8. RNN and LSTM.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Recurrent Neural networks\n",
    "====="
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### RNN  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"imgs/rnn.png\" width=\"20%\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A recurrent neural network (RNN) is a class of artificial neural network where connections between units form a directed cycle. This creates an internal state of the network which allows it to exhibit dynamic temporal behavior."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "```python\n",
    "keras.layers.recurrent.SimpleRNN(units, activation='tanh', use_bias=True, \n",
    "                                 kernel_initializer='glorot_uniform', \n",
    "                                 recurrent_initializer='orthogonal', \n",
    "                                 bias_initializer='zeros', \n",
    "                                 kernel_regularizer=None, \n",
    "                                 recurrent_regularizer=None, \n",
    "                                 bias_regularizer=None, \n",
    "                                 activity_regularizer=None, \n",
    "                                 kernel_constraint=None, recurrent_constraint=None, \n",
    "                                 bias_constraint=None, dropout=0.0, recurrent_dropout=0.0)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Arguments:\n",
    "\n",
    "<ul>\n",
    "<li><strong>units</strong>: Positive integer, dimensionality of the output space.</li>\n",
    "<li><strong>activation</strong>: Activation function to use\n",
    "    (see <a href=\"http://keras.io/activations/\">activations</a>).\n",
    "    If you pass None, no activation is applied\n",
    "    (ie. \"linear\" activation: <code>a(x) = x</code>).</li>\n",
    "<li><strong>use_bias</strong>: Boolean, whether the layer uses a bias vector.</li>\n",
    "<li><strong>kernel_initializer</strong>: Initializer for the <code>kernel</code> weights matrix,\n",
    "    used for the linear transformation of the inputs.\n",
    "    (see <a href=\"https://keras.io/initializers/\">initializers</a>).</li>\n",
    "<li><strong>recurrent_initializer</strong>: Initializer for the <code>recurrent_kernel</code>\n",
    "    weights matrix,\n",
    "    used for the linear transformation of the recurrent state.\n",
    "    (see <a href=\"https://keras.io/initializers/\">initializers</a>).</li>\n",
    "<li><strong>bias_initializer</strong>: Initializer for the bias vector\n",
    "    (see <a href=\"https://keras.io/initializers/\">initializers</a>).</li>\n",
    "<li><strong>kernel_regularizer</strong>: Regularizer function applied to\n",
    "    the <code>kernel</code> weights matrix\n",
    "    (see <a href=\"https://keras.io/regularizers/\">regularizer</a>).</li>\n",
    "<li><strong>recurrent_regularizer</strong>: Regularizer function applied to\n",
    "    the <code>recurrent_kernel</code> weights matrix\n",
    "    (see <a href=\"https://keras.io/regularizers/\">regularizer</a>).</li>\n",
    "<li><strong>bias_regularizer</strong>: Regularizer function applied to the bias vector\n",
    "    (see <a href=\"https://keras.io/regularizers/\">regularizer</a>).</li>\n",
    "<li><strong>activity_regularizer</strong>: Regularizer function applied to\n",
    "    the output of the layer (its \"activation\").\n",
    "    (see <a href=\"https://keras.io/regularizers/\">regularizer</a>).</li>\n",
    "<li><strong>kernel_constraint</strong>: Constraint function applied to\n",
    "    the <code>kernel</code> weights matrix\n",
    "    (see <a href=\"https://keras.io/constraints/\">constraints</a>).</li>\n",
    "<li><strong>recurrent_constraint</strong>: Constraint function applied to\n",
    "    the <code>recurrent_kernel</code> weights matrix\n",
    "    (see <a href=\"https://keras.io/constraints/\">constraints</a>).</li>\n",
    "<li><strong>bias_constraint</strong>: Constraint function applied to the bias vector\n",
    "    (see <a href=\"https://keras.io/constraints/\">constraints</a>).</li>\n",
    "<li><strong>dropout</strong>: Float between 0 and 1.\n",
    "    Fraction of the units to drop for\n",
    "    the linear transformation of the inputs.</li>\n",
    "<li><strong>recurrent_dropout</strong>: Float between 0 and 1.\n",
    "    Fraction of the units to drop for\n",
    "    the linear transformation of the recurrent state.</li>\n",
    "</ul>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Backprop Through time  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Contrary to feed-forward neural networks, the RNN is characterized by the ability of encoding longer past information, thus very suitable for sequential models. The BPTT extends the ordinary BP algorithm to suit the recurrent neural\n",
    "architecture."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "scrolled": true
   },
   "source": [
    "<img src=\"imgs/rnn2.png\" width=\"45%\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Reference**: [Backpropagation through Time](http://ir.hit.edu.cn/~jguo/docs/notes/bptt.pdf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import theano\n",
    "import theano.tensor as T\n",
    "import keras \n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from sklearn.preprocessing import LabelEncoder\n",
    "from sklearn.preprocessing import StandardScaler\n",
