ML0120EN-4.1-Review-RBMMNIST.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-DL0120EN-SkillsNetwork/images/IDSN-logo.png\" width=\"300\" alt=\"cognitiveclass.ai logo\">\n",
    "\n",
    "<h1 align=\"center\"><font size=\"5\">RESTRICTED BOLTZMANN MACHINES</font></h1>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Estimated time needed: **25** minutes\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>Introduction</h3>\n",
    "<b>Restricted Boltzmann Machine (RBM):</b>  RBMs are shallow neural nets that learn to reconstruct data by themselves in an unsupervised fashion.  \n",
    "\n",
    "\n",
    "<h4>Why are RBMs important?</h4>\n",
    "An RBM are a basic form of autoencoder.  It can automatically extract <b>meaningful</b> features from a given input.\n",
    "\n",
    "\n",
    "<h4>How does it work?</h4>\n",
    "RBM is a 2 layer neural network. Simply, RBM takes the inputs and translates those into a set of binary values that represents them in the hidden layer. Then, these numbers can be translated back to reconstruct the inputs. Through several forward and backward passes, the RBM will be trained, and a trained RBM can reveal which features are the most important ones when detecting patterns.   \n",
    "\n",
    "\n",
    "<h4>What are the applications of an RBM?</h4>\n",
    "RBM is useful for <a href='http://www.cs.utoronto.ca/~hinton/absps/netflixICML.pdf?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkDL0120ENSkillsNetwork954-2022-01-01'>  Collaborative Filtering</a>, dimensionality reduction, classification, regression, feature learning, topic modeling and even <b>Deep Belief Networks</b>.\n",
    "\n",
    "<h4>Is RBM a generative or Discriminative model?</h4>\n",
    "RBM is a generative model. Let me explain it by first, see what is different between discriminative and generative models: \n",
    "\n",
    "<b>Discriminative:</b> Consider a classification problem where we want to learn to distinguish between Sedan cars (y = 1) and SUV cars (y = 0), based on some features of cars. Given a training set, an algorithm like logistic regression tries to find a straight line, or <i>decision boundary</i>, that separates the suv and sedan.  \n",
    "\n",
    "<b>Generative:</b> looking at cars, we can build a model of what Sedan cars look like. Then, looking at SUVs, we can build a separate model of what SUV cars look like. Finally, to classify a new car, we can match the new car against the Sedan model, and match it against the SUV model, to see whether the new car looks more like the SUV or Sedan. \n",
    "\n",
    "Generative Models specify a probability distribution over a dataset of input vectors. We can carry out both supervised and unsupervised tasks with generative models:\n",
    "<ul>\n",
    "    <li>In an unsupervised task, we try to form a model for $P(x)$, where $P$ is the probability given $x$ as an input vector.</li>\n",
    "    <li>In the supervised task, we first form a model for $P(x|y)$, where $P$ is the probability of $x$ given $y$(the label for $x$). For example, if $y = 0$ indicates that a car is an SUV, and $y = 1$ indicates that a car is a sedan, then $p(x|y = 0)$ models the distribution of SUV features, and $p(x|y = 1)$ models the distribution of sedan features. If we manage to find $P(x|y)$ and $P(y)$, then we can use <b>Bayes rule</b> to estimate $P(y|x)$, because:   \n",
    "        $$p(y|x) = \\frac{p(x|y)p(y)}{p(x)}$$</li>\n",
    "</ul>\n",
    "Now the question is, can we build a generative model, and then use it to create synthetic data by directly sampling from the modeled probability distributions? Lets see. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h2>Table of Contents</h2>\n",
    "<ol>\n",
    "    <li><a href=\"#ref1\">Initialization</a></li>\n",
    "    <li><a href=\"#ref2\">RBM layers</a></li>\n",
    "    <li><a href=\"#ref3\">What RBM can do after training?</a></li>\n",
    "    <li><a href=\"#ref4\">How to train the model?</a></li>\n",
    "    <li><a href=\"#ref5\">Learned features</a></li>\n",
    "</ol>\n",
    "<p></p>\n",
    "</div>\n",
    "<br>\n",
    "\n",
    "<hr>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"ref1\"></a>\n",
    "<h3>Initialization</h3>\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.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import urllib.request\n",
    "with urllib.request.urlopen(\"https://cf-courses-data.s3.us.cloud-object-storage.appdomain.cloud/IBMDeveloperSkillsNetwork-DL0120EN-SkillsNetwork/labs/Week4/data/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": [
    "<h2>Installing TensorFlow </h2>\n",
    "\n",
    "We will installing TensorFlow version 2.2.0 and its required prerequistes.  Also installing pillow...\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
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     ]
    }
   ],
   "source": [
    "!pip install grpcio==1.24.3\n",
    "!pip install tensorflow==2.2.0\n",
    "!pip install pillow==8.1.0"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>Notice:</b> This notebook has been created with TensorFlow version 2.2, and might not work with other versions. Therefore we check:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import tensorflow as tf\n",
    "from IPython.display import Markdown, display\n",
    "\n",
    "def printmd(string):\n",
