjloRXQEQGi8gKEVklIr8JOp5IIjJORLJFJHQ7hYpIWxGZKSLLRCRTRO4IOqZIIlJfROaLyFdefH8IOqayRCRRRBaKyNtBx1KWiHwnIktEZJGILAg6nkgi0kxEpojI1yKyXEROCzqmEiLSxfudlVx2isj/BR1XTWJjdtWFedy2Mbt6wjxmQ3jH7ViO2VYTXoa3w+dKYCCwHvgfMExVlwUamEdEzgBygRdUtWfQ8UQSkdZAa1X9UkSSgS+AS0L0uxOgkarmikgSMAe4Q1XnBhxaKRG5E0gHmqjqhUHHE0lEvgPSVTV0GyuIyERgtqqOEZG6QENV3R50XGV548sG4FRVrcpmNKYMG7OrJ8zjto3Z1RPmMRviY9z2e8y2mfDy+gCrVHW1qu4DJgEXBxxTKVWdBfwQdBwVUdVNqvqld30XsBxICzaq/dTJ9W4meZfQfAoVkTbABcCYoGOJJyLSFDgDGAugqvvCNpBHOBf4xhLwqLIxuxrCPG7bmF1zxdG47euYbUl4eWnAuojb6wnJgBRPRKQDcBIwL9hIDuR9dbgIyAZmqGqY4nsK+DVQHHQgB6HA+yLyhYiMDDqYCB2BHGC897XwGBFpFHRQB3E18GrQQdQwNmZHSRjHbRuzqyWsYzbEz7jt65htSbiJOhFpDLwO/J+q7gw6nkiqWqSqvYE2QB8RCcXXwyJyIZCtql8EHUsl+qvqj4AhwC+8r9nDoA7wI+A5VT0JyANCVRcM4H3dOhT4d9CxGFNWWMdtG7OrJaxjNsTBuB2LMduS8PI2AG0jbrfxjpnD4NXtvQ68rKr/CTqeg/G+9poJDA46Fk8/YKhXwzcJOEdEXgo2pAOp6gbvZzbwBq4MIAzWA+sjZsim4Ab3sBkCfKmq3wcdSA1jY3Y1xcO4bWP2kQvxmA3xMW77PmZbEl7e/4DOItLR+xR0NTA14JjigreIZiywXFX/GnQ8ZYlIiog08643wC3k+jrYqBxVvUdV26hqB9x/cx+p6nUBh1VKRBp5i7bwvjIcBISi24OqbgbWiUgX79C5QOCLyiowDCtF8YON2dUQ5nHbxuyqC/OYDXEzbvs+Ztfx88njkaoWisitwHQgERinqpkBh1VKRF4FzgJaish64AFVHRtsVKX6AdcDS7waPoDfquq0AGOK1BqY6K12TgAmq2ro2kqF1NHAG+7fa+oAr6jqe8GGdIDbgJe9JGw18JOA4zmA94/gQODmoGOpaWzMrrYwj9s2Zldd2MdsCPG4Hasx21oUGmOMMcYYE2NWjmKMMcYYY0yMWRJujDHGGGNMjFkSbowxxhhjTIxZEm6MMcYYY0yMWRJujDHGGGNMjFkSboxHRIpEZFHEJWq7d4lIBxEJTY9WY4yJdzZmm3hnfcKN2W+3tz2yMcaY8LMx28Q1mwk35hBE5DsReVxElojIfBHp5B3vICIfichiEflQRNp5x48WkTdE5Cvvcrr3VIki8i8RyRSR970d4IwxxkSRjdkmXlgSbsx+Dcp8tXlVxH07VPUE4BngKe/Y34GJqnoi8DLwtHf8aeATVe0F/Ago2b2vM/CsqvYAtgOX+/x+jDGmJrMx28Q12zHTGI+I5Kpq4wqOfweco6qrRSQJ2KyqLURkC9BaVQu845tUtaWI5ABtVHVvxHN0AGaoamfv9t1Akqo+7P87M8aYmsfGbBPvbCbcmMOjB7l+JPZGXC/C1mQYY4xfbMw2oWdJuDGH56qIn5971z8DrvauXwvM9q5/CIwCEJFEEWkaqyCNMcYANmabOGCf6ozZr4GILIq4/Z6qlrS8OkpEFuNmRoZ5x24DxovIXUAO8BPv+B3AaBG5ETd7MgrY5Hv0xhhTu9iYbeKa1YQbcwhefWG6qm4JOhZjjDGVszHbxAsrRzHGGGOMMSbGbCbcGGOMMcaYGLOZcGOMMcYYY2LMknBjjDHGGGNizJJwY4wxxhhjYsyScGOMMcYYY2LMknBjjDHGGGNi7P8DT+DVV584P14AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 864x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Display the results. \n",
    "neural_network_graph(history_dense2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "40/40 [==============================] - 0s 38us/step\n",
      "Test loss: 3.25\n",
      "Test accuracy: 65.00%\n"
     ]
    }
   ],
   "source": [
    "# Evaluate test score. \n",
    "(test_loss, test_score_dense2) = model_dense2.evaluate(X_te_standardized, y_te_encoded, batch_size = batch_size)\n",
    "\n",
    "print('Test loss: {:.2f}'.format(test_loss))\n",
    "print('Test accuracy: {:.2f}%'.format(100 * test_score_dense2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 0, 1, 1, 0, 0,\n",
       "       1, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 0, 1])"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Compute and display the predictions of the neural network. \n",
    "y_pred_dense2 = encoding_order[model_dense2.predict_classes(X_te_standardized)]\n",
    "y_pred_dense2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.65"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Security check: compute the accuracy from these predictions. \n",
    "test_score_dense2_from_pred = np.sum(y_pred_dense2 == y_te) / len(y_te)\n",
    "test_score_dense2_from_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Verify if the two accuracies are equal. \n",
    "np.round(test_score_dense2_from_pred, 4) == np.round(test_score_dense2, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4"
      ]
     },
     "execution_count": 99,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Display again the baseline. \n",
    "neural_networks_baseline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Result:** The 2-layer neural network model performs better than the baseline. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>Predictions</th>\n",
       "      <th>rest</th>\n",
       "      <th>task</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>True class</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>rest</th>\n",
       "      <td>17</td>\n",
       "      <td>7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>task</th>\n",
       "      <td>7</td>\n",
       "      <td>9</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "Predictions  rest  task\n",