    "from sklearn.model_selection import train_test_split\n",
    "# -- Keras Import\n",
    "from keras.models import Sequential\n",
    "from keras.layers import Dense, Activation\n",
    "from keras.preprocessing import image\n",
    "\n",
    "from keras.datasets import imdb\n",
    "from keras.datasets import mnist\n",
    "\n",
    "from keras.models import Sequential\n",
    "from keras.layers import Dense, Dropout, Activation, Flatten\n",
    "from keras.layers import Conv2D, MaxPooling2D\n",
    "\n",
    "from keras.utils import np_utils\n",
    "from keras.preprocessing import sequence\n",
    "from keras.layers.embeddings import Embedding\n",
    "from keras.layers.recurrent import LSTM, GRU, SimpleRNN\n",
    "\n",
    "from keras.layers import Activation, TimeDistributed, RepeatVector\n",
    "from keras.callbacks import EarlyStopping, ModelCheckpoint"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## IMDB sentiment classification task"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is a dataset for binary sentiment classification containing substantially more data than previous benchmark datasets. \n",
    "\n",
    "IMDB provided a set of 25,000 highly polar movie reviews for training, and 25,000 for testing. \n",
    "\n",
    "There is additional unlabeled data for use as well. Raw text and already processed bag of words formats are provided. \n",
    "\n",
    "http://ai.stanford.edu/~amaas/data/sentiment/"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Data Preparation - IMDB"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Loading data...\n",
      "Downloading data from https://s3.amazonaws.com/text-datasets/imdb.npz\n",
      "25000 train sequences\n",
      "25000 test sequences\n",
      "Example:\n",
      "[ [1, 14, 22, 16, 43, 530, 973, 1622, 1385, 65, 458, 4468, 66, 3941, 4, 173, 36, 256, 5, 25, 100, 43, 838, 112, 50, 670, 2, 9, 35, 480, 284, 5, 150, 4, 172, 112, 167, 2, 336, 385, 39, 4, 172, 4536, 1111, 17, 546, 38, 13, 447, 4, 192, 50, 16, 6, 147, 2025, 19, 14, 22, 4, 1920, 4613, 469, 4, 22, 71, 87, 12, 16, 43, 530, 38, 76, 15, 13, 1247, 4, 22, 17, 515, 17, 12, 16, 626, 18, 19193, 5, 62, 386, 12, 8, 316, 8, 106, 5, 4, 2223, 5244, 16, 480, 66, 3785, 33, 4, 130, 12, 16, 38, 619, 5, 25, 124, 51, 36, 135, 48, 25, 1415, 33, 6, 22, 12, 215, 28, 77, 52, 5, 14, 407, 16, 82, 10311, 8, 4, 107, 117, 5952, 15, 256, 4, 2, 7, 3766, 5, 723, 36, 71, 43, 530, 476, 26, 400, 317, 46, 7, 4, 12118, 1029, 13, 104, 88, 4, 381, 15, 297, 98, 32, 2071, 56, 26, 141, 6, 194, 7486, 18, 4, 226, 22, 21, 134, 476, 26, 480, 5, 144, 30, 5535, 18, 51, 36, 28, 224, 92, 25, 104, 4, 226, 65, 16, 38, 1334, 88, 12, 16, 283, 5, 16, 4472, 113, 103, 32, 15, 16, 5345, 19, 178, 32]]\n",
      "Pad sequences (samples x time)\n",
      "X_train shape: (25000, 100)\n",
      "X_test shape: (25000, 100)\n"
     ]
    }
   ],
   "source": [
    "max_features = 20000\n",
    "maxlen = 100  # cut texts after this number of words (among top max_features most common words)\n",
    "batch_size = 32\n",
    "\n",
    "print(\"Loading data...\")\n",
    "(X_train, y_train), (X_test, y_test) = imdb.load_data(num_words=max_features)\n",
    "print(len(X_train), 'train sequences')\n",
    "print(len(X_test), 'test sequences')\n",
    "\n",
    "print('Example:')\n",
    "print(X_train[:1])\n",
    "\n",
    "print(\"Pad sequences (samples x time)\")\n",
    "X_train = sequence.pad_sequences(X_train, maxlen=maxlen)\n",
    "X_test = sequence.pad_sequences(X_test, maxlen=maxlen)\n",
    "print('X_train shape:', X_train.shape)\n",
    "print('X_test shape:', X_test.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Model building "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Build model...\n",
      "Train...\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/valerio/anaconda3/envs/deep-learning-pydatait-tutorial/lib/python3.5/site-packages/keras/backend/tensorflow_backend.py:2094: UserWarning: Expected no kwargs, you passed 1\n",
      "kwargs passed to function are ignored with Tensorflow backend\n",
      "  warnings.warn('\\n'.join(msg))\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 25000 samples, validate on 25000 samples\n",
      "Epoch 1/1\n",
      "25000/25000 [==============================] - 104s - loss: 0.7329 - val_loss: 0.6832\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<keras.callbacks.History at 0x138767780>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "print('Build model...')\n",
    "model = Sequential()\n",
    "model.add(Embedding(max_features, 128, input_length=maxlen))\n",
    "model.add(SimpleRNN(128))  \n",
    "model.add(Dropout(0.5))\n",
    "model.add(Dense(1))\n",
    "model.add(Activation('sigmoid'))\n",
    "\n",
    "# try using different optimizers and different optimizer configs\n",
    "model.compile(loss='binary_crossentropy', optimizer='adam')\n",
    "\n",
    "print(\"Train...\")\n",
    "model.fit(X_train, y_train, batch_size=batch_size, epochs=1, \n",
    "          validation_data=(X_test, y_test))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### LSTM  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "A LSTM network is an artificial neural network that contains LSTM blocks instead of, or in addition to, regular network units. A LSTM block may be described as a \"smart\" network unit that can remember a value for an arbitrary length of time. \n",
    "\n",
