Code/RBM/Notebook.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# RESTRICTED BOLTZMANN MACHINES\n",
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Initialization\n",
    "\n",
    "First we have to load the utility file which contains different utility functions that are not connected\n",
    "in any way to the networks presented in the tutorials, but rather help in\n",
    "processing the outputs into a more understandable way."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import urllib.request\n",
    "with urllib.request.urlopen(\"http://deeplearning.net/tutorial/code/utils.py\") as url:\n",
    "    response = url.read()\n",
    "target = open('utils.py', 'w')\n",
    "target.write(response.decode('utf-8'))\n",
    "target.close()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we load in all the packages that we use to create the net including the TensorFlow package:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/tensorflow/python/framework/dtypes.py:519: FutureWarning: Passing (type, 1) or '1type' as a synonym of type is deprecated; in a future version of numpy, it will be understood as (type, (1,)) / '(1,)type'.\n",
      "  _np_qint8 = np.dtype([(\"qint8\", np.int8, 1)])\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/tensorflow/python/framework/dtypes.py:520: FutureWarning: Passing (type, 1) or '1type' as a synonym of type is deprecated; in a future version of numpy, it will be understood as (type, (1,)) / '(1,)type'.\n",
      "  _np_quint8 = np.dtype([(\"quint8\", np.uint8, 1)])\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/tensorflow/python/framework/dtypes.py:521: FutureWarning: Passing (type, 1) or '1type' as a synonym of type is deprecated; in a future version of numpy, it will be understood as (type, (1,)) / '(1,)type'.\n",
      "  _np_qint16 = np.dtype([(\"qint16\", np.int16, 1)])\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/tensorflow/python/framework/dtypes.py:522: FutureWarning: Passing (type, 1) or '1type' as a synonym of type is deprecated; in a future version of numpy, it will be understood as (type, (1,)) / '(1,)type'.\n",
      "  _np_quint16 = np.dtype([(\"quint16\", np.uint16, 1)])\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/tensorflow/python/framework/dtypes.py:523: FutureWarning: Passing (type, 1) or '1type' as a synonym of type is deprecated; in a future version of numpy, it will be understood as (type, (1,)) / '(1,)type'.\n",
      "  _np_qint32 = np.dtype([(\"qint32\", np.int32, 1)])\n",
      "/home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/tensorflow/python/framework/dtypes.py:528: FutureWarning: Passing (type, 1) or '1type' as a synonym of type is deprecated; in a future version of numpy, it will be understood as (type, (1,)) / '(1,)type'.\n",
      "  np_resource = np.dtype([(\"resource\", np.ubyte, 1)])\n"
     ]
    }
   ],
   "source": [
    "import tensorflow as tf\n",
    "import numpy as np\n",
    "from tensorflow.examples.tutorials.mnist import input_data\n",
    "#!pip install pillow\n",
    "from PIL import Image\n",
    "from utils import tile_raster_images\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we define the <b>bias</b> of second layer as well. We will denote the bias as “h_bias” for the hidden units. The <b>h_bias</b> is shared among all hidden units"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "v_bias = tf.placeholder(\"float\", [7])\n",