       "True class             \n",
       "rest           17     7\n",
       "task            7     9"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Rename the labels. \n",
    "y_te_renamed = np.array(['rest', 'task'])[y_te]\n",
    "y_pred_dense2_renamed = np.array(['rest', 'task'])[y_pred_dense2]\n",
    "\n",
    "# Display a Scikit-learn confusion matrix. \n",
    "confusion_matrix_dense2 = scikit_learn_confusion_matrix(y_te_renamed, y_pred_dense2_renamed)\n",
    "confusion_matrix_dense2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### **3.3 Dense neural network: 2-layer, target: blocks**\n",
    "\n",
    "In the following cells, we **run and compute the predictions from a 2-layer neural network model**. Our target will be the **blocks** of the eegfmriNF run. Here, our objective is to find out if our neural networks can discriminate between the individual blocks of 20 seconds, and not just between the rest condition and the task condition. Since we have a larger number of target values, we will perform a train-test split with stratification. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0  0  0  0  0  0  0  0  0  0  1  1  1  1  1  1  1  1  1  1  2  2  2  2\n",
      "  2  2  2  2  2  2  3  3  3  3  3  3  3  3  3  3  4  4  4  4  4  4  4  4\n",
      "  4  4  5  5  5  5  5  5  5  5  5  5  6  6  6  6  6  6  6  6  6  6  7  7\n",
      "  7  7  7  7  7  7  7  7  8  8  8  8  8  8  8  8  8  8  9  9  9  9  9  9\n",
      "  9  9  9  9 10 10 10 10 10 10 10 10 10 10 11 11 11 11 11 11 11 11 11 11\n",
      " 12 12 12 12 12 12 12 12 12 12 13 13 13 13 13 13 13 13 13 13 14 14 14 14\n",
      " 14 14 14 14 14 14 15 15 15 15 15 15 15 15 15 15 16 16 16 16 16 16 16 16\n",
      " 16 16 17 17 17 17 17 17 17 17 17 17 18 18 18 18 18 18 18 18 18 18 19 19\n",
      " 19 19 19 19 19 19 19 19]\n"
     ]
    }
   ],
   "source": [
    "# Define and display the new target variable. \n",
    "y = np.repeat(range(20), 10)\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(200,)"
      ]
     },
     "execution_count": 102,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Display the shape of the target variable. \n",
    "y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "20"
      ]
     },
     "execution_count": 103,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Store the number of different target values. \n",
    "nb_target_values = np.unique(y).shape[0]\n",
    "nb_target_values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Divide the data into a train set and a test set. \n",
    "X_tr, X_te, y_tr, y_te = train_test_split(X, y, test_size = test_set_proportion, stratify = y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.05"
      ]
     },
     "execution_count": 105,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a baseline containing only the most frequent value in the train set. \n",
    "most_frequent_value = np.bincount(y_tr.astype(int)).argmax()\n",
    "neural_networks_baseline3 = np.sum(y_te.astype(int) == most_frequent_value) / y_te.shape[0]\n",
    "neural_networks_baseline3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train: (160, 320)\n",
      "Test: (40, 320)\n"
     ]
    }
   ],
   "source": [
    "# Rescale features variables. \n",
    "scaler = StandardScaler()\n",
    "X_tr_standardized = scaler.fit_transform(X_tr)\n",
    "X_te_standardized = scaler.transform(X_te)\n",
    "\n",
    "print('Train:', X_tr_standardized.shape)\n",
    "print('Test:', X_te_standardized.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 107,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Encode target variable. \n",
    "y_tr_encoded = pd.get_dummies(y_tr)\n",
    "y_te_encoded = pd.get_dummies(y_te)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0,  1,  2,  3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16,\n",
       "       17, 18, 19])"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Get and display the encoding order. \n",
    "encoding_order = np.unique(y_te)\n",
    "encoding_order"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "dense_10 (Dense)             (None, 128)               41088     \n",
      "_________________________________________________________________\n",
      "dropout_4 (Dropout)          (None, 128)               0         \n",