    "    display(Markdown('# <span style=\"color:red\">'+string+'</span>'))\n",
    "\n",
    "\n",
    "if not tf.__version__ == '2.2.0':\n",
    "    printmd('<<<<<!!!!! ERROR !!!! please upgrade to TensorFlow 2.2.0, or restart your Kernel (Kernel->Restart & Clear Output)>>>>>')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we load in all the packages that we use to create the net including the TensorFlow package:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "import tensorflow as tf\n",
    "import numpy as np\n",
    "import sys\n",
    "sys.path.append('..')\n",
    "from ML0120EN import utils\n",
    "from PIL import Image\n",
    "# from ML0120EN import utils.tile_raster_images\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"ref2\"></a>\n",
    "<h3>RBM layers</h3>\n",
    "\n",
    "An RBM has two layers. The first layer of the RBM is called the <b>visible</b> (or input layer). Imagine that our toy example, has only vectors with 7 values, so the visible layer must have $V=7$ input nodes. \n",
    "The second layer is the <b>hidden</b> layer, which has $H$ neurons in our case. Each hidden node takes on values of either 0 or 1 (i.e., $h_i = 1$ or $h_i$ = 0), with a probability that is a logistic function of the inputs it receives from the other $V$ visible units, called for example, $p(h_i = 1)$. For our toy sample, we'll use 2 nodes in the hidden layer, so $H = 2$.\n",
    "\n",
    "<center><img src=\"https://ibm.box.com/shared/static/eu26opvcefgls6vnwuo29uwp0nudmokh.png\" alt=\"RBM Model\" style=\"width: 400px;\"></center>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "     \n",
    "\n",
    "Each node in the first layer also has a <b>bias</b>. We will denote the bias as $v_{bias}$, and this single value is shared among the $V$ visible units.\n",
    "\n",
    "The <b>bias</b> of the second is defined similarly as $h_{bias}$, and this single value among the $H$ hidden units.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "2023-05-15 16:34:20.916900: W tensorflow/stream_executor/platform/default/dso_loader.cc:55] Could not load dynamic library 'libcuda.so.1'; dlerror: libcuda.so.1: cannot open shared object file: No such file or directory\n",
      "2023-05-15 16:34:20.916958: E tensorflow/stream_executor/cuda/cuda_driver.cc:313] failed call to cuInit: UNKNOWN ERROR (303)\n",
      "2023-05-15 16:34:20.917010: I tensorflow/stream_executor/cuda/cuda_diagnostics.cc:156] kernel driver does not appear to be running on this host (jupyterlab-pedromgomes): /proc/driver/nvidia/version does not exist\n",
      "2023-05-15 16:34:20.917538: I tensorflow/core/platform/cpu_feature_guard.cc:143] Your CPU supports instructions that this TensorFlow binary was not compiled to use: AVX2 AVX512F FMA\n",
      "2023-05-15 16:34:20.935120: I tensorflow/core/platform/profile_utils/cpu_utils.cc:102] CPU Frequency: 2394310000 Hz\n",
      "2023-05-15 16:34:20.935741: I tensorflow/compiler/xla/service/service.cc:168] XLA service 0x7f1c78000b20 initialized for platform Host (this does not guarantee that XLA will be used). Devices:\n",
      "2023-05-15 16:34:20.935776: I tensorflow/compiler/xla/service/service.cc:176]   StreamExecutor device (0): Host, Default Version\n"
     ]
    }
   ],
   "source": [
    "v_bias = tf.Variable(tf.zeros([7]), tf.float32)\n",
    "h_bias = tf.Variable(tf.zeros([2]), tf.float32)"
   ]
  },
  {
   "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. We define a tensor $\\mathbf{W}$ of shape = (7,2), where the number of visible neurons = 7, and the number of hidden neurons = 2. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "tags": []
   },
   "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": [
    "<hr>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"ref3\"></a>\n",
    "<h3>What RBM can do after training?</h3>\n",
    "Think of RBM as a model that has been trained based on images of a dataset of many SUV and sedan cars. Also, imagine that the RBM network has only two hidden nodes, where one node encodes the weight and, and the other encodes the size.  \n",
    "In a sense, the different configurations represent different cars, where one is an SUV and the other is Sedan.  In a training process, through many forward and backward passes, the RBM adjust its weights to send a stronger signal to either the SUV node (0, 1) or the sedan node (1, 0) in the hidden layer, given the pixels of images. Now, given an SUV in hidden layer, which distribution of pixels should we expect? RBM can give you 2 things. First, it encodes your images in hidden layer. Second, it gives you the probability of observing a case, given some hidden values.\n",
    "\n",
    "\n",
    "<h3>The Inference Process</h3>\n",
    "\n",
    "RBM has two phases:\n",
    "<ul>\n",
    "    <li>Forward Pass</li>  \n",
    "    <li>Backward Pass or Reconstruction</li>\n",
    "</ul>\n",
    "\n",
    "<b>Phase 1) Forward pass:</b>  \n",
    "\n",
    "Input one training sample (one image) $\\mathbf{x}$ through all visible nodes, and pass it to all hidden nodes. Processing happens in each node in the hidden layer. This computation begins by making stochastic decisions about whether to transmit that input or not (i.e. to determine the state of each hidden layer).  First, the probability vector is computed using the input feature vector $\\mathbf{x}$, the weight matrix $\\mathbf{W}$, and the bias term $h_{bias}$, as \n",