    "h_bias = tf.placeholder(\"float\", [2])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have to define weights among the input layer and hidden layer nodes. In the weight matrix, the number of rows are equal to the input nodes, and the number of columns are equal to the output nodes. Let <b>W</b> be the Tensor of 7x2 (7 - number of visible neurons, 2 - number of hidden neurons) that represents weights between neurons. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "W = tf.constant(np.random.normal(loc=0.0, scale=1.0, size=(7, 2)).astype(np.float32))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before we go further, let's look at a toy example for one case out of all input. Assume that we have a trained RBM, and a very simple input vector such as [1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0], lets see what would be the output of forward pass:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Input:  [[1. 0. 0. 1. 0. 0. 0.]]\n",
      "hb:  [0.1 0.1]\n",
      "w:  [[ 0.5332662  -1.9102893 ]\n",
      " [-0.64729184  0.7917447 ]\n",
      " [ 0.6837602   1.0867532 ]\n",
      " [-0.63897103  1.027463  ]\n",
      " [ 0.01046412 -0.5906408 ]\n",
      " [ 1.0411279   1.2823282 ]\n",
      " [-1.8994617   1.3905194 ]]\n",
      "p(h|v):  [[0.4985738  0.31371108]]\n",
      "h0 states: [[0. 0.]]\n"
     ]
    }
   ],
   "source": [
    "sess = tf.Session()\n",
    "X = tf.constant([[1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0]])\n",
    "v_state = X\n",
    "print (\"Input: \", sess.run(v_state))\n",
    "\n",
    "h_bias = tf.constant([0.1, 0.1])\n",
    "print (\"hb: \", sess.run(h_bias))\n",
    "print (\"w: \", sess.run(W))\n",
    "\n",
    "# Calculate the probabilities of turning the hidden units on:\n",
    "h_prob = tf.nn.sigmoid(tf.matmul(v_state, W) + h_bias)  #probabilities of the hidden units\n",
    "print (\"p(h|v): \", sess.run(h_prob))\n",
    "\n",
    "# Draw samples from the distribution:\n",
    "h_state = tf.nn.relu(tf.sign(h_prob - tf.random_uniform(tf.shape(h_prob)))) #states\n",
    "print (\"h0 states:\", sess.run(h_state))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, in the second phase (i.e. reconstruction phase), the samples from the hidden layer (i.e. h) play the role of input. That is, <b>h</b> becomes the input in the backward pass. The same weight matrix and visible layer biases are used to go through the sigmoid function. The produced output is a reconstruction which is an approximation of the original input."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b:  [0.1 0.2 0.1 0.1 0.1 0.2 0.1]\n",
      "p(vi∣h):  [[0.5249792  0.54983395 0.5249792  0.5249792  0.5249792  0.54983395\n",
      "  0.5249792 ]]\n",
      "v probability states:  [[0. 0. 1. 0. 1. 0. 0.]]\n"
     ]
    }
   ],
   "source": [
    "vb = tf.constant([0.1, 0.2, 0.1, 0.1, 0.1, 0.2, 0.1])\n",
    "print (\"b: \", sess.run(vb))\n",
    "v_prob = sess.run(tf.nn.sigmoid(tf.matmul(h_state, tf.transpose(W)) + vb))\n",
    "print (\"p(vi∣h): \", v_prob)\n",
    "v_state = tf.nn.relu(tf.sign(v_prob - tf.random_uniform(tf.shape(v_prob))))\n",
    "print (\"v probability states: \", sess.run(v_state))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "RBM learns a probability distribution over the input, and then, after being trained, the RBM can generate new samples from the learned probability distribution. As you know, <b>probability distribution</b>, is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.\n",
    "\n",
    "The (conditional) probability distribution over the visible units v is given by\n",
    "\n",