      "_________________________________________________________________\n",
      "dense_11 (Dense)             (None, 20)                2580      \n",
      "=================================================================\n",
      "Total params: 43,668\n",
      "Trainable params: 43,668\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "# Create model. \n",
    "model_dense3 = Sequential()\n",
    "\n",
    "# Hidden layer. \n",
    "model_dense3.add(Dense(\n",
    "    units = 128, activation = activations.relu, input_dim = X_tr_standardized.shape[1],\n",
    "    kernel_initializer = initializers.VarianceScaling(scale = 2.0, seed = 0),\n",
    "    kernel_regularizer = l2(0.01), bias_regularizer = l2(0.01)))\n",
    "model_dense3.add(Dropout(0.5, seed = 0))\n",
    "\n",
    "# Output layer. \n",
    "model_dense3.add(Dense(\n",
    "    units = nb_target_values, activation = activations.softmax,\n",
    "    kernel_initializer = initializers.VarianceScaling(scale = 1.0, seed = 0)))\n",
    "\n",
    "# Define loss function, optimizer and metrics to track during training. \n",
    "model_dense3.compile(optimizer = 'sgd', loss = 'categorical_crossentropy', metrics = ['acc'])\n",
    "\n",
    "# Print network summary. \n",
    "model_dense3.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 128 samples, validate on 32 samples\n",
      "Epoch 1/100\n",
      "128/128 [==============================] - 1s 6ms/step - loss: 6.3970 - acc: 0.0313 - val_loss: 6.1498 - val_acc: 0.1250\n",
      "Epoch 2/100\n",
      "128/128 [==============================] - 0s 87us/step - loss: 6.3689 - acc: 0.0469 - val_loss: 6.0152 - val_acc: 0.0938\n",
      "Epoch 3/100\n",
      "128/128 [==============================] - 0s 82us/step - loss: 6.1951 - acc: 0.0625 - val_loss: 5.9431 - val_acc: 0.0938\n",
      "Epoch 4/100\n",
      "128/128 [==============================] - 0s 77us/step - loss: 6.0041 - acc: 0.0703 - val_loss: 5.8617 - val_acc: 0.1250\n",
      "Epoch 5/100\n",
      "128/128 [==============================] - 0s 98us/step - loss: 5.8588 - acc: 0.1016 - val_loss: 5.8325 - val_acc: 0.0938\n",
      "Epoch 6/100\n",
      "128/128 [==============================] - 0s 99us/step - loss: 5.7090 - acc: 0.0859 - val_loss: 5.7691 - val_acc: 0.0938\n",
      "Epoch 7/100\n",
      "128/128 [==============================] - 0s 85us/step - loss: 5.8440 - acc: 0.1016 - val_loss: 5.7258 - val_acc: 0.1250\n",
      "Epoch 8/100\n",
      "128/128 [==============================] - 0s 83us/step - loss: 5.7646 - acc: 0.0781 - val_loss: 5.6903 - val_acc: 0.0938\n",
      "Epoch 9/100\n",
      "128/128 [==============================] - 0s 84us/step - loss: 5.6776 - acc: 0.0859 - val_loss: 5.6560 - val_acc: 0.0938\n",
      "Epoch 10/100\n",
      "128/128 [==============================] - 0s 86us/step - loss: 5.4803 - acc: 0.1094 - val_loss: 5.6005 - val_acc: 0.1250\n",
      "Epoch 11/100\n",
      "128/128 [==============================] - 0s 81us/step - loss: 5.7190 - acc: 0.1016 - val_loss: 5.5682 - val_acc: 0.1562\n",
      "Epoch 12/100\n",
      "128/128 [==============================] - 0s 89us/step - loss: 5.5157 - acc: 0.1328 - val_loss: 5.5378 - val_acc: 0.1562\n",
      "Epoch 13/100\n",
      "128/128 [==============================] - 0s 85us/step - loss: 5.3681 - acc: 0.1719 - val_loss: 5.5232 - val_acc: 0.1562\n",
      "Epoch 14/100\n",
      "128/128 [==============================] - 0s 86us/step - loss: 5.4466 - acc: 0.1562 - val_loss: 5.4907 - val_acc: 0.1562\n",
      "Epoch 15/100\n",
      "128/128 [==============================] - 0s 86us/step - loss: 5.3202 - acc: 0.1641 - val_loss: 5.4827 - val_acc: 0.1562\n",
      "Epoch 16/100\n",
      "128/128 [==============================] - 0s 79us/step - loss: 5.5720 - acc: 0.1016 - val_loss: 5.4743 - val_acc: 0.1562\n",
      "Epoch 17/100\n",
      "128/128 [==============================] - 0s 72us/step - loss: 5.3571 - acc: 0.1406 - val_loss: 5.4814 - val_acc: 0.1562\n",
      "Epoch 18/100\n",
      "128/128 [==============================] - 0s 83us/step - loss: 5.4251 - acc: 0.1563 - val_loss: 5.4812 - val_acc: 0.1250\n",
      "Epoch 19/100\n",
      "128/128 [==============================] - 0s 86us/step - loss: 5.3141 - acc: 0.1094 - val_loss: 5.4837 - val_acc: 0.1250\n",
      "Epoch 20/100\n",