    "\n",
    "\n",
    "$$p({h_j}|\\mathbf x)= \\sigma( \\sum_{i=1}^V W_{ij} x_i + h_{bias} )$$, \n",
    "\n",
    "where $\\sigma(z) = (1+e^{-z})^{-1}$ is the logistic function.\n",
    "\n",
    "\n",
    "So, what does $p({h_j})$ represent? It is the <b>probability distribution</b> of the hidden units. That is, RBM uses inputs $x_i$ to make predictions about hidden node activations. For example, imagine that the hidden node activation values are [0.51 0.84] for the first training item. It tells you that the conditional probability for each hidden neuron for Phase 1 is: \n",
    "\n",
    "$$p(h_{1} = 1|\\mathbf{v}) = 0.51$$\n",
    "$$p(h_{2} = 1|\\mathbf{v}) = 0.84$$\n",
    "\n",
    "As a result, for each row in the training set, vector of probabilities is generated.  In TensorFlow, this is referred to as a `tensor` with a shape of (1,2). \n",
    "\n",
    "We then turn unit $j$ with probability $p(h_{j}|\\mathbf{v})$, and turn it off with probability $1 - p(h_{j}|\\mathbf{v})$ by generating a uniform random number vector $\\mathbf{\\xi}$, and comparing it to the activation probability as \n",
    "\n",
    "<center>If $\\xi_j>p(h_{j}|\\mathbf{v})$, then $h_j=1$, else $h_j=0$.</center>\n",
    "\n",
    "\n",
    "Therefore, the conditional probability of a configuration of $\\mathbf{h}$ given $\\mathbf{v}$ (for a training sample) is:\n",
    "\n",
    "$$p(\\mathbf{h} \\mid \\mathbf{v}) = \\prod_{j=1}^H p(h_j \\mid \\mathbf{v})$$\n",
    "\n",
    "\n",
    "where $H$ is the number of hidden units.\n",
    "\n"
   ]
  },
  {
   "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].   \n",
    "Let's see what the output of forward pass would look like:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Input:  tf.Tensor([[1. 0. 0. 1. 0. 0. 0.]], shape=(1, 7), dtype=float32)\n",
      "hb:  tf.Tensor([0.1 0.1], shape=(2,), dtype=float32)\n",
      "w:  tf.Tensor(\n",
      "[[-0.7595062   1.6710001 ]\n",
      " [ 3.260736   -0.05216897]\n",
      " [ 0.30022728 -1.4370509 ]\n",
      " [ 0.12354292  0.49047974]\n",
      " [ 0.8486836  -1.0737582 ]\n",
      " [-0.06142515  1.7132702 ]\n",
      " [-1.7121717   0.2007537 ]], shape=(7, 2), dtype=float32)\n",
      "p(h|v):  tf.Tensor([[0.36912712 0.9056362 ]], shape=(1, 2), dtype=float32)\n",
      "h0 states: tf.Tensor([[1. 1.]], shape=(1, 2), dtype=float32)\n"
     ]
    }
   ],
   "source": [
    "X = tf.constant([[1.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0]], tf.float32)\n",
    "\n",
    "v_state = X\n",
    "print (\"Input: \", v_state)\n",
    "\n",
    "h_bias = tf.constant([0.1, 0.1])\n",
    "print (\"hb: \", h_bias)\n",
    "print (\"w: \", 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): \", 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:\", h_state)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<b>Phase 2) Backward Pass (Reconstruction):</b>\n",
    "The RBM reconstructs data by making several forward and backward passes between the visible and hidden layers.\n",
    "\n",
    "So, in the second phase (i.e. reconstruction phase), the samples from the hidden layer (i.e. $\\mathbf h$) becomes the input in the backward pass. The same weight matrix and visible layer biases are used to passed to the sigmoid function. The reproduced output is a reconstruction which is an approximation of the original input.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "b:  tf.Tensor([0.1 0.2 0.1 0.1 0.1 0.2 0.1], shape=(7,), dtype=float32)\n",
      "p(vi∣h):  tf.Tensor(\n",
      "[[0.7333124  0.9679712  0.26176333 0.67128944 0.46877202 0.8643435\n",
      "  0.1960105 ]], shape=(1, 7), dtype=float32)\n",
      "v probability states:  tf.Tensor([[1. 1. 1. 0. 1. 1. 1.]], shape=(1, 7), dtype=float32)\n"
     ]
    }
   ],
   "source": [
    "vb = tf.constant([0.1, 0.2, 0.1, 0.1, 0.1, 0.2, 0.1])\n",
    "print (\"b: \", vb)\n",
    "v_prob = 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: \", 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",
    "$$p(\\mathbf{v} \\mid \\mathbf{h}) = \\prod_{i=1}^V p(v_i \\mid \\mathbf{h}),$$\n",
    "\n",
    "\n",
    "where,\n",
    "\n",
    "$$p(v_i \\mid \\mathbf{h}) = \\sigma\\left(\\sum_{j=1}^H W_{ji} h_j + v_{bias} \\right)$$\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?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "input X: [[1. 0. 0. 1. 0. 0. 0.]]\n",
      "probablity vector: [0.7333124  0.9679712  0.26176333 0.67128944 0.46877202 0.8643435\n",
      " 0.1960105 ]\n",
      "probability of generating X:  0.0006743835\n"
     ]
    }
   ],
   "source": [
    "inp = X\n",
    "print(\"input X:\" , inp.numpy())\n",
    "\n",
    "print(\"probablity vector:\" , v_prob[0].numpy())\n",
    "v_probability = 1\n",
    "\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",
    "\n",
    "print(\"probability of generating X: \" , v_probability.numpy())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How similar are vectors $\\mathbf{x}$ and $\\mathbf{v}$? Of course, the reconstructed values most likely will not look anything like the input vector, because our network has not been 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. \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n"
   ]
  },
  {