    "Unlike traditional RNNs, an Long short-term memory network is well-suited to learn from experience to classify, process and predict time series when there are very long time lags of unknown size between important events."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "scrolled": true
   },
   "source": [
    "<img src=\"imgs/gru.png\" width=\"60%\">"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "```python\n",
    "keras.layers.recurrent.LSTM(units, activation='tanh', recurrent_activation='hard_sigmoid', use_bias=True, \n",
    "                            kernel_initializer='glorot_uniform', recurrent_initializer='orthogonal', \n",
    "                            bias_initializer='zeros', unit_forget_bias=True, kernel_regularizer=None, \n",
    "                            recurrent_regularizer=None, bias_regularizer=None, activity_regularizer=None, \n",
    "                            kernel_constraint=None, recurrent_constraint=None, bias_constraint=None, \n",
    "                            dropout=0.0, recurrent_dropout=0.0)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Arguments\n",
    "\n",
    "<ul>\n",
    "<li><strong>units</strong>: Positive integer, dimensionality of the output space.</li>\n",
    "<li><strong>activation</strong>: Activation function to use\n",
    "    If you pass None, no activation is applied\n",
    "    (ie. \"linear\" activation: <code>a(x) = x</code>).</li>\n",
    "<li><strong>recurrent_activation</strong>: Activation function to use\n",
    "    for the recurrent step.</li>\n",
    "<li><strong>use_bias</strong>: Boolean, whether the layer uses a bias vector.</li>\n",
    "<li><strong>kernel_initializer</strong>: Initializer for the <code>kernel</code> weights matrix,\n",
    "    used for the linear transformation of the inputs.</li>\n",
    "<li><strong>recurrent_initializer</strong>: Initializer for the <code>recurrent_kernel</code>\n",
    "    weights matrix,\n",
    "    used for the linear transformation of the recurrent state.</li>\n",
    "<li><strong>bias_initializer</strong>: Initializer for the bias vector.</li>\n",
    "<li><strong>unit_forget_bias</strong>: Boolean.\n",
    "    If True, add 1 to the bias of the forget gate at initialization.\n",
    "    Setting it to true will also force <code>bias_initializer=\"zeros\"</code>.\n",
    "    This is recommended in <a href=\"http://www.jmlr.org/proceedings/papers/v37/jozefowicz15.pdf\">Jozefowicz et al.</a></li>\n",
    "<li><strong>kernel_regularizer</strong>: Regularizer function applied to\n",
    "    the <code>kernel</code> weights matrix.</li>\n",
    "<li><strong>recurrent_regularizer</strong>: Regularizer function applied to\n",
    "    the <code>recurrent_kernel</code> weights matrix.</li>\n",
    "<li><strong>bias_regularizer</strong>: Regularizer function applied to the bias vector.</li>\n",
    "<li><strong>activity_regularizer</strong>: Regularizer function applied to\n",
    "    the output of the layer (its \"activation\").</li>\n",
    "<li><strong>kernel_constraint</strong>: Constraint function applied to\n",
    "    the <code>kernel</code> weights matrix.</li>\n",
    "<li><strong>recurrent_constraint</strong>: Constraint function applied to\n",
    "    the <code>recurrent_kernel</code> weights matrix.</li>\n",
    "<li><strong>bias_constraint</strong>: Constraint function applied to the bias vector.</li>\n",
    "<li><strong>dropout</strong>: Float between 0 and 1.\n",
    "    Fraction of the units to drop for\n",
    "    the linear transformation of the inputs.</li>\n",
    "<li><strong>recurrent_dropout</strong>: Float between 0 and 1.\n",
    "    Fraction of the units to drop for\n",
    "    the linear transformation of the recurrent state.</li>\n",
    "</ul>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### GRU  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Gated recurrent units are a gating mechanism in recurrent neural networks. \n",
    "\n",
    "Much similar to the LSTMs, they have fewer parameters than LSTM, as they lack an output gate.\n",
    "\n",
    "<img src=\"imgs/gru.png\" />"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "```python\n",
    "keras.layers.recurrent.GRU(units, activation='tanh', recurrent_activation='hard_sigmoid', use_bias=True, \n",
    "                           kernel_initializer='glorot_uniform', recurrent_initializer='orthogonal', \n",
    "                           bias_initializer='zeros', kernel_regularizer=None, recurrent_regularizer=None, \n",
    "                           bias_regularizer=None, activity_regularizer=None, kernel_constraint=None, \n",
    "                           recurrent_constraint=None, bias_constraint=None, \n",
    "                           dropout=0.0, recurrent_dropout=0.0)\n",
    "```"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Your Turn! - Hands on Rnn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "print('Build model...')\n",
    "model = Sequential()\n",
    "model.add(Embedding(max_features, 128, input_length=maxlen))\n",
    "\n",
    "# !!! Play with those! try and get better results!\n",
    "#model.add(SimpleRNN(128))  \n",
    "#model.add(GRU(128))  \n",
    "#model.add(LSTM(128))  \n",
    "\n",
    "model.add(Dropout(0.5))\n",
    "model.add(Dense(1))\n",
    "model.add(Activation('sigmoid'))\n",
    "\n",
    "# try using different optimizers and different optimizer configs\n",
    "model.compile(loss='binary_crossentropy', optimizer='adam')\n",