      "128/128 [==============================] - 0s 84us/step - loss: 5.3535 - acc: 0.1406 - val_loss: 5.4792 - val_acc: 0.1250\n",
      "Epoch 21/100\n",
      "128/128 [==============================] - 0s 86us/step - loss: 5.2722 - acc: 0.1562 - val_loss: 5.4701 - val_acc: 0.1250\n",
      "Epoch 22/100\n",
      "128/128 [==============================] - 0s 88us/step - loss: 5.2557 - acc: 0.1562 - val_loss: 5.4739 - val_acc: 0.0938\n",
      "Epoch 23/100\n",
      "128/128 [==============================] - 0s 75us/step - loss: 5.1722 - acc: 0.2266 - val_loss: 5.4751 - val_acc: 0.1250\n",
      "Epoch 24/100\n",
      "128/128 [==============================] - 0s 80us/step - loss: 5.3524 - acc: 0.1562 - val_loss: 5.4831 - val_acc: 0.0938\n",
      "Epoch 25/100\n",
      "128/128 [==============================] - 0s 90us/step - loss: 5.1895 - acc: 0.1562 - val_loss: 5.4813 - val_acc: 0.0938\n",
      "Epoch 26/100\n",
      "128/128 [==============================] - 0s 74us/step - loss: 5.2059 - acc: 0.1562 - val_loss: 5.4682 - val_acc: 0.1250\n",
      "Epoch 27/100\n",
      "128/128 [==============================] - 0s 73us/step - loss: 5.2278 - acc: 0.1719 - val_loss: 5.4718 - val_acc: 0.1250\n",
      "Epoch 28/100\n",
      "128/128 [==============================] - 0s 85us/step - loss: 5.1234 - acc: 0.1953 - val_loss: 5.4577 - val_acc: 0.1250\n",
      "Epoch 29/100\n",
      "128/128 [==============================] - 0s 78us/step - loss: 5.1387 - acc: 0.1953 - val_loss: 5.4670 - val_acc: 0.0938\n",
      "Epoch 30/100\n",
      "128/128 [==============================] - 0s 74us/step - loss: 5.1768 - acc: 0.1719 - val_loss: 5.4688 - val_acc: 0.1250\n",
      "Epoch 31/100\n",
      "128/128 [==============================] - 0s 73us/step - loss: 5.1314 - acc: 0.1875 - val_loss: 5.4641 - val_acc: 0.0938\n",
      "Epoch 32/100\n",
      "128/128 [==============================] - 0s 72us/step - loss: 5.1131 - acc: 0.1641 - val_loss: 5.4507 - val_acc: 0.1562\n",
      "Epoch 33/100\n",
      "128/128 [==============================] - 0s 88us/step - loss: 5.0539 - acc: 0.2266 - val_loss: 5.4522 - val_acc: 0.0938\n",
      "Epoch 34/100\n",
      "128/128 [==============================] - 0s 82us/step - loss: 5.0954 - acc: 0.2109 - val_loss: 5.4467 - val_acc: 0.1562\n",
      "Epoch 35/100\n",
      "128/128 [==============================] - 0s 82us/step - loss: 5.0262 - acc: 0.1875 - val_loss: 5.4523 - val_acc: 0.0938\n",
      "Epoch 36/100\n",
      "128/128 [==============================] - 0s 84us/step - loss: 5.1876 - acc: 0.1562 - val_loss: 5.4393 - val_acc: 0.1250\n",
      "Epoch 37/100\n",
      "128/128 [==============================] - 0s 76us/step - loss: 5.0030 - acc: 0.2031 - val_loss: 5.4280 - val_acc: 0.0938\n",
      "Epoch 38/100\n",
      "128/128 [==============================] - 0s 75us/step - loss: 5.0156 - acc: 0.1953 - val_loss: 5.4292 - val_acc: 0.0625\n",
      "Epoch 39/100\n",
      "128/128 [==============================] - 0s 93us/step - loss: 5.2569 - acc: 0.1797 - val_loss: 5.4269 - val_acc: 0.0625\n",
      "Epoch 40/100\n",
      "128/128 [==============================] - 0s 89us/step - loss: 5.0797 - acc: 0.2031 - val_loss: 5.4196 - val_acc: 0.0938\n",
      "Epoch 41/100\n",
      "128/128 [==============================] - 0s 78us/step - loss: 5.0588 - acc: 0.1875 - val_loss: 5.4219 - val_acc: 0.0625\n",
      "Epoch 42/100\n",
      "128/128 [==============================] - 0s 76us/step - loss: 4.9644 - acc: 0.2031 - val_loss: 5.4235 - val_acc: 0.0938\n",
      "Epoch 43/100\n",
      "128/128 [==============================] - 0s 81us/step - loss: 5.1607 - acc: 0.1562 - val_loss: 5.4301 - val_acc: 0.0938\n",
      "Epoch 44/100\n",
      "128/128 [==============================] - 0s 76us/step - loss: 5.1112 - acc: 0.1562 - val_loss: 5.4152 - val_acc: 0.1250\n",
      "Epoch 45/100\n",
      "128/128 [==============================] - 0s 79us/step - loss: 5.0330 - acc: 0.1641 - val_loss: 5.4178 - val_acc: 0.0938\n",
      "Epoch 46/100\n",
      "128/128 [==============================] - 0s 84us/step - loss: 5.0445 - acc: 0.2031 - val_loss: 5.4237 - val_acc: 0.0625\n",
      "Epoch 47/100\n",
      "128/128 [==============================] - 0s 76us/step - loss: 5.0893 - acc: 0.2109 - val_loss: 5.3948 - val_acc: 0.1250\n",