    "$p(\\mathbf{v} \\mid \\mathbf{h}) = \\prod_{i=0}^V p(v_i \\mid \\mathbf{h}),$\n",
    "\n",
    "\n",
    "where,\n",
    "\n",
    "$p(v_i \\mid \\mathbf{h}) = \\sigma\\left( a_i + \\sum_{j=0}^H w_{ji} h_j \\right)$\n",
    "\n",
    "so, given current state of hidden units and weights, what is the probability of generating [1. 0. 0. 1. 0. 0. 0.] in reconstruction phase, based on the above <b>probability distribution</b> function?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1. 0. 0. 1. 0. 0. 0.]]\n",
      "[0.5249792  0.54983395 0.5249792  0.5249792  0.5249792  0.54983395\n",
      " 0.5249792 ]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "0.0059864253744900215"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "inp = sess.run(X)\n",
    "print(inp)\n",
    "print(v_prob[0])\n",
    "v_probability = 1\n",
    "for elm, p in zip(inp[0],v_prob[0]) :\n",
    "    if elm ==1:\n",
    "        v_probability *= p\n",
    "    else:\n",
    "        v_probability *= (1-p)\n",
    "v_probability"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How similar X and V vectors are? Of course, the reconstructed values most likely will not look anything like the input vector because our network has not trained yet. Our objective is to train the model in such a way that the input vector and reconstructed vector to be same. Therefore, based on how different the input values look to the ones that we just reconstructed, the weights are adjusted. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "<h2>MNIST</h2>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We will be using the MNIST dataset to practice the usage of RBMs. The following cell loads the MNIST dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "WARNING:tensorflow:From <ipython-input-8-a0c1bc5755ed>:1: read_data_sets (from tensorflow.contrib.learn.python.learn.datasets.mnist) is deprecated and will be removed in a future version.\n",
      "Instructions for updating:\n",
      "Please use alternatives such as official/mnist/dataset.py from tensorflow/models.\n",
      "WARNING:tensorflow:From /home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/tensorflow/contrib/learn/python/learn/datasets/mnist.py:260: maybe_download (from tensorflow.contrib.learn.python.learn.datasets.base) is deprecated and will be removed in a future version.\n",
      "Instructions for updating:\n",
      "Please write your own downloading logic.\n",
      "WARNING:tensorflow:From /home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/tensorflow/contrib/learn/python/learn/datasets/mnist.py:262: extract_images (from tensorflow.contrib.learn.python.learn.datasets.mnist) is deprecated and will be removed in a future version.\n",
      "Instructions for updating:\n",
      "Please use tf.data to implement this functionality.\n",
      "Extracting MNIST_data/train-images-idx3-ubyte.gz\n",
      "WARNING:tensorflow:From /home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/tensorflow/contrib/learn/python/learn/datasets/mnist.py:267: extract_labels (from tensorflow.contrib.learn.python.learn.datasets.mnist) is deprecated and will be removed in a future version.\n",
      "Instructions for updating:\n",
      "Please use tf.data to implement this functionality.\n",
      "Extracting MNIST_data/train-labels-idx1-ubyte.gz\n",
      "WARNING:tensorflow:From /home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/tensorflow/contrib/learn/python/learn/datasets/mnist.py:110: dense_to_one_hot (from tensorflow.contrib.learn.python.learn.datasets.mnist) is deprecated and will be removed in a future version.\n",