    "\n",
    "print(\"Train...\")\n",
    "model.fit(X_train, y_train, batch_size=batch_size, \n",
    "          epochs=4, validation_data=(X_test, y_test))\n",
    "score, acc = model.evaluate(X_test, y_test, batch_size=batch_size)\n",
    "print('Test score:', score)\n",
    "print('Test accuracy:', acc)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Convolutional LSTM\n",
    "\n",
    "> This section demonstrates the use of a **Convolutional LSTM network**.\n",
    "\n",
    "> This network is used to predict the next frame of an artificially\n",
    "generated movie which contains moving squares.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Artificial Data Generation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Generate movies with `3` to `7` moving squares inside.\n",
    "\n",
    "The squares are of shape $1 \\times 1$ or $2 \\times 2$ pixels, which move linearly over time.\n",
    "\n",
    "For convenience we first create movies with bigger width and height (`80x80`) \n",
    "and at the end we select a $40 \\times 40$ window."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Artificial Data Generation\n",
    "def generate_movies(n_samples=1200, n_frames=15):\n",
    "    row = 80\n",
    "    col = 80\n",
    "    noisy_movies = np.zeros((n_samples, n_frames, row, col, 1), dtype=np.float)\n",
    "    shifted_movies = np.zeros((n_samples, n_frames, row, col, 1),\n",
    "                              dtype=np.float)\n",
    "\n",
    "    for i in range(n_samples):\n",
    "        # Add 3 to 7 moving squares\n",
    "        n = np.random.randint(3, 8)\n",
    "\n",
    "        for j in range(n):\n",
    "            # Initial position\n",
    "            xstart = np.random.randint(20, 60)\n",
    "            ystart = np.random.randint(20, 60)\n",
    "            # Direction of motion\n",
    "            directionx = np.random.randint(0, 3) - 1\n",
    "            directiony = np.random.randint(0, 3) - 1\n",
    "\n",
    "            # Size of the square\n",
    "            w = np.random.randint(2, 4)\n",
    "\n",
    "            for t in range(n_frames):\n",
    "                x_shift = xstart + directionx * t\n",
    "                y_shift = ystart + directiony * t\n",
    "                noisy_movies[i, t, x_shift - w: x_shift + w,\n",
    "                             y_shift - w: y_shift + w, 0] += 1\n",
    "\n",
    "                # Make it more robust by adding noise.\n",
    "                # The idea is that if during inference,\n",
    "                # the value of the pixel is not exactly one,\n",
    "                # we need to train the network to be robust and still\n",
    "                # consider it as a pixel belonging to a square.\n",
    "                if np.random.randint(0, 2):\n",
    "                    noise_f = (-1)**np.random.randint(0, 2)\n",
    "                    noisy_movies[i, t,\n",
    "                                 x_shift - w - 1: x_shift + w + 1,\n",
    "                                 y_shift - w - 1: y_shift + w + 1,\n",
    "                                 0] += noise_f * 0.1\n",
    "\n",
    "                # Shift the ground truth by 1\n",
    "                x_shift = xstart + directionx * (t + 1)\n",
    "                y_shift = ystart + directiony * (t + 1)\n",
    "                shifted_movies[i, t, x_shift - w: x_shift + w,\n",
    "                               y_shift - w: y_shift + w, 0] += 1\n",
    "\n",
    "    # Cut to a 40x40 window\n",
    "    noisy_movies = noisy_movies[::, ::, 20:60, 20:60, ::]\n",
    "    shifted_movies = shifted_movies[::, ::, 20:60, 20:60, ::]\n",
    "    noisy_movies[noisy_movies >= 1] = 1\n",
    "    shifted_movies[shifted_movies >= 1] = 1\n",
    "    return noisy_movies, shifted_movies"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "from keras.models import Sequential\n",
    "from keras.layers.convolutional import Conv3D\n",
    "from keras.layers.convolutional_recurrent import ConvLSTM2D\n",
    "from keras.layers.normalization import BatchNormalization\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We create a layer which take as input movies of shape `(n_frames, width, height, channels)` and returns a movie\n",
    "of identical shape."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "seq = Sequential()\n",
    "seq.add(ConvLSTM2D(filters=40, kernel_size=(3, 3),\n",
    "                   input_shape=(None, 40, 40, 1),\n",
    "                   padding='same', return_sequences=True))\n",
    "seq.add(BatchNormalization())\n",
    "\n",
    "seq.add(ConvLSTM2D(filters=40, kernel_size=(3, 3),\n",
    "                   padding='same', return_sequences=True))\n",
    "seq.add(BatchNormalization())\n",
    "\n",
    "seq.add(ConvLSTM2D(filters=40, kernel_size=(3, 3),\n",
    "                   padding='same', return_sequences=True))\n",
    "seq.add(BatchNormalization())\n",
    "\n",
    "seq.add(ConvLSTM2D(filters=40, kernel_size=(3, 3),\n",
    "                   padding='same', return_sequences=True))\n",
    "seq.add(BatchNormalization())\n",
    "\n",
    "seq.add(Conv3D(filters=1, kernel_size=(3, 3, 3),\n",
    "               activation='sigmoid',\n",
    "               padding='same', data_format='channels_last'))\n",
    "seq.compile(loss='binary_crossentropy', optimizer='adadelta')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train the Network\n",