      "Epoch 48/100\n",
      "128/128 [==============================] - 0s 81us/step - loss: 4.9791 - acc: 0.2734 - val_loss: 5.4113 - val_acc: 0.0625\n",
      "Epoch 49/100\n",
      "128/128 [==============================] - 0s 87us/step - loss: 5.0870 - acc: 0.1641 - val_loss: 5.4027 - val_acc: 0.0625\n",
      "Epoch 50/100\n",
      "128/128 [==============================] - 0s 84us/step - loss: 4.9802 - acc: 0.1797 - val_loss: 5.4227 - val_acc: 0.0625\n",
      "Epoch 51/100\n",
      "128/128 [==============================] - 0s 75us/step - loss: 4.9183 - acc: 0.2266 - val_loss: 5.4185 - val_acc: 0.0625\n",
      "Epoch 52/100\n",
      "128/128 [==============================] - 0s 86us/step - loss: 5.0404 - acc: 0.1797 - val_loss: 5.4184 - val_acc: 0.0625\n",
      "Epoch 53/100\n",
      "128/128 [==============================] - 0s 81us/step - loss: 5.0118 - acc: 0.2188 - val_loss: 5.4037 - val_acc: 0.0938\n"
     ]
    }
   ],
   "source": [
    "# End training when accuracy stops improving. \n",
    "early_stopping = keras.callbacks.EarlyStopping(monitor = 'val_loss', patience = 6)\n",
    "\n",
    "# Fit model. \n",
    "history_dense3 = model_dense3.fit(\n",
    "    x = X_tr_standardized, y = y_tr_encoded,\n",
    "    validation_split = validation_split, batch_size = batch_size, epochs = 100,\n",
    "    shuffle = True, callbacks = [early_stopping]\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Display the results. \n",
    "neural_network_graph(history_dense3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "40/40 [==============================] - 0s 41us/step\n",
      "Test loss: 5.39\n",
      "Test accuracy: 12.50%\n"
     ]
    }
   ],
   "source": [
    "# Evaluate test score. \n",
    "(test_loss, test_score_dense3) = model_dense3.evaluate(X_te_standardized, y_te_encoded, batch_size = batch_size)\n",
    "\n",
    "print('Test loss: {:.2f}'.format(test_loss))\n",
    "print('Test accuracy: {:.2f}%'.format(100 * test_score_dense3))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0, 11,  0,  5, 12,  2, 16,  2, 18,  0, 12, 11, 14, 18, 12, 16, 18,\n",
       "       12,  0,  7,  3,  0, 10, 18,  2, 15,  0, 18, 11,  7,  2,  0, 16,  3,\n",
       "       12,  2,  5, 12,  5,  7])"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Compute and display the predictions of the neural network. \n",
    "y_pred_dense3 = encoding_order[model_dense3.predict_classes(X_te_standardized)]\n",
    "y_pred_dense3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.125"
      ]
     },
     "execution_count": 114,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Security check: compute the accuracy from these predictions. \n",
    "test_score_dense3_from_pred = np.sum(y_pred_dense3 == y_te) / len(y_te)\n",
    "test_score_dense3_from_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 115,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 115,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Verify if the two accuracies are equal. \n",
    "np.round(test_score_dense3_from_pred, 4) == np.round(test_score_dense3, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.05"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Display again the baseline. \n",
    "neural_networks_baseline3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Result:** The 2-layer neural network model performs better than the baseline. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### **3.4 Dense neural network: 2-layer, target: block positions**\n",
    "\n",
    "In the following cells, we **run and compute the predictions from a 2-layer neural network model**. Our target will be the **block positions** of the eegfmriNF run. Here, our objective is to find out if our neural networks can discriminate not only between the rest and task blocks, but also between the beginning and the end of these blocks. Again, we will perform a train-test split with stratification. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 117,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 0 0 0 0 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 0 0 0 0 0 1 1 1 1 1 2 2 2 2 2 3 3\n",
      " 3 3 3 0 0 0 0 0 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 0 0 0 0 0 1 1 1 1 1 2 2 2 2\n",
      " 2 3 3 3 3 3 0 0 0 0 0 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 0 0 0 0 0 1 1 1 1 1 2\n",