      "Instructions for updating:\n",
      "Please use tf.one_hot on tensors.\n",
      "Extracting MNIST_data/t10k-images-idx3-ubyte.gz\n",
      "Extracting MNIST_data/t10k-labels-idx1-ubyte.gz\n",
      "WARNING:tensorflow:From /home/jupyterlab/conda/envs/python/lib/python3.6/site-packages/tensorflow/contrib/learn/python/learn/datasets/mnist.py:290: DataSet.__init__ (from tensorflow.contrib.learn.python.learn.datasets.mnist) is deprecated and will be removed in a future version.\n",
      "Instructions for updating:\n",
      "Please use alternatives such as official/mnist/dataset.py from tensorflow/models.\n"
     ]
    }
   ],
   "source": [
    "mnist = input_data.read_data_sets(\"MNIST_data/\", one_hot=True)\n",
    "trX, trY, teX, teY = mnist.train.images, mnist.train.labels, mnist.test.images, mnist.test.labels"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets look at the dimension of the images."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(784,)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "trX[1].shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "MNIST images have 784 pixels, so the visible layer must have 784 input nodes.  For our case, we'll use 50 nodes in the hidden layer, so i = 50."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "vb = tf.placeholder(\"float\", [784])\n",
    "hb = tf.placeholder(\"float\", [50])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let <b>W</b> be the Tensor of 784x50 (784 - number of visible neurons, 50 - number of hidden neurons) that represents weights between the neurons. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "W = tf.placeholder(\"float\", [784, 50])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets define the visible layer:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "v0_state = tf.placeholder(\"float\", [None, 784])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we can define hidden layer:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "h0_prob = tf.nn.sigmoid(tf.matmul(v0_state, W) + hb)  #probabilities of the hidden units\n",
    "h0_state = tf.nn.relu(tf.sign(h0_prob - tf.random_uniform(tf.shape(h0_prob)))) #sample_h_given_X"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we define reconstruction part:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "v1_prob = tf.nn.sigmoid(tf.matmul(h0_state, tf.transpose(W)) + vb) \n",
    "v1_state = tf.nn.relu(tf.sign(v1_prob - tf.random_uniform(tf.shape(v1_prob)))) #sample_v_given_h"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>What is objective function?</h3>\n",
    "\n",
    "<b>Goal</b>: Maximize the likelihood of our data being drawn from that distribution\n",
    "\n",
    "<b>Calculate error:</b>  \n",
    "In each epoch, we compute the \"error\" as a sum of the squared difference between step 1 and step n,\n",
    "e.g the error shows the difference between the data and its reconstruction.\n",
    "\n",
    "<b>Note:</b> tf.reduce_mean computes the mean of elements across dimensions of a tensor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "err = tf.reduce_mean(tf.square(v0_state - v1_state))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Train the model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Ok, lets assume that k=1, that is we just get one more step:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "h1_prob = tf.nn.sigmoid(tf.matmul(v1_state, W) + hb)\n",