   "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.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Downloading data from https://storage.googleapis.com/tensorflow/tf-keras-datasets/mnist.npz\n",
      "11493376/11490434 [==============================] - 0s 0us/step\n"
     ]
    }
   ],
   "source": [
    "#loading training and test data\n",
    "mnist = tf.keras.datasets.mnist\n",
    "(trX, trY), (teX, teY) = mnist.load_data()\n",
    "\n",
    "# showing an example of the Flatten class and operation\n",
    "from tensorflow.keras.layers import Flatten\n",
    "flatten = Flatten(dtype='float32')\n",
    "trX = flatten(trX/255.0)\n",
    "trY = flatten(trY/255.0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets look at the dimension of the images.\n"
   ]
  },
  {
   "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.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "vb = tf.Variable(tf.zeros([784]), tf.float32)\n",
    "hb = tf.Variable(tf.zeros([50]), tf.float32)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let $\\mathbf W$ be the Tensor of 784x50 (784 - number of visible neurons, 50 - number of hidden neurons) that represents weights between the neurons. \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "W = tf.Variable(tf.zeros([784,50]), tf.float32)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Lets define the visible layer:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<tf.Tensor: shape=(1, 50), dtype=float32, numpy=\n",
       "array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
       "        0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
       "        0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,\n",
       "        0., 0.]], dtype=float32)>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v0_state = tf.Variable(tf.zeros([784]), tf.float32)\n",
    "\n",
    "#testing to see if the matrix product works\n",
    "tf.matmul( [v0_state], W)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we can define hidden layer:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "h0_state shape:  tf.Tensor([ 1 50], shape=(2,), dtype=int32)\n",
      "first 15 hidden states:  tf.Tensor([1. 1. 1. 1. 0. 1. 1. 1. 1. 1. 0. 1. 1. 0. 1.], shape=(15,), dtype=float32)\n"
     ]
    }
   ],
   "source": [
    "#computing the hidden nodes probability vector and checking shape\n",
    "h0_prob = tf.nn.sigmoid(tf.matmul([v0_state], W) + hb)  #probabilities of the hidden units\n",
    "print(\"h0_state shape: \" , tf.shape(h0_prob))\n",
    "\n",
    "#defining a function to return only the generated hidden states \n",
    "def hidden_layer(v0_state, W, hb):\n",
    "    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\n",
    "    return h0_state\n",
    "\n",
    "\n",
    "h0_state = hidden_layer(v0_state, W, hb)\n",
    "print(\"first 15 hidden states: \", h0_state[0][0:15])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we define reconstruction part:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "hidden state shape:  (1, 50)\n",
      "v0 state shape:   (784,)\n",
      "v1 state shape:   (784,)\n"
     ]
    }
   ],
   "source": [
    "def reconstructed_output(h0_state, W, vb):\n",
    "    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\n",
    "    return v1_state[0]\n",
    "\n",
    "v1_state = reconstructed_output(h0_state, W, vb)\n",
    "print(\"hidden state shape: \", h0_state.shape)\n",
    "print(\"v0 state shape:  \", v0_state.shape)\n",
    "print(\"v1 state shape:  \", v1_state.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<h3>What is the 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.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "error 0.52678573\n"
     ]
    }
   ],
   "source": [
    "def error(v0_state, v1_state):\n",
    "    return tf.reduce_mean(tf.square(v0_state - v1_state))\n",
    "\n",
    "err = tf.reduce_mean(tf.square(v0_state - v1_state))\n",
    "print(\"error\" , err.numpy())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"ref4\"></a>\n",
    "<h3>Training the Model</h3>\n",
    "<b>Warning...</b> The following part is math-heavy, but you can skip it if you just want to run the cells in the next section.\n",
    "\n",
    "As mentioned, we want to give a high probability to the input data we train on. So, in order to train an RBM, we have to maximize the product of probabilities assigned to all rows $\\mathbf{v}$ (images) in the training set $\\mathbf{V}$ (a matrix, where each row of it is treated as a visible vector $\\mathbf{v}$)\n",
    "\n",
    "$$\\arg \\max_W \\prod_{\\mathbf{v}\\in\\mathbf{V}_T} p(\\mathbf{v})$$\n",
    "\n",
    "\n",
    "which is equivalent to maximizing the expectation of the log probability, given as\n",
    "\n",
    "$$\\arg\\max_W\\left[ \\mathbb{E} \\left(\\prod_{\\mathbf v\\in \\mathbf V}\\text{log} \\left(p(\\mathbf v)\\right) \\right) \\right].$$\n",
    "\n",
    "\n",
    "So, we have to update the weights $W_{ij}$  to increase $p(\\mathbf{v})$ for all $\\mathbf{v}$ in our training data during training. So we have to calculate the derivative:\n",
    "\n",
    "\n",
    "$$\\frac{\\partial \\log p(\\mathbf v)}{\\partial W_{ij}}$$\n",
    "\n",
    "This cannot be easily done by typical <b>gradient descent (SGD)</b>, so we can use another approach, which has 2 steps:\n",
    "<ol>\n",
    "    <li>Gibbs Sampling</li>\n",