    "\n",
    "#### Beware: This takes time (~3 mins per epoch on my hardware)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Train on 950 samples, validate on 50 samples\n",
      "Epoch 1/50\n",
      "950/950 [==============================] - 180s - loss: 0.3293 - val_loss: 0.6113\n",
      "Epoch 2/50\n",
      "950/950 [==============================] - 181s - loss: 0.0629 - val_loss: 0.4206\n",
      "Epoch 3/50\n",
      "950/950 [==============================] - 180s - loss: 0.0187 - val_loss: 0.2585\n",
      "Epoch 4/50\n",
      "950/950 [==============================] - 180s - loss: 0.0062 - val_loss: 0.2087\n",
      "Epoch 5/50\n",
      "950/950 [==============================] - 179s - loss: 0.0134 - val_loss: 0.1884\n",
      "Epoch 6/50\n",
      "950/950 [==============================] - 180s - loss: 0.0024 - val_loss: 0.1025\n",
      "Epoch 7/50\n",
      "950/950 [==============================] - 179s - loss: 0.0013 - val_loss: 0.0079\n",
      "Epoch 8/50\n",
      "950/950 [==============================] - 180s - loss: 8.1664e-04 - val_loss: 7.7649e-04\n",
      "Epoch 9/50\n",
      "950/950 [==============================] - 180s - loss: 5.9629e-04 - val_loss: 4.9810e-04\n",
      "Epoch 10/50\n",
      "950/950 [==============================] - 180s - loss: 4.8772e-04 - val_loss: 4.5704e-04\n",
      "Epoch 11/50\n",
      "950/950 [==============================] - 179s - loss: 4.1252e-04 - val_loss: 3.7326e-04\n",
      "Epoch 12/50\n",
      "950/950 [==============================] - 180s - loss: 3.6413e-04 - val_loss: 3.3256e-04\n",
      "Epoch 13/50\n",
      "950/950 [==============================] - 179s - loss: 3.2918e-04 - val_loss: 2.8421e-04\n",
      "Epoch 14/50\n",
      "950/950 [==============================] - 179s - loss: 2.9520e-04 - val_loss: 2.8827e-04\n",
      "Epoch 15/50\n",
      "950/950 [==============================] - 179s - loss: 2.7647e-04 - val_loss: 2.5144e-04\n",
      "Epoch 16/50\n",
      "950/950 [==============================] - 181s - loss: 2.5863e-04 - val_loss: 2.5015e-04\n",
      "Epoch 17/50\n",
      "950/950 [==============================] - 180s - loss: 2.4067e-04 - val_loss: 2.2645e-04\n",
      "Epoch 18/50\n",
      "950/950 [==============================] - 180s - loss: 2.2378e-04 - val_loss: 2.1206e-04\n",
      "Epoch 19/50\n",
      "950/950 [==============================] - 179s - loss: 2.1416e-04 - val_loss: 2.0406e-04\n",
      "Epoch 20/50\n",
      "950/950 [==============================] - 179s - loss: 2.0244e-04 - val_loss: 1.9820e-04\n",
      "Epoch 21/50\n",
      " 20/950 [..............................] - ETA: 170s - loss: 1.8054e-04"
     ]
    },
    {
     "ename": "KeyboardInterrupt",
     "evalue": "",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m                         Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-4-5547645715ec>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0mnoisy_movies\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mshifted_movies\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mgenerate_movies\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mn_samples\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1200\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m seq.fit(noisy_movies[:1000], shifted_movies[:1000], batch_size=10,\n\u001b[0;32m----> 4\u001b[0;31m         epochs=50, validation_split=0.05)\n\u001b[0m",
      "\u001b[0;32m/home/valerio/anaconda3/lib/python3.5/site-packages/keras/models.py\u001b[0m in \u001b[0;36mfit\u001b[0;34m(self, x, y, batch_size, epochs, verbose, callbacks, validation_split, validation_data, shuffle, class_weight, sample_weight, initial_epoch, **kwargs)\u001b[0m\n\u001b[1;32m    854\u001b[0m                               \u001b[0mclass_weight\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mclass_weight\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    855\u001b[0m                               \u001b[0msample_weight\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0msample_weight\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 856\u001b[0;31m                               initial_epoch=initial_epoch)\n\u001b[0m\u001b[1;32m    857\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    858\u001b[0m     def evaluate(self, x, y, batch_size=32, verbose=1,\n",
      "\u001b[0;32m/home/valerio/anaconda3/lib/python3.5/site-packages/keras/engine/training.py\u001b[0m in \u001b[0;36mfit\u001b[0;34m(self, x, y, batch_size, epochs, verbose, callbacks, validation_split, validation_data, shuffle, class_weight, sample_weight, initial_epoch, **kwargs)\u001b[0m\n\u001b[1;32m   1496\u001b[0m                               \u001b[0mval_f\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mval_f\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mval_ins\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mval_ins\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mshuffle\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mshuffle\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1497\u001b[0m                               \u001b[0mcallback_metrics\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mcallback_metrics\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1498\u001b[0;31m                               initial_epoch=initial_epoch)\n\u001b[0m\u001b[1;32m   