    "h1_state = tf.nn.relu(tf.sign(h1_prob - tf.random_uniform(tf.shape(h1_prob)))) #sample_h_given_X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "alpha = 0.01\n",
    "W_Delta = tf.matmul(tf.transpose(v0_state), h0_prob) - tf.matmul(tf.transpose(v1_state), h1_prob)\n",
    "update_w = W + alpha * W_Delta\n",
    "update_vb = vb + alpha * tf.reduce_mean(v0_state - v1_state, 0)\n",
    "update_hb = hb + alpha * tf.reduce_mean(h0_state - h1_state, 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's start a session and initialize the variables:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "cur_w = np.zeros([784, 50], np.float32)\n",
    "cur_vb = np.zeros([784], np.float32)\n",
    "cur_hb = np.zeros([50], np.float32)\n",
    "prv_w = np.zeros([784, 50], np.float32)\n",
    "prv_vb = np.zeros([784], np.float32)\n",
    "prv_hb = np.zeros([50], np.float32)\n",
    "sess = tf.Session()\n",
    "init = tf.global_variables_initializer()\n",
    "sess.run(init)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets look at the error of the first run:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.48145455"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sess.run(err, feed_dict={v0_state: trX, W: prv_w, vb: prv_vb, hb: prv_hb})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 0 reconstruction error: 0.099943\n",
      "Epoch: 1 reconstruction error: 0.089058\n",
      "Epoch: 2 reconstruction error: 0.085385\n",
      "Epoch: 3 reconstruction error: 0.084212\n",
      "Epoch: 4 reconstruction error: 0.083248\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Parameters\n",
    "epochs = 5\n",
    "batchsize = 100\n",
    "weights = []\n",
    "errors = []\n",
    "\n",
    "for epoch in range(epochs):\n",
    "    for start, end in zip( range(0, len(trX), batchsize), range(batchsize, len(trX), batchsize)):\n",
    "        batch = trX[start:end]\n",
    "        cur_w = sess.run(update_w, feed_dict={ v0_state: batch, W: prv_w, vb: prv_vb, hb: prv_hb})\n",
    "        cur_vb = sess.run(update_vb, feed_dict={v0_state: batch, W: prv_w, vb: prv_vb, hb: prv_hb})\n",
    "        cur_hb = sess.run(update_hb, feed_dict={ v0_state: batch, W: prv_w, vb: prv_vb, hb: prv_hb})\n",
    "        prv_w = cur_w\n",
    "        prv_vb = cur_vb\n",
    "        prv_hb = cur_hb\n",
    "        if start % 10000 == 0:\n",
    "            errors.append(sess.run(err, feed_dict={v0_state: trX, W: cur_w, vb: cur_vb, hb: cur_hb}))\n",
    "            weights.append(cur_w)\n",
    "    print ('Epoch: %d' % epoch,'reconstruction error: %f' % errors[-1])\n",
    "plt.plot(errors)\n",
    "plt.xlabel(\"Batch Number\")\n",
    "plt.ylabel(\"Error\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What is the final weight after training?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.953128   -1.0605879  -0.99059737 ... -0.9327604  -1.0077841\n",
      "  -0.96909   ]\n",
      " [-1.9837399  -1.8666668  -1.9596486  ... -1.7513443  -1.8298361\n",
      "  -1.8580841 ]\n",
      " [-0.62390214 -0.65390897 -0.5916143  ... -0.6201386  -0.6691202\n",
      "  -0.5844657 ]\n",
      " ...\n",
      " [-0.37899655 -0.33749086 -0.3439962  ... -0.3196499  -0.34715736\n",
      "  -0.32027036]\n",
      " [-2.7894008  -2.9224937  -2.7512028  ... -2.8350337  -2.900528\n",
      "  -2.853664  ]\n",
      " [-1.2511277  -1.1305019  -1.1654112  ... -1.0987622  -1.186039\n",
      "  -1.1033281 ]]\n"
     ]
    }
   ],
   "source": [
    "uw = weights[-1].T\n",
    "print (uw) # a weight matrix of shape (50,784)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"ref5\"></a>\n",