    "    <li>Contrastive Divergence</li>\n",
    "</ol>    \n",
    "    \n",
    "<h3>Gibbs Sampling</h3>   \n",
    "\n",
    "<h4>Gibbs Sampling Step 1</h4> \n",
    "Given an input vector $\\mathbf{v}$, we are using $p(\\mathbf{h}|\\mathbf{v})$ to predict the hidden values $\\mathbf{h}$. \n",
    "  $$p({h_j}|\\mathbf v)= \\sigma\\left(\\sum_{i=1}^V W_{ij} v_i + h_{bias} \\right)$$\n",
    "The samples are generated from this distribution by generating the uniform random variate vector $\\mathbf{\\xi} \\sim U[0,1]$ of length $H$ and comparing to the computed probabilities as\n",
    "\n",
    "\n",
    "<center>If $\\xi_j>p(h_{j}|\\mathbf{v})$, then $h_j=1$, else $h_j=0$.</center>\n",
    "\n",
    "\n",
    "<h4>Gibbs Sampling Step 2</h4> \n",
    "Then, knowing the hidden values, we use $p(\\mathbf v| \\mathbf h)$ for reconstructing of new input values v. \n",
    "\n",
    "   $$p({v_i}|\\mathbf h)= \\sigma\\left(\\sum_{j=1}^H W^{T}_{ij} h_j + v_{bias} \\right)$$\n",
    "\n",
    "\n",
    "The samples are generated from this distribution by generating a uniform random variate vector $\\mathbf{\\xi} \\sim U[0,1]$ of length $V$ and comparing to the computed probabilities as\n",
    "\n",
    "<center>If $\\xi_i>p(v_{i}|\\mathbf{h})$, then $v_i=1$, else $v_i=0$.</center>\n",
    "\n",
    "Let vectors $\\mathbf v_k$ and $\\mathbf h_k$ be for the $k$th iteration.  In general, the $kth$ state is generrated as: \n",
    "\n",
    "\n",
    "    \n",
    "<b>Iteration</b> $k$: \n",
    "\n",
    "$$\\mathbf v_{k-1} \\Rightarrow p(\\mathbf h_{k-1}|\\mathbf v_{k-1})\\Rightarrow \\mathbf h_{k-1}\\Rightarrow p(\\mathbf v_{k}|\\mathbf h_{k-1})\\Rightarrow \\mathbf v_k$$       \n",
    "    \n",
    "<h3>Contrastive Divergence (CD-k)</h3>\n",
    "The update of the weight matrix is done during the Contrastive Divergence step. \n",
    "\n",
    "Vectors v0 and vk are used to calculate the activation probabilities for hidden values h0 and hk. The difference between the outer products of those probabilities with input vectors v0 and vk results in the update matrix:\n",
    "\n",
    "\n",
    "$$\\Delta \\mathbf W_k =\\mathbf v_k \\otimes \\mathbf h_k - \\mathbf v_{k-1} \\otimes \\mathbf h_{k-1}$$\n",
    "\n",
    "Contrastive Divergence is actually matrix of values that is computed and used to adjust values of the $\\mathbf W$ matrix. Changing $\\mathbf W$ incrementally leads to training of the  $\\mathbf W$ values. Then, on each step (epoch), $\\mathbf W$ is updated using the following:\n",
    "\n",
    "$$\\mathbf W_k = \\mathbf W_{k-1} + \\alpha * \\Delta \\mathbf W_k$$\n",
    "\n",
    "\n",
    "\n",
    "Reconstruction steps:\n",
    "<ul>\n",
    "    <li> Get one data point from data set, like <i>x</i>, and pass it through the following steps:</li>\n",
    "    \n",
    "<b>Iteration</b> $k=1$: \n",
    "    \n",
    "Sampling (starting with input image)\n",
    "    $$\\mathbf x = \\mathbf v_0 \\Rightarrow p(\\mathbf h_0|\\mathbf v_0)\\Rightarrow \\mathbf h_0 \\Rightarrow p(\\mathbf v_1|\\mathbf h_0)\\Rightarrow \\mathbf v_1$$   \n",
    "    followed by the CD-k step\n",
    "$$\\Delta \\mathbf W_1 =\\mathbf v_1 \\otimes \\mathbf h_1 - \\mathbf v_{0} \\otimes \\mathbf h_{0}$$     \n",
    "$$\\mathbf W_1 = \\mathbf W_{0} + \\alpha * \\Delta \\mathbf W_1$$ \n",
    " \n",
    "<li> $\\mathbf v_1$ is the reconstruction of $\\mathbf x$ sent to the next iteration).</li>\n",
    "\n",
    "<b>Iteration</b> $k=2$: \n",
    "\n",
    "Sampling (starting with $\\mathbf v_1$)\n",
    "\n",
    "$$\\mathbf v_1 \\Rightarrow p(\\mathbf h_1|\\mathbf v_1)\\Rightarrow \\mathbf h_1\\Rightarrow p(\\mathbf v_2|\\mathbf h_1)\\Rightarrow \\mathbf v_2$$   \n",
    "\n",
    "followed by the CD-k step\n",
    "$$\\Delta \\mathbf W_2 =\\mathbf v_2 \\otimes \\mathbf h_2 - \\mathbf v_{1} \\otimes \\mathbf h_{1}$$     \n",
    "$$\\mathbf W_2 = \\mathbf W_{1} + \\alpha * \\Delta \\mathbf W_2$$ \n",
    "\n",
    "<li> $\\mathbf v_2$ is the reconstruction of $\\mathbf v_1$ sent to the next iteration).</li>    \n",
    "      \n",
    "<b>Iteration</b> $k=K$:\n",
    "    \n",
    "Sampling (starting with $\\mathbf v_{K-1}$)\n",
    "\n",
    "$$\\mathbf v_{K-1} \\Rightarrow p(\\mathbf h_{K-1}|\\mathbf v_{K-1})\\Rightarrow \\mathbf h_{K-1}\\Rightarrow p(\\mathbf v_K|\\mathbf h_{K-1})\\Rightarrow \\mathbf v_K$$   \n",
    "\n",
    "followed by the CD-k step\n",
    "$$\\Delta \\mathbf W_K =\\mathbf v_K \\otimes \\mathbf h_K - \\mathbf v_{K-1} \\otimes \\mathbf h_{K-1}$$     \n",
    "$$\\mathbf W_K = \\mathbf W_{K-1} + \\alpha * \\Delta \\mathbf W_K$$ \n",
    "    \n",
    "<b>What is $\\alpha$?</b>  \n",
    "Here, alpha is some small step size, and is also known as the \"learning rate\".\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$K$ is adjustable, and good performance can be achieved with $K=1$, so that we just take one set of sampling steps per image.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "tags": []
   },
   "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": "markdown",
   "metadata": {},
   "source": [
    "Lets look at the error of the first run:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "error:  tf.Tensor(0.52678573, shape=(), dtype=float32)\n"
     ]
    }
   ],
   "source": [