1499\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1500\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0mevaluate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0my\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbatch_size\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m32\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mverbose\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msample_weight\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mNone\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/home/valerio/anaconda3/lib/python3.5/site-packages/keras/engine/training.py\u001b[0m in \u001b[0;36m_fit_loop\u001b[0;34m(self, f, ins, out_labels, batch_size, epochs, verbose, callbacks, val_f, val_ins, shuffle, callback_metrics, initial_epoch)\u001b[0m\n\u001b[1;32m   1150\u001b[0m                 \u001b[0mbatch_logs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'size'\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbatch_ids\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1151\u001b[0m                 \u001b[0mcallbacks\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mon_batch_begin\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mbatch_index\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbatch_logs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1152\u001b[0;31m                 \u001b[0mouts\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mf\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mins_batch\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1153\u001b[0m                 \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0misinstance\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mouts\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlist\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1154\u001b[0m                     \u001b[0mouts\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mouts\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/home/valerio/anaconda3/lib/python3.5/site-packages/keras/backend/tensorflow_backend.py\u001b[0m in \u001b[0;36m__call__\u001b[0;34m(self, inputs)\u001b[0m\n\u001b[1;32m   2227\u001b[0m         \u001b[0msession\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mget_session\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2228\u001b[0m         updated = session.run(self.outputs + [self.updates_op],\n\u001b[0;32m-> 2229\u001b[0;31m                               feed_dict=feed_dict)\n\u001b[0m\u001b[1;32m   2230\u001b[0m         \u001b[0;32mreturn\u001b[0m \u001b[0mupdated\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0moutputs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2231\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/home/valerio/anaconda3/lib/python3.5/site-packages/tensorflow/python/client/session.py\u001b[0m in \u001b[0;36mrun\u001b[0;34m(self, fetches, feed_dict, options, run_metadata)\u001b[0m\n\u001b[1;32m    776\u001b[0m     \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    777\u001b[0m       result = self._run(None, fetches, feed_dict, options_ptr,\n\u001b[0;32m--> 778\u001b[0;31m                          run_metadata_ptr)\n\u001b[0m\u001b[1;32m    779\u001b[0m       \u001b[0;32mif\u001b[0m \u001b[0mrun_metadata\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    780\u001b[0m         \u001b[0mproto_data\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtf_session\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mTF_GetBuffer\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrun_metadata_ptr\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/home/valerio/anaconda3/lib/python3.5/site-packages/tensorflow/python/client/session.py\u001b[0m in \u001b[0;36m_run\u001b[0;34m(self, handle, fetches, feed_dict, options, run_metadata)\u001b[0m\n\u001b[1;32m    980\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mfinal_fetches\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mfinal_targets\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    981\u001b[0m       results = self._do_run(handle, final_targets, final_fetches,\n\u001b[0;32m--> 982\u001b[0;31m                              feed_dict_string, options, run_metadata)\n\u001b[0m\u001b[1;32m    983\u001b[0m     \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    984\u001b[0m       \u001b[0mresults\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/home/valerio/anaconda3/lib/python3.5/site-packages/tensorflow/python/client/session.py\u001b[0m in \u001b[0;36m_do_run\u001b[0;34m(self, handle, target_list, fetch_list, feed_dict, options, run_metadata)\u001b[0m\n\u001b[1;32m   1030\u001b[0m     \u001b[0;32mif\u001b[0m \u001b[0mhandle\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1031\u001b[0m       return self._do_call(_run_fn, self._session, feed_dict, fetch_list,\n\u001b[0;32m-> 1032\u001b[0;31m                            target_list, options, run_metadata)\n\u001b[0m\u001b[1;32m   1033\u001b[0m     \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1034\u001b[0m       return self._do_call(_prun_fn, self._session, handle, feed_dict,\n",