    "<h3>Learned features</h3> "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can take each hidden unit and visualize the connections between that hidden unit and each element in the input vector. In our case, we have 50 hidden units. Lets visualize those."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot the current weights:\n",
    "<b>tile_raster_images</b> helps in generating an easy to grasp image from a set of samples or weights. It transform the <b>uw</b> (with one flattened image per row of size 784), into an array (of size $25\\times20$) in which images are reshaped and laid out like tiles on a floor."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1296x1296 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "tile_raster_images(X=cur_w.T, img_shape=(28, 28), tile_shape=(5, 10), tile_spacing=(1, 1))\n",
    "image = Image.fromarray(tile_raster_images(X=cur_w.T, img_shape=(28, 28) ,tile_shape=(5, 10), tile_spacing=(1, 1)))\n",
    "### Plot image\n",
    "plt.rcParams['figure.figsize'] = (18.0, 18.0)\n",
    "imgplot = plt.imshow(image)\n",
    "imgplot.set_cmap('gray')  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Each tile in the above visualization corresponds to a vector of connections between a hidden unit and visible layer's units. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at one of the learned weights corresponding to one of hidden units for example. In this particular square, the gray color represents weight = 0, and the whiter it is, the more positive the weights are (closer to 1). Conversely, the darker pixels are, the more negative the weights. The positive pixels will increase the probability of activation in hidden units (after multiplying by input/visible pixels), and negative pixels will decrease the probability of a unit hidden to be 1 (activated). So, why is this important?  So we can see that this specific square (hidden unit) can detect a feature (e.g. a \"/\" shape) and if it exists in the input."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "image = Image.fromarray(tile_raster_images(X =cur_w.T[10:11], img_shape=(28, 28),tile_shape=(1, 1), tile_spacing=(1, 1)))\n",
    "### Plot image\n",
    "plt.rcParams['figure.figsize'] = (4.0, 4.0)\n",
    "imgplot = plt.imshow(image)\n",
    "imgplot.set_cmap('gray')  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at the reconstruction of an image now. Imagine that we have a destructed image of figure 3. Lets see if our trained network can fix it:\n",
    "\n",
    "First we plot the image:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--2020-07-09 07:15:09--  https://ibm.box.com/shared/static/vvm1b63uvuxq88vbw9znpwu5ol380mco.jpg\n",
      "Resolving ibm.box.com (ibm.box.com)... 107.152.29.197\n",
      "Connecting to ibm.box.com (ibm.box.com)|107.152.29.197|:443... connected.\n",
      "HTTP request sent, awaiting response... 301 Moved Permanently\n",
      "Location: /public/static/vvm1b63uvuxq88vbw9znpwu5ol380mco.jpg [following]\n",
      "--2020-07-09 07:15:10--  https://ibm.box.com/public/static/vvm1b63uvuxq88vbw9znpwu5ol380mco.jpg\n",
      "Reusing existing connection to ibm.box.com:443.\n",
      "HTTP request sent, awaiting response... 301 Moved Permanently\n",
      "Location: https://ibm.ent.box.com/public/static/vvm1b63uvuxq88vbw9znpwu5ol380mco.jpg [following]\n",
      "--2020-07-09 07:15:10--  https://ibm.ent.box.com/public/static/vvm1b63uvuxq88vbw9znpwu5ol380mco.jpg\n",
      "Resolving ibm.ent.box.com (ibm.ent.box.com)... 107.152.27.211\n",