    "print(\"error: \", error(v0_state, v1_state))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Epoch: 0 batch #: 1  of 300 sample #: 199 reconstruction error: 0.189413\n",
      "Epoch: 0 batch #: 2  of 300 sample #: 199 reconstruction error: 0.202253\n",
      "Epoch: 0 batch #: 3  of 300 sample #: 199 reconstruction error: 0.134095\n",
      "Epoch: 0 batch #: 4  of 300 sample #: 199 reconstruction error: 0.104528\n",
      "Epoch: 0 batch #: 5  of 300 sample #: 199 reconstruction error: 0.102119\n",
      "Epoch: 0 batch #: 6  of 300 sample #: 199 reconstruction error: 0.170632\n",
      "Epoch: 0 batch #: 7  of 300 sample #: 199 reconstruction error: 0.096442\n",
      "Epoch: 0 batch #: 8  of 300 sample #: 199 reconstruction error: 0.116613\n",
      "Epoch: 0 batch #: 9  of 300 sample #: 199 reconstruction error: 0.091214\n",
      "Epoch: 0 batch #: 10  of 300 sample #: 199 reconstruction error: 0.177522\n",
      "Epoch: 0 batch #: 11  of 300 sample #: 199 reconstruction error: 0.078671\n",
      "Epoch: 0 batch #: 12  of 300 sample #: 199 reconstruction error: 0.124796\n",
      "Epoch: 0 batch #: 13  of 300 sample #: 199 reconstruction error: 0.065294\n",
      "Epoch: 0 batch #: 14  of 300 sample #: 199 reconstruction error: 0.124046\n",
      "Epoch: 0 batch #: 15  of 300 sample #: 199 reconstruction error: 0.110815\n",
      "Epoch: 0 batch #: 16  of 300 sample #: 199 reconstruction error: 0.119587\n",
      "Epoch: 0 batch #: 17  of 300 sample #: 199 reconstruction error: 0.082876\n",
      "Epoch: 0 batch #: 18  of 300 sample #: 199 reconstruction error: 0.112036\n",
      "Epoch: 0 batch #: 19  of 300 sample #: 199 reconstruction error: 0.134393\n",
      "Epoch: 0 batch #: 20  of 300 sample #: 199 reconstruction error: 0.101026\n",
      "Epoch: 0 batch #: 21  of 300 sample #: 199 reconstruction error: 0.091414\n",
      "Epoch: 0 batch #: 22  of 300 sample #: 199 reconstruction error: 0.089999\n",
      "Epoch: 0 batch #: 23  of 300 sample #: 199 reconstruction error: 0.115297\n",
      "Epoch: 0 batch #: 24  of 300 sample #: 199 reconstruction error: 0.130206\n",
      "Epoch: 0 batch #: 25  of 300 sample #: 199 reconstruction error: 0.092217\n",
      "Epoch: 0 batch #: 26  of 300 sample #: 199 reconstruction error: 0.110571\n",
      "Epoch: 0 batch #: 27  of 300 sample #: 199 reconstruction error: 0.114390\n",
      "Epoch: 0 batch #: 28  of 300 sample #: 199 reconstruction error: 0.097031\n",
      "Epoch: 0 batch #: 29  of 300 sample #: 199 reconstruction error: 0.112390\n",
      "Epoch: 0 batch #: 30  of 300 sample #: 199 reconstruction error: 0.083541\n",
      "Epoch: 0 batch #: 31  of 300 sample #: 199 reconstruction error: 0.089658\n",
      "Epoch: 0 batch #: 32  of 300 sample #: 199 reconstruction error: 0.113477\n",
      "Epoch: 0 batch #: 33  of 300 sample #: 199 reconstruction error: 0.059833\n",
      "Epoch: 0 batch #: 34  of 300 sample #: 199 reconstruction error: 0.076586\n",
      "Epoch: 0 batch #: 35  of 300 sample #: 199 reconstruction error: 0.077106\n",
      "Epoch: 0 batch #: 36  of 300 sample #: 199 reconstruction error: 0.086530\n",
      "Epoch: 0 batch #: 37  of 300 sample #: 199 reconstruction error: 0.063474\n",
      "Epoch: 0 batch #: 38  of 300 sample #: 199 reconstruction error: 0.059244\n",
      "Epoch: 0 batch #: 39  of 300 sample #: 199 reconstruction error: 0.090766\n",
      "Epoch: 0 batch #: 40  of 300 sample #: 199 reconstruction error: 0.124539\n",
      "Epoch: 0 batch #: 41  of 300 sample #: 199 reconstruction error: 0.077383\n",
      "Epoch: 0 batch #: 42  of 300 sample #: 199 reconstruction error: 0.074748\n",
      "Epoch: 0 batch #: 43  of 300 sample #: 199 reconstruction error: 0.121492\n",
      "Epoch: 0 batch #: 44  of 300 sample #: 199 reconstruction error: 0.084780\n",
      "Epoch: 0 batch #: 45  of 300 sample #: 199 reconstruction error: 0.055970\n",
      "Epoch: 0 batch #: 46  of 300 sample #: 199 reconstruction error: 0.035868\n",
      "Epoch: 0 batch #: 47  of 300 sample #: 199 reconstruction error: 0.042516\n",
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      "Epoch: 0 batch #: 50  of 300 sample #: 199 reconstruction error: 0.049562\n",
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      "Epoch: 0 batch #: 52  of 300 sample #: 199 reconstruction error: 0.030008\n",
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      "Epoch: 0 batch #: 56  of 300 sample #: 199 reconstruction error: 0.065834\n",
      "Epoch: 0 batch #: 57  of 300 sample #: 199 reconstruction error: 0.046114\n",
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      "Epoch: 0 batch #: 60  of 300 sample #: 199 reconstruction error: 0.109576\n",
      "Epoch: 0 batch #: 61  of 300 sample #: 199 reconstruction error: 0.071403\n",
      "Epoch: 0 batch #: 62  of 300 sample #: 199 reconstruction error: 0.082149\n",
      "Epoch: 0 batch #: 63  of 300 sample #: 199 reconstruction error: 0.060488\n",
      "Epoch: 0 batch #: 64  of 300 sample #: 199 reconstruction error: 0.079460\n",
      "Epoch: 0 batch #: 65  of 300 sample #: 199 reconstruction error: 0.089326\n",
      "Epoch: 0 batch #: 66  of 300 sample #: 199 reconstruction error: 0.061936\n",
      "Epoch: 0 batch #: 67  of 300 sample #: 199 reconstruction error: 0.041982\n",
      "Epoch: 0 batch #: 68  of 300 sample #: 199 reconstruction error: 0.047607\n",