      "\u001b[0;32m/home/valerio/anaconda3/lib/python3.5/site-packages/tensorflow/python/client/session.py\u001b[0m in \u001b[0;36m_do_call\u001b[0;34m(self, fn, *args)\u001b[0m\n\u001b[1;32m   1037\u001b[0m   \u001b[0;32mdef\u001b[0m \u001b[0m_do_call\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfn\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1038\u001b[0m     \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1039\u001b[0;31m       \u001b[0;32mreturn\u001b[0m \u001b[0mfn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1040\u001b[0m     \u001b[0;32mexcept\u001b[0m \u001b[0merrors\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mOpError\u001b[0m \u001b[0;32mas\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1041\u001b[0m       \u001b[0mmessage\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcompat\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mas_text\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0me\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmessage\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/home/valerio/anaconda3/lib/python3.5/site-packages/tensorflow/python/client/session.py\u001b[0m in \u001b[0;36m_run_fn\u001b[0;34m(session, feed_dict, fetch_list, target_list, options, run_metadata)\u001b[0m\n\u001b[1;32m   1019\u001b[0m         return tf_session.TF_Run(session, options,\n\u001b[1;32m   1020\u001b[0m                                  \u001b[0mfeed_dict\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfetch_list\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtarget_list\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 1021\u001b[0;31m                                  status, run_metadata)\n\u001b[0m\u001b[1;32m   1022\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1023\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m_prun_fn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msession\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mhandle\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfeed_dict\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mfetch_list\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mKeyboardInterrupt\u001b[0m: "
     ]
    }
   ],
   "source": [
    "# Train the network\n",
    "noisy_movies, shifted_movies = generate_movies(n_samples=1200)\n",
    "seq.fit(noisy_movies[:1000], shifted_movies[:1000], batch_size=10,\n",
    "        epochs=20, validation_split=0.05)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Test the Network"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Testing the network on one movie\n",
    "# feed it with the first 7 positions and then\n",
    "# predict the new positions\n",
    "which = 1004\n",
    "track = noisy_movies[which][:7, ::, ::, ::]\n",
    "\n",
    "for j in range(16):\n",
    "    new_pos = seq.predict(track[np.newaxis, ::, ::, ::, ::])\n",
    "    new = new_pos[::, -1, ::, ::, ::]\n",
    "    track = np.concatenate((track, new), axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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fmj5yb6aZyyrKFl7HbZl37B/0vjSrdiI5Oj2nZDnv6s1M2+tvVyIV17Er/yqJiecorupo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\nKU8bzvwYzXy5pE9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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4256032908>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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a7+7d0U16JK0v0BgBYMXoXwAKLacw5e4pd98jqV3S3WZ222XXuzLv9hYws0fN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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4255f11390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f415ab26ac8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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f7m5l7isBHwcezS1/FPhEQSqUpCWyf0kqhkXNmYqI8og4ALQDP0opPQusTymd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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f415aa46668>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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3U0q7ge/mPpekG4n9S1LRzRum0oRLuU+rcx8J+CTwZG75k8DPFqVCSVok+5ek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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4159f375f8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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sas5URJRHxAGgHXg8pfQssD6ldC63ynlgfYFqlKQls39JKrRFhamU0nhKaS+w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\ncKaWmLUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4159e2a2e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4159d0f860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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SvuruWw7c5u6u5vsRWnH3u929yt2rKqwyUmMBIB+xxC8RvwAEyyqZMrMKNQei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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4159d33128>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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9+eZVIYTR+e2jgdXV6aIklc/8JanaOi2mQggBuBWYG2P81l6bfg5clv/8MuC+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\nP+qVv/Kxe1QOq2f+ysevWw7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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4159b71f60>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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HHcr+9gy+Eo7Yy3vsTe3vvFQ9f0nqFAq5Z+pU4BLguRDC9Fzb52hOQreFED4I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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4159a64da0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f415994e358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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JkqQMHM0nH3S8pyn3A43T+PsiqYPyzJQkSVIGFlOSJEkZWExJkiRlYDElSZKU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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