      " 2 2 2 2 3 3 3 3 3 0 0 0 0 0 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 0 0 0 0 0 1 1 1\n",
      " 1 1 2 2 2 2 2 3 3 3 3 3 0 0 0 0 0 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 0 0 0 0 0\n",
      " 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3]\n"
     ]
    }
   ],
   "source": [
    "# Define and display the new target variable. \n",
    "y = np.tile(np.repeat([0, 1, 2, 3], 5), 10)\n",
    "print(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(200,)"
      ]
     },
     "execution_count": 118,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Display the shape of the target variable. \n",
    "y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 119,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Store the number of different target values. \n",
    "nb_target_values = np.unique(y).shape[0]\n",
    "nb_target_values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Divide the data into a train set and a test set. \n",
    "X_tr, X_te, y_tr, y_te = train_test_split(X, y, test_size = test_set_proportion, stratify = y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.25"
      ]
     },
     "execution_count": 121,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a baseline containing only the most frequent value in the train set. \n",
    "most_frequent_value = np.bincount(y_tr.astype(int)).argmax()\n",
    "neural_networks_baseline4 = np.sum(y_te.astype(int) == most_frequent_value) / y_te.shape[0]\n",
    "neural_networks_baseline4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train: (160, 320)\n",
      "Test: (40, 320)\n"
     ]
    }
   ],
   "source": [
    "# Rescale features variables. \n",
    "scaler = StandardScaler()\n",
    "X_tr_standardized = scaler.fit_transform(X_tr)\n",
    "X_te_standardized = scaler.transform(X_te)\n",
    "\n",
    "print('Train:', X_tr_standardized.shape)\n",
    "print('Test:', X_te_standardized.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Encode target variable. \n",
    "y_tr_encoded = pd.get_dummies(y_tr)\n",
    "y_te_encoded = pd.get_dummies(y_te)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 124,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3])"
      ]
     },
     "execution_count": 124,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Get and display the encoding order. \n",
    "encoding_order = np.unique(y_te)\n",
    "encoding_order"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "_________________________________________________________________\n",
      "Layer (type)                 Output Shape              Param #   \n",
      "=================================================================\n",
      "dense_12 (Dense)             (None, 128)               41088     \n",
      "_________________________________________________________________\n",
      "dropout_5 (Dropout)          (None, 128)               0         \n",
      "_________________________________________________________________\n",
      "dense_13 (Dense)             (None, 4)                 516       \n",
      "=================================================================\n",
      "Total params: 41,604\n",
      "Trainable params: 41,604\n",
      "Non-trainable params: 0\n",
      "_________________________________________________________________\n"
     ]
    }
   ],
   "source": [
    "# Create model. \n",
    "model_dense4 = Sequential()\n",
    "\n",
    "# Hidden layer. \n",
    "model_dense4.add(Dense(\n",
    "    units = 128, activation = activations.relu, input_dim = X_tr_standardized.shape[1],\n",
    "    kernel_initializer = initializers.VarianceScaling(scale = 2.0, seed = 0),\n",
    "    kernel_regularizer = l2(0.01), bias_regularizer = l2(0.01)))\n",
    "model_dense4.add(Dropout(0.5, seed = 0))\n",
    "\n",
    "# Output layer. \n",
    "model_dense4.add(Dense(\n",
    "    units = nb_target_values, activation = activations.softmax,\n",
    "    kernel_initializer = initializers.VarianceScaling(scale = 1.0, seed = 0)))\n",
    "\n",
    "# Define loss function, optimizer and metrics to track during training. \n",
    "model_dense4.compile(optimizer = 'sgd', loss = 'categorical_crossentropy', metrics = ['acc'])\n",
    "\n",
    "# Print network summary. \n",