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      "Epoch: 0 batch #: 90  of 300 sample #: 199 reconstruction error: 0.069367\n",
      "Epoch: 0 batch #: 91  of 300 sample #: 199 reconstruction error: 0.060961\n",
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      "Epoch: 0 batch #: 99  of 300 sample #: 199 reconstruction error: 0.058106\n",
      "Epoch: 0 batch #: 100  of 300 sample #: 199 reconstruction error: 0.101160\n",
      "Epoch: 0 batch #: 101  of 300 sample #: 199 reconstruction error: 0.076998\n",
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      "Epoch: 0 batch #: 104  of 300 sample #: 199 reconstruction error: 0.071933\n",
      "Epoch: 0 batch #: 105  of 300 sample #: 199 reconstruction error: 0.062622\n",
      "Epoch: 0 batch #: 106  of 300 sample #: 199 reconstruction error: 0.113415\n",
      "Epoch: 0 batch #: 107  of 300 sample #: 199 reconstruction error: 0.135822\n",
      "Epoch: 0 batch #: 108  of 300 sample #: 199 reconstruction error: 0.047468\n",
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      "Epoch: 0 batch #: 111  of 300 sample #: 199 reconstruction error: 0.089692\n",
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      "Epoch: 0 batch #: 114  of 300 sample #: 199 reconstruction error: 0.066151\n",
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      "Epoch: 0 batch #: 117  of 300 sample #: 199 reconstruction error: 0.047389\n",
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      "Epoch: 0 batch #: 141  of 300 sample #: 199 reconstruction error: 0.072911\n",
      "Epoch: 0 batch #: 142  of 300 sample #: 199 reconstruction error: 0.065998\n",
      "Epoch: 0 batch #: 143  of 300 sample #: 199 reconstruction error: 0.046782\n",
      "Epoch: 0 batch #: 144  of 300 sample #: 199 reconstruction error: 0.055928\n",
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      "Epoch: 0 batch #: 146  of 300 sample #: 199 reconstruction error: 0.089154\n",
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      "Epoch: 0 batch #: 149  of 300 sample #: 199 reconstruction error: 0.059253\n",
      "Epoch: 0 batch #: 150  of 300 sample #: 199 reconstruction error: 0.046056\n",
      "Epoch: 0 batch #: 151  of 300 sample #: 199 reconstruction error: 0.105421\n",
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      "Epoch: 0 batch #: 158  of 300 sample #: 199 reconstruction error: 0.063442\n",
      "Epoch: 0 batch #: 159  of 300 sample #: 199 reconstruction error: 0.075198\n",
      "Epoch: 0 batch #: 160  of 300 sample #: 199 reconstruction error: 0.073109\n",
      "Epoch: 0 batch #: 161  of 300 sample #: 199 reconstruction error: 0.074692\n",
      "Epoch: 0 batch #: 162  of 300 sample #: 199 reconstruction error: 0.119521\n",
      "Epoch: 0 batch #: 163  of 300 sample #: 199 reconstruction error: 0.053587\n",
      "Epoch: 0 batch #: 164  of 300 sample #: 199 reconstruction error: 0.059638\n",
      "Epoch: 0 batch #: 165  of 300 sample #: 199 reconstruction error: 0.076558\n",
      "Epoch: 0 batch #: 166  of 300 sample #: 199 reconstruction error: 0.060420\n",
      "Epoch: 0 batch #: 167  of 300 sample #: 199 reconstruction error: 0.108178\n",
      "Epoch: 0 batch #: 168  of 300 sample #: 199 reconstruction error: 0.043489\n",
      "Epoch: 0 batch #: 169  of 300 sample #: 199 reconstruction error: 0.041633\n",
      "Epoch: 0 batch #: 170  of 300 sample #: 199 reconstruction error: 0.052221\n",
      "Epoch: 0 batch #: 171  of 300 sample #: 199 reconstruction error: 0.031386\n",
      "Epoch: 0 batch #: 172  of 300 sample #: 199 reconstruction error: 0.064247\n",
      "Epoch: 0 batch #: 173  of 300 sample #: 199 reconstruction error: 0.088505\n",
      "Epoch: 0 batch #: 174  of 300 sample #: 199 reconstruction error: 0.088500\n",
      "Epoch: 0 batch #: 175  of 300 sample #: 199 reconstruction error: 0.075929\n",
      "Epoch: 0 batch #: 176  of 300 sample #: 199 reconstruction error: 0.050428\n",
      "Epoch: 0 batch #: 177  of 300 sample #: 199 reconstruction error: 0.036897\n",
      "Epoch: 0 batch #: 178  of 300 sample #: 199 reconstruction error: 0.126719\n",
      "Epoch: 0 batch #: 179  of 300 sample #: 199 reconstruction error: 0.068567\n",
      "Epoch: 0 batch #: 180  of 300 sample #: 199 reconstruction error: 0.105190\n",
      "Epoch: 0 batch #: 181  of 300 sample #: 199 reconstruction error: 0.080987\n",
      "Epoch: 0 batch #: 182  of 300 sample #: 199 reconstruction error: 0.083819\n",
      "Epoch: 0 batch #: 183  of 300 sample #: 199 reconstruction error: 0.094403\n",
      "Epoch: 0 batch #: 184  of 300 sample #: 199 reconstruction error: 0.066114\n",
      "Epoch: 0 batch #: 185  of 300 sample #: 199 reconstruction error: 0.072223\n",
      "Epoch: 0 batch #: 186  of 300 sample #: 199 reconstruction error: 0.098817\n",
      "Epoch: 0 batch #: 187  of 300 sample #: 199 reconstruction error: 0.053457\n",
      "Epoch: 0 batch #: 188  of 300 sample #: 199 reconstruction error: 0.120854\n",
      "Epoch: 0 batch #: 189  of 300 sample #: 199 reconstruction error: 0.070053\n",
      "Epoch: 0 batch #: 190  of 300 sample #: 199 reconstruction error: 0.059101\n",
      "Epoch: 0 batch #: 191  of 300 sample #: 199 reconstruction error: 0.104668\n",
      "Epoch: 0 batch #: 192  of 300 sample #: 199 reconstruction error: 0.115777\n",
      "Epoch: 0 batch #: 193  of 300 sample #: 199 reconstruction error: 0.084841\n",