f415995e0f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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3TZIKxvglqVjyTqZCCL2B+4DPxhjXA7cABwLjafzL76aU464MIdSGEGp3sK0A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\nkiQpg/8PuVCKyVZBTwgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f41597aea58>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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JkjIwTEmSJGVgmJIkScpgh2EqIrpHxNMR8XxETI2IK3PtAyPi4YiYkfs8oPzD\nlaTiWb8kVUIxZ6Y2Au9OKR0KjAdOi4ijgK8Cj6aU9gEezX0vSR2J9UtS2e0wTKUma3Lf1uU+EnAG\ncEuu/RbgzLKMUJLayfolqRKKumYqImojYjKwBHg4pfQUMCSltDC3yiJgSJnGKEntZv2SVG5FhamU\nUkNKaTywBzAxIsa9bXmi6dVeCxFxQUTUR0T9ZjZmHrAktYX1S1K5tWk2X0ppJTAJOA1YHBHDAHKf\nlxTY5vqU0oSU0oQ6umUdryS1i/VLUrkUM5tvcET0z33dAzgFmA7cB5yfW+184N5yDVKS2sP6JakS\ninnQ8TDgloiopSl83Z5S+t+IeBK4PSI+CbwOnFPGcUpSe1i/JJXdDsNUSukF4LA87W8AJ5VjUJJU\nCtYvSZXgHdAlSZIyMExJkiRlYJiSJEnKwDAlSZKUgWFKkiQpA8OUJElSBoYpSZKkDAxTkiRJGRim\nJEmSMjBMSZIkZWCYkiRJyqCYBx2rs4rI355S4U265P+VSo35t4m6wr+CaePGwmOTJKmD8MyUJElS\nBoYpSZKkDAxTkiRJGRimJEmSMjBMSZIkZVD52Xx5ZojV9O5deP29R+bfzez5edsb164vuKu0eVPr\nY9uF1fTpU3DZ6/+9Z97254++JW97I40F99Ut6vK2r2hYl7d9ZWPhfX12z2MLLpMkqaPwzJQkSVIG\nhilJkqQMDFOSJEkZGKYkSZIyMExJkiRlsMPZfBHRHXgc6JZb/86U0uURcQXwaWBpbtWvp5Tub21f\nWwb3YtmHjmrRfu+l3y24zbcXn5y3/U+/PTxve9dVhZ8bN/T+OXnb05o1edsbVr5ZcF87m5q+hWfz\nPX3UjXnb66J7gS1q29z/gNqeedv71hSezacqasdzGTuiUtYvSSqkmFsjbATenVJaExF1wBMR8UBu\n2Q9SSt8r3/AkKRPrl6Sy22GYSiklYOupm7rcx8718lRSp2T9klQJRV0zFRG1ETEZWAI8nFJ6Krfo\nooh4ISJujogBBba9ICLqI6J+y/q1JRq2JBWnVPVrMxsrNmZJO5eiwlRKqSGlNB7YA5gYEeOA64Ax\nwHhgIXBNgW2vTylNSClN6NKjV4mGLUnFKVX9qqNbxcYsaefSptl8KaWVwCTgtJTS4lyRagRuACaW\nY4CSVArWL0nlssMwFRGDI6J/7usewCnA9IgYtt1qHwCmlGeIktQ+1i9JlVDMbL5hwC0RUUtT+Lo9\npfS/EfFN96pqAAAGbklEQVTLiBhP08Wcs4HP7GhHY4cuynsbhD26FH7Q8U9H/DX/gi8VaG/FQ/+W\n/yG835j5vrztfT64ueC+Gtflf3BvR/W9P99ZcFmPgrdAKL/a8FZnHVKhWyAUumUCQMf8tyxZ/ZKk\nQoqZzfcCcFie9vPKMiJJKhHrl6RK6JAvJSVJknYWhilJkqQMDFOSJEkZGKYkSZIyKGY2X8msTV15\nasPwFu179F5Vkf5P7Zl/dt5JB+ef6TbhE58vuK/df/pU/gWNDW0eVyWMqcs/kxGqO6OuIfmg451K\nKw86ji4FHoDdMf8kJKlkPDMlSZKUgWFKkiQpA8OUJElSBoYpSZKkDAxTkiRJGVR0Nl/fms2c3HNx\nniU9KjmMFgrNZvvr164tuM3hJ34sb/vID8/I2542b2rzuFpV4Blpc24fl7e9W0wubf/S2zkzU1In\n5ZkpSZKkDAxTkiRJGRimJEmSMjBMSZIkZWCYkiRJysAwJUmSlEFFb42wZEtPfrT8sBbtlw2aXslh\nFK0LBR7cCjx4xM/ytn+69uS87Sn/M5ZL7isHP5i3vbUHClfiQceF+p++eWPBbaJL/l/P1OCTc6um\nld+V1Fj4IciStCvzzJQkSVIGhilJkqQMDFOSJEkZGKYkSZIyMExJkiRlEClVbgZORCwFXs99OwhY\nVrHOW+rM/XfmY692/53x2PdMKQ2ucJ8lZ/2y/w7Qd2fvv8PWr4qGqWYdR9SnlCZUpfNO3n9nPvZq\n99+Zj31XUu2fo/37N9wZ+6/2sbfGt/kkSZIyMExJkiRlUM0wdX0V++7s/XfmY692/5352Hcl1f45\n2n/n7Luz91/tYy+oatdMSZIk7Qp8m0+SJCmDqoSpiDgtIl6OiJkR8dUK9z07Il6MiMkRUV+B/m6O\niCURMWW7toER8XBEzMh9HlDh/q+IiPm5n8HkiDi9TH2PjIhJEfFSREyNiItz7RU5/lb6r9Txd4+I\npyPi+Vz/V+bay378rfRdkWPflVWzfuX67zQ1rJr1K9dX1WpYZ65fO+i/Q9awir/NFxG1wCvAKcA8\n4Bng3JTSSxXqfzYwIaVUkXtVRMTxwBrgFymlcbm2q4HlKaWrcsV4QErpKxXs/wpgTUrpe+Xoc7u+\nhwHDUkrPRUQf4FngTOBjVOD4W+n/HCpz/AH0SimtiYg64AngYuCDlPn4W+n7NCpw7Luqatev3Bhm\n00lqWDXrV66vqtWwzly/dtB/h6xh1TgzNRGYmVKalVLaBPwGOKMK46iIlNLjwPK3NZ8B3JL7+haa\n/kAq2X9FpJQWppSey329GpgGjKBCx99K/xWRmqzJfVuX+0hU4Phb6VvZdKr6BdWtYdWsX7n+q1bD\nOnP92kH/HVI1wtQIYO5238+jgr8gNP1jPBIRz0bEBRXsd3tDUkoLc18vAoZUYQwXRcQLudPoZXub\ncauIGA0cBjxFFY7/bf1DhY4/ImojYjKwBHg4pVSx4y/QN1T4334XU+36BdYwqMLvcDVrWGesX630\nDx2whnXGC9CPTSmNB94LXJg7jVw1qel91kqn7euAMcB4YCFwTTk7i4jewF3AF1NKq7ZfVonjz9N/\nxY4/pdSQ+33bA5gYEePetrxsx1+g74r+26ssOnsNq/jvcDVrWGetX6303yFrWDXC1Hxg5Hbf75Fr\nq4iU0vzc5yXA72g6bV9pi3Pvh299X3xJJTtPKS3O/ZI2AjdQxp9B7r3uu4BbU0p355ordvz5+q/k\n8W+VUloJTKLp/f6K/vtv33c1jn0XU9X6BdawSv8OV7OGWb9a9t9Ra1g1wtQzwD4RsVdEdAU+DNxX\niY4jolfuQj4iohdwKjCl9a3K4j7g/NzX5wP3VrLzrX8IOR+gTD+D3AWENwHTUkrf325RRY6/UP8V\nPP7BEdE/93UPmi5ank4Fjr9Q35U69l1Y1eoXWMOgcn+/ub6qVsM6c/1qrf8OW8NSShX/AE6naUbM\nq8ClFex3DPB87mNqJfoGbqPpVORmmq6v+CSwG/AoMAN4BBhY4f5/CbwIvEDTH8awMvV9LE2ngF8A\nJuc+Tq/U8bfSf6WO/xDgb7l+pgD/kWsv+/G30ndFjn1X/qhW/cr13alqWDXrV67/qtWwzly/dtB/\nh6xh3gFdkiQpg854AbokSVLJGKYkSZIyMExJkiRlYJiSJEnKwDAlSZKUgWFKkiQpA8OUJElSBoYp\nSZKkDP4/4JbfO0xlN0QAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f41596a0860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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4MCLqI6J+K5szT1iS2sL+Janc2nQ1X0ppNTAZOB1YGhFDAHJ/LiuwzQ0ppQkp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\nwDAlSZKUwf8HD4NxRaiqXe8AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f4159587dd8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# And then compare the predictions\n",
    "# to the ground truth\n",
    "track2 = noisy_movies[which][::, ::, ::, ::]\n",
    "for i in range(15):\n",
    "    fig = plt.figure(figsize=(10, 5))\n",
    "\n",
    "    ax = fig.add_subplot(121)\n",
    "\n",
    "    if i >= 7:\n",
    "        ax.text(1, 3, 'Predictions !', fontsize=20, color='w')\n",
    "    else:\n",
    "        ax.text(1, 3, 'Inital trajectory', fontsize=20)\n",
    "\n",
    "    toplot = track[i, ::, ::, 0]\n",
    "\n",
    "    plt.imshow(toplot)\n",
    "    ax = fig.add_subplot(122)\n",
    "    plt.text(1, 3, 'Ground truth', fontsize=20)\n",
    "\n",
    "    toplot = track2[i, ::, ::, 0]\n",
    "    if i >= 2:\n",
    "        toplot = shifted_movies[which][i - 1, ::, ::, 0]\n",
    "\n",
    "    plt.imshow(toplot)\n",
    "    plt.savefig('imgs/convlstm/%i_animate.png' % (i + 1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python [default]",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}