    "model_dense4.summary()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 128 samples, validate on 32 samples\n",
      "Epoch 1/100\n",
      "128/128 [==============================] - 1s 6ms/step - loss: 4.7653 - acc: 0.2188 - val_loss: 4.9594 - val_acc: 0.2500\n",
      "Epoch 2/100\n",
      "128/128 [==============================] - 0s 90us/step - loss: 4.4623 - acc: 0.2187 - val_loss: 4.8082 - val_acc: 0.2812\n",
      "Epoch 3/100\n",
      "128/128 [==============================] - 0s 88us/step - loss: 4.2230 - acc: 0.2578 - val_loss: 4.6794 - val_acc: 0.3438\n",
      "Epoch 4/100\n",
      "128/128 [==============================] - 0s 93us/step - loss: 4.3995 - acc: 0.2187 - val_loss: 4.6035 - val_acc: 0.2812\n",
      "Epoch 5/100\n",
      "128/128 [==============================] - 0s 95us/step - loss: 4.1596 - acc: 0.3047 - val_loss: 4.4972 - val_acc: 0.2812\n",
      "Epoch 6/100\n",
      "128/128 [==============================] - 0s 70us/step - loss: 4.1736 - acc: 0.2422 - val_loss: 4.3983 - val_acc: 0.2812\n",
      "Epoch 7/100\n",
      "128/128 [==============================] - 0s 67us/step - loss: 4.0744 - acc: 0.3281 - val_loss: 4.3165 - val_acc: 0.2500\n",
      "Epoch 8/100\n",
      "128/128 [==============================] - 0s 74us/step - loss: 4.0145 - acc: 0.3516 - val_loss: 4.2137 - val_acc: 0.2188\n",
      "Epoch 9/100\n",
      "128/128 [==============================] - 0s 74us/step - loss: 4.0370 - acc: 0.3125 - val_loss: 4.1243 - val_acc: 0.2500\n",
      "Epoch 10/100\n",
      "128/128 [==============================] - 0s 73us/step - loss: 4.1257 - acc: 0.3125 - val_loss: 4.1210 - val_acc: 0.2500\n",
      "Epoch 11/100\n",
      "128/128 [==============================] - 0s 65us/step - loss: 4.0169 - acc: 0.3828 - val_loss: 4.0793 - val_acc: 0.2500\n",
      "Epoch 12/100\n",
      "128/128 [==============================] - 0s 74us/step - loss: 3.9042 - acc: 0.3516 - val_loss: 4.0608 - val_acc: 0.2500\n",
      "Epoch 13/100\n",
      "128/128 [==============================] - 0s 66us/step - loss: 3.9743 - acc: 0.3125 - val_loss: 4.0123 - val_acc: 0.2812\n",
      "Epoch 14/100\n",
      "128/128 [==============================] - 0s 76us/step - loss: 4.0212 - acc: 0.3516 - val_loss: 3.9969 - val_acc: 0.2500\n",
      "Epoch 15/100\n",
      "128/128 [==============================] - 0s 71us/step - loss: 3.8825 - acc: 0.3750 - val_loss: 3.9771 - val_acc: 0.2812\n",
      "Epoch 16/100\n",
      "128/128 [==============================] - 0s 75us/step - loss: 3.9844 - acc: 0.4062 - val_loss: 3.9590 - val_acc: 0.2812\n",
      "Epoch 17/100\n",
      "128/128 [==============================] - 0s 68us/step - loss: 3.8990 - acc: 0.3516 - val_loss: 3.9377 - val_acc: 0.2500\n",
      "Epoch 18/100\n",
      "128/128 [==============================] - 0s 66us/step - loss: 3.9040 - acc: 0.3359 - val_loss: 3.9239 - val_acc: 0.2812\n",
      "Epoch 19/100\n",
      "128/128 [==============================] - 0s 72us/step - loss: 3.8541 - acc: 0.3516 - val_loss: 3.9234 - val_acc: 0.2812\n",
      "Epoch 20/100\n",
      "128/128 [==============================] - 0s 65us/step - loss: 3.9757 - acc: 0.3516 - val_loss: 3.9113 - val_acc: 0.3438\n",
      "Epoch 21/100\n",
      "128/128 [==============================] - 0s 68us/step - loss: 3.8485 - acc: 0.3828 - val_loss: 3.9003 - val_acc: 0.3438\n",
      "Epoch 22/100\n",
      "128/128 [==============================] - 0s 67us/step - loss: 3.9582 - acc: 0.3437 - val_loss: 3.8911 - val_acc: 0.3438\n",
      "Epoch 23/100\n",
      "128/128 [==============================] - 0s 70us/step - loss: 3.8660 - acc: 0.3672 - val_loss: 3.8848 - val_acc: 0.3438\n",
      "Epoch 24/100\n",
      "128/128 [==============================] - 0s 68us/step - loss: 3.8721 - acc: 0.3984 - val_loss: 3.8801 - val_acc: 0.3438\n",
      "Epoch 25/100\n",
      "128/128 [==============================] - 0s 66us/step - loss: 3.8327 - acc: 0.3594 - val_loss: 3.8802 - val_acc: 0.3750\n",
      "Epoch 26/100\n",
      "128/128 [==============================] - 0s 69us/step - loss: 3.8641 - acc: 0.3828 - val_loss: 3.8766 - val_acc: 0.3750\n",
      "Epoch 27/100\n",
      "128/128 [==============================] - 0s 66us/step - loss: 3.7958 - acc: 0.4453 - val_loss: 3.8657 - val_acc: 0.3438\n",