      "Connecting to ibm.ent.box.com (ibm.ent.box.com)|107.152.27.211|:443... connected.\n",
      "HTTP request sent, awaiting response... 302 Found\n",
      "Location: https://public.boxcloud.com/d/1/b1!3CkE4E8uDYvQO194G_kwMyVWd_70YnL1oUdA9ZirER353mZB7CKbg_WsMboTnRLjBdvAyy9JJhY3rt_xF-I12m3mR2vlmIEDg1W3tMn7c06AHwM02juO4PBsE5UHSyyYBy1DSZr_TIGPGuT-DqPDGIyZVM0GzApB8WjwvMq2tXrsJ7AAjSCOmCax4Bokl_aoyp0K1Y_yB5VCUK_nqVYzSK5NG3dyfQZ-x9bzFRUuImy655xA77xpGbVhQgltenUfLrRnpAerkFGdpuxnVLUPbN8NXaRFKmErY93eme0rJd4Ei0l1DLEMMljjp4v75pKV4f3DseBxo5D0fS3hmvWHeW9MeDgkaixb26fAfEBvZcpGUqboxibfCAaNnflH_527ragmra-UfA3BCVN-Uv006Fq9qbW_N28Vfvf5DuusR3uIX2jqjCQPg_rYmU12bnSOC3wWvclcpmD2dVTY2kyrCYrxn5USjSt9NpdX8Y9Byysogb8f-eI-BHrdTvPFttxML3lqp8yNrljsnlJnck0_F_jH84-A6Bv4qNWTUKrlAZJbXZ7Y_SqTefrFZxmG0giC7hFRdG5YEZOgEZL8oo3nJDkiUHq0j0iUcqLUx1wncPEvqJi_4gW7SDYGqkMeNDJo4fgniS1fr8RSWvlu6Vy5aE0YYmTYxohVaU2-VgP6eGTmCvluKnQRZY-3lv8S3qfBmo_2yo318eLWSfa7EEVLEaqcglErJK2GZATgXU9K07OBaiHkkrlbARt_ofNMEdavZzTDKvjklOQqE4T_MAWJzRl8X-hQEt5zvFrCDM7iPsR4KA3kzdq6ooh0kwUErpuuLF7uOo3GbWbIepJwUukyUu0Ul6aF_za0oh4FXGxpebuktVkYsxJ6-opk-5vFymd7rKw_O5D42lL81vjoGmN5OnTyWfvgtTP64EjBBpkVw5lmTUZs1A4bkh94hPoMkA9HpqMcezfY_neYqwv1RDwqUNhuISFGChjuQBknB7Rew0z1l-sYgX-cmOQHZBszUtmeGkSQfstGqwps5VbNIK5XDxND7UkyLrTVArbrXulOyijAnXoLWEsKTPcRe7kW5Aci7SNjQnn08MfgxlxGP7BDUfkkF_4e0IIJGI0hA0kUce-2WNIB9hObwZ0iu_33A_-z-NhS9IKYz6gM2HZdp7Ruse2tzBod-lxny5ZkLmj15q7h8ekSSgKST7qoMJmUASYzzPdMfFZxSYkVXKklUJC-Opv7dK6vpcLnBvBzy939ySq-5-84O6PYU76oeh0XtcYAkDTo-wIzVt8QS8N_zRvWqZSJhdhJpKxok-mlZQHNq42OOt_u1-Kz4fgIAZIlFHpBcEFRGuS95SAjKDnoceMRsCUPrYzfegAwkQTZfWRE7Z4NQMEN4SKccAm75l3dRFPeBECw0oFzRe8HUTO0RrAlKX_9lWM9/download [following]\n",
      "--2020-07-09 07:15:11--  https://public.boxcloud.com/d/1/b1!3CkE4E8uDYvQO194G_kwMyVWd_70YnL1oUdA9ZirER353mZB7CKbg_WsMboTnRLjBdvAyy9JJhY3rt_xF-I12m3mR2vlmIEDg1W3tMn7c06AHwM02juO4PBsE5UHSyyYBy1DSZr_TIGPGuT-DqPDGIyZVM0GzApB8WjwvMq2tXrsJ7AAjSCOmCax4Bokl_aoyp0K1Y_yB5VCUK_nqVYzSK5NG3dyfQZ-x9bzFRUuImy655xA77xpGbVhQgltenUfLrRnpAerkFGdpuxnVLUPbN8NXaRFKmErY93eme0rJd4Ei0l1DLEMMljjp4v75pKV4f3DseBxo5D0fS3hmvWHeW9MeDgkaixb26fAfEBvZcpGUqboxibfCAaNnflH_527ragmra-UfA3BCVN-Uv006Fq9qbW_N28Vfvf5DuusR3uIX2jqjCQPg_rYmU12bnSOC3wWvclcpmD2dVTY2kyrCYrxn5USjSt9NpdX8Y9Byysogb8f-eI-BHrdTvPFttxML3lqp8yNrljsnlJnck0_F_jH84-A6Bv4qNWTUKrlAZJbXZ7Y_SqTefrFZxmG0giC7hFRdG5YEZOgEZL8oo3nJDkiUHq0j0iUcqLUx1wncPEvqJi_4gW7SDYGqkMeNDJo4fgniS1fr8RSWvlu6Vy5aE0YYmTYxohVaU2-VgP6eGTmCvluKnQRZY-3lv8S3qfBmo_2yo318eLWSfa7EEVLEaqcglErJK2GZATgXU9K07OBaiHkkrlbARt_ofNMEdavZzTDKvjklOQqE4T_MAWJzRl8X-hQEt5zvFrCDM7iPsR4KA3kzdq6ooh0kwUErpuuLF7uOo3GbWbIepJwUukyUu0Ul6aF_za0oh4FXGxpebuktVkYsxJ6-opk-5vFymd7rKw_O5D42lL81vjoGmN5OnTyWfvgtTP64EjBBpkVw5lmTUZs1A4bkh94hPoMkA9HpqMcezfY_neYqwv1RDwqUNhuISFGChjuQBknB7Rew0z1l-sYgX-cmOQHZBszUtmeGkSQfstGqwps5VbNIK5XDxND7UkyLrTVArbrXulOyijAnXoLWEsKTPcRe7kW5Aci7SNjQnn08MfgxlxGP7BDUfkkF_4e0IIJGI0hA0kUce-2WNIB9hObwZ0iu_33A_-z-NhS9IKYz6gM2HZdp7Ruse2tzBod-lxny5ZkLmj15q7h8ekSSgKST7qoMJmUASYzzPdMfFZxSYkVXKklUJC-Opv7dK6vpcLnBvBzy939ySq-5-84O6PYU76oeh0XtcYAkDTo-wIzVt8QS8N_zRvWqZSJhdhJpKxok-mlZQHNq42OOt_u1-Kz4fgIAZIlFHpBcEFRGuS95SAjKDnoceMRsCUPrYzfegAwkQTZfWRE7Z4NQMEN4SKccAm75l3dRFPeBECw0oFzRe8HUTO0RrAlKX_9lWM9/download\n",
      "Resolving public.boxcloud.com (public.boxcloud.com)... 107.152.29.200\n",
      "Connecting to public.boxcloud.com (public.boxcloud.com)|107.152.29.200|:443... connected.\n",
      "HTTP request sent, awaiting response... 200 OK\n",
      "Length: 24383 (24K) [image/jpeg]\n",
      "Saving to: ‘destructed3.jpg’\n",
      "\n",