      "Epoch: 0 batch #: 194  of 300 sample #: 199 reconstruction error: 0.075858\n",
      "Epoch: 0 batch #: 195  of 300 sample #: 199 reconstruction error: 0.038710\n",
      "Epoch: 0 batch #: 196  of 300 sample #: 199 reconstruction error: 0.045337\n",
      "Epoch: 0 batch #: 197  of 300 sample #: 199 reconstruction error: 0.056420\n",
      "Epoch: 0 batch #: 198  of 300 sample #: 199 reconstruction error: 0.086157\n",
      "Epoch: 0 batch #: 199  of 300 sample #: 199 reconstruction error: 0.072931\n",
      "Epoch: 0 batch #: 200  of 300 sample #: 199 reconstruction error: 0.112885\n",
      "Epoch: 0 batch #: 201  of 300 sample #: 199 reconstruction error: 0.105408\n",
      "Epoch: 0 batch #: 202  of 300 sample #: 199 reconstruction error: 0.027248\n",
      "Epoch: 0 batch #: 203  of 300 sample #: 199 reconstruction error: 0.083384\n",
      "Epoch: 0 batch #: 204  of 300 sample #: 199 reconstruction error: 0.045722\n",
      "Epoch: 0 batch #: 205  of 300 sample #: 199 reconstruction error: 0.022146\n",
      "Epoch: 0 batch #: 206  of 300 sample #: 199 reconstruction error: 0.068024\n",
      "Epoch: 0 batch #: 207  of 300 sample #: 199 reconstruction error: 0.087260\n",
      "Epoch: 0 batch #: 208  of 300 sample #: 199 reconstruction error: 0.063414\n",
      "Epoch: 0 batch #: 209  of 300 sample #: 199 reconstruction error: 0.032487\n",
      "Epoch: 0 batch #: 210  of 300 sample #: 199 reconstruction error: 0.104719\n",
      "Epoch: 0 batch #: 211  of 300 sample #: 199 reconstruction error: 0.102568\n",
      "Epoch: 0 batch #: 212  of 300 sample #: 199 reconstruction error: 0.108937\n",
      "Epoch: 0 batch #: 213  of 300 sample #: 199 reconstruction error: 0.102959\n",
      "Epoch: 0 batch #: 214  of 300 sample #: 199 reconstruction error: 0.114489\n",
      "Epoch: 0 batch #: 215  of 300 sample #: 199 reconstruction error: 0.029332\n",
      "Epoch: 0 batch #: 216  of 300 sample #: 199 reconstruction error: 0.101497\n",
      "Epoch: 0 batch #: 217  of 300 sample #: 199 reconstruction error: 0.093156\n",
      "Epoch: 0 batch #: 218  of 300 sample #: 199 reconstruction error: 0.062474\n",
      "Epoch: 0 batch #: 219  of 300 sample #: 199 reconstruction error: 0.092995\n",
      "Epoch: 0 batch #: 220  of 300 sample #: 199 reconstruction error: 0.059030\n",
      "Epoch: 0 batch #: 221  of 300 sample #: 199 reconstruction error: 0.106035\n",
      "Epoch: 0 batch #: 222  of 300 sample #: 199 reconstruction error: 0.088462\n",
      "Epoch: 0 batch #: 223  of 300 sample #: 199 reconstruction error: 0.066641\n",
      "Epoch: 0 batch #: 224  of 300 sample #: 199 reconstruction error: 0.062355\n",
      "Epoch: 0 batch #: 225  of 300 sample #: 199 reconstruction error: 0.073194\n",
      "Epoch: 0 batch #: 226  of 300 sample #: 199 reconstruction error: 0.127442\n",
      "Epoch: 0 batch #: 227  of 300 sample #: 199 reconstruction error: 0.082088\n",
      "Epoch: 0 batch #: 228  of 300 sample #: 199 reconstruction error: 0.067871\n",
      "Epoch: 0 batch #: 229  of 300 sample #: 199 reconstruction error: 0.079181\n",
      "Epoch: 0 batch #: 230  of 300 sample #: 199 reconstruction error: 0.040911\n",
      "Epoch: 0 batch #: 231  of 300 sample #: 199 reconstruction error: 0.028405\n",
      "Epoch: 0 batch #: 232  of 300 sample #: 199 reconstruction error: 0.068083\n",
      "Epoch: 0 batch #: 233  of 300 sample #: 199 reconstruction error: 0.066554\n",
      "Epoch: 0 batch #: 234  of 300 sample #: 199 reconstruction error: 0.059185\n",
      "Epoch: 0 batch #: 235  of 300 sample #: 199 reconstruction error: 0.084596\n",
      "Epoch: 0 batch #: 236  of 300 sample #: 199 reconstruction error: 0.084330\n",
      "Epoch: 0 batch #: 237  of 300 sample #: 199 reconstruction error: 0.067130\n",
      "Epoch: 0 batch #: 238  of 300 sample #: 199 reconstruction error: 0.128446\n",
      "Epoch: 0 batch #: 239  of 300 sample #: 199 reconstruction error: 0.030621\n",
      "Epoch: 0 batch #: 240  of 300 sample #: 199 reconstruction error: 0.096596\n",
      "Epoch: 0 batch #: 241  of 300 sample #: 199 reconstruction error: 0.062327\n",
      "Epoch: 0 batch #: 242  of 300 sample #: 199 reconstruction error: 0.071065\n",
      "Epoch: 0 batch #: 243  of 300 sample #: 199 reconstruction error: 0.064368\n",
      "Epoch: 0 batch #: 244  of 300 sample #: 199 reconstruction error: 0.083829\n",
      "Epoch: 0 batch #: 245  of 300 sample #: 199 reconstruction error: 0.065329\n",
      "Epoch: 0 batch #: 246  of 300 sample #: 199 reconstruction error: 0.100475\n",
      "Epoch: 0 batch #: 247  of 300 sample #: 199 reconstruction error: 0.042023\n",
      "Epoch: 0 batch #: 248  of 300 sample #: 199 reconstruction error: 0.069373\n",
      "Epoch: 0 batch #: 249  of 300 sample #: 199 reconstruction error: 0.045231\n",
      "Epoch: 0 batch #: 250  of 300 sample #: 199 reconstruction error: 0.097640\n",
      "Epoch: 0 batch #: 251  of 300 sample #: 199 reconstruction error: 0.045185\n",
      "Epoch: 0 batch #: 252  of 300 sample #: 199 reconstruction error: 0.062924\n",
      "Epoch: 0 batch #: 253  of 300 sample #: 199 reconstruction error: 0.048547\n",
      "Epoch: 0 batch #: 254  of 300 sample #: 199 reconstruction error: 0.033919\n",
      "Epoch: 0 batch #: 255  of 300 sample #: 199 reconstruction error: 0.057864\n",
      "Epoch: 0 