      "Epoch 28/100\n",
      "128/128 [==============================] - 0s 67us/step - loss: 3.8071 - acc: 0.4062 - val_loss: 3.8773 - val_acc: 0.3750\n",
      "Epoch 29/100\n",
      "128/128 [==============================] - 0s 69us/step - loss: 3.7963 - acc: 0.4141 - val_loss: 3.8774 - val_acc: 0.3750\n",
      "Epoch 30/100\n",
      "128/128 [==============================] - 0s 72us/step - loss: 3.7870 - acc: 0.4062 - val_loss: 3.8680 - val_acc: 0.3750\n",
      "Epoch 31/100\n",
      "128/128 [==============================] - 0s 74us/step - loss: 3.7831 - acc: 0.3750 - val_loss: 3.8815 - val_acc: 0.3438\n",
      "Epoch 32/100\n",
      "128/128 [==============================] - 0s 72us/step - loss: 3.8114 - acc: 0.4141 - val_loss: 3.8748 - val_acc: 0.3438\n",
      "Epoch 33/100\n",
      "128/128 [==============================] - 0s 79us/step - loss: 3.8350 - acc: 0.4297 - val_loss: 3.8688 - val_acc: 0.3750\n"
     ]
    }
   ],
   "source": [
    "# End training when accuracy stops improving. \n",
    "early_stopping = keras.callbacks.EarlyStopping(monitor = 'val_loss', patience = 6)\n",
    "\n",
    "# Fit model. \n",
    "history_dense4 = model_dense4.fit(\n",
    "    x = X_tr_standardized, y = y_tr_encoded,\n",
    "    validation_split = validation_split, batch_size = batch_size, epochs = 100,\n",
    "    shuffle = True, callbacks = [early_stopping]\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Display the results. \n",
    "neural_network_graph(history_dense4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "40/40 [==============================] - 0s 41us/step\n",
      "Test loss: 3.82\n",
      "Test accuracy: 32.50%\n"
     ]
    }
   ],
   "source": [
    "# Evaluate test score. \n",
    "(test_loss, test_score_dense4) = model_dense4.evaluate(X_te_standardized, y_te_encoded, batch_size = batch_size)\n",
    "\n",
    "print('Test loss: {:.2f}'.format(test_loss))\n",
    "print('Test accuracy: {:.2f}%'.format(100 * test_score_dense4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 3, 1, 3, 0, 3, 0, 0, 0, 0, 3, 0, 2, 3, 0, 0, 1, 3, 0, 3, 2,\n",
       "       0, 0, 0, 3, 3, 3, 3, 3, 2, 2, 1, 3, 2, 0, 1, 3, 0, 2])"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Compute and display the predictions of the neural network. \n",
    "y_pred_dense4 = encoding_order[model_dense4.predict_classes(X_te_standardized)]\n",
    "y_pred_dense4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.325"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Security check: compute the accuracy from these predictions. \n",
    "test_score_dense4_from_pred = np.sum(y_pred_dense4 == y_te) / len(y_te)\n",
    "test_score_dense4_from_pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 131,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 131,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Verify if the two accuracies are equal. \n",
    "np.round(test_score_dense4_from_pred, 4) == np.round(test_score_dense4, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.25"
      ]
     },
     "execution_count": 132,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Display again the baseline. \n",
    "neural_networks_baseline4"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Result:** The 2-layer neural network model performs better than the baseline. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Save the results into a .npz file. \n",
    "np.savez(results_path + 'neural_networks_with_EEG_predictors_single_subject.npz', \n",
    "         test_score_dense1 = test_score_dense1, \n",
    "         test_score_dense2 = test_score_dense2, \n",
    "         test_score_dense3 = test_score_dense3, \n",
    "         test_score_dense4 = test_score_dense4, \n",
    "         y_pred_dense1 = y_pred_dense1, \n",
    "         y_pred_dense2 = y_pred_dense2, \n",
    "         y_pred_dense3 = y_pred_dense3,\n",
    "         y_pred_dense4 = y_pred_dense4,\n",
    "         neural_networks_baseline1 = neural_networks_baseline,\n",
    "         neural_networks_baseline2 = neural_networks_baseline,\n",
    "         neural_networks_baseline3 = neural_networks_baseline3,\n",
    "         neural_networks_baseline4 = neural_networks_baseline4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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