      "destructed3.jpg     100%[===================>]  23.81K  47.6KB/s    in 0.5s    \n",
      "\n",
      "2020-07-09 07:15:12 (47.6 KB/s) - ‘destructed3.jpg’ saved [24383/24383]\n",
      "\n"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<PIL.JpegImagePlugin.JpegImageFile image mode=RGB size=181x181 at 0x7F2EF4233978>"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "!wget -O destructed3.jpg  https://ibm.box.com/shared/static/vvm1b63uvuxq88vbw9znpwu5ol380mco.jpg\n",
    "img = Image.open('destructed3.jpg')\n",
    "img"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's pass this image through the net:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "# convert the image to a 1d numpy array\n",
    "sample_case = np.array(img.convert('I').resize((28,28))).ravel().reshape((1, -1))/255.0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Feed the sample case into the network and reconstruct the output:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability nodes in hidden layer: [[9.9892718e-01 8.1086311e-09 3.7734915e-27 2.6990129e-14 8.2951122e-28\n",
      "  3.8330681e-16 8.8073670e-05 2.0802519e-18 3.7166988e-11 9.9974662e-01\n",
      "  9.9999893e-01 1.4928387e-32 3.1941692e-08 7.4635659e-10 1.4205844e-04\n",
      "  3.4380002e-15 3.7135236e-30 2.8047074e-12 7.0822817e-37 3.2935455e-27\n",
      "  4.4888272e-36 1.2075593e-25 5.0595038e-24 5.1491979e-35 1.4505398e-17\n",
      "  5.1114156e-32 1.6398930e-07 1.6077958e-06 9.9998212e-01 9.0040693e-32\n",
      "  1.0000000e+00 9.9999690e-01 6.9221625e-07 0.0000000e+00 8.5345040e-05\n",
      "  5.0425881e-01 4.3955403e-08 2.6598283e-12 6.4313590e-17 1.5330162e-25\n",
      "  4.3724039e-01 5.2249816e-06 0.0000000e+00 8.2016410e-03 0.0000000e+00\n",
      "  3.8476525e-08 9.3922824e-01 2.5971815e-28 9.9999988e-01 3.8474019e-35]]\n",
      "activated nodes in hidden layer: [[1. 0. 0. 0. 0. 0. 0. 0. 0. 1. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0.\n",
      "  0. 0. 0. 0. 1. 0. 1. 1. 0. 0. 0. 1. 0. 0. 0. 0. 0. 0. 0. 0. 0. 0. 1. 0.\n",
      "  1. 0.]]\n"
     ]
    }
   ],
   "source": [
    "hh0_p = tf.nn.sigmoid(tf.matmul(v0_state, W) + hb)\n",
    "#hh0_s = tf.nn.relu(tf.sign(hh0_p - tf.random_uniform(tf.shape(hh0_p)))) \n",
    "hh0_s = tf.round(hh0_p)\n",
    "hh0_p_val,hh0_s_val  = sess.run((hh0_p, hh0_s), feed_dict={ v0_state: sample_case, W: prv_w, hb: prv_hb})\n",
    "print(\"Probability nodes in hidden layer:\" ,hh0_p_val)\n",
    "print(\"activated nodes in hidden layer:\" ,hh0_s_val)\n",
    "\n",
    "# reconstruct\n",
    "vv1_p = tf.nn.sigmoid(tf.matmul(hh0_s_val, tf.transpose(W)) + vb)\n",
    "rec_prob = sess.run(vv1_p, feed_dict={ hh0_s: hh0_s_val, W: prv_w, vb: prv_vb})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we plot the reconstructed image:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 288x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "img = Image.fromarray(tile_raster_images(X=rec_prob, img_shape=(28, 28),tile_shape=(1, 1), tile_spacing=(1, 1)))\n",
    "plt.rcParams['figure.figsize'] = (4.0, 4.0)\n",
    "imgplot = plt.imshow(img)\n",
    "imgplot.set_cmap('gray') "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Thanks for reading :)\n",
    "Created by [Saeed Aghabozorgi](https://www.linkedin.com/in/saeedaghabozorgi/) and modified by [Tarun Kamboj](https://www.linkedin.com/in/kambojtarun/)."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  },
  "widgets": {
   "state": {},
   "version": "1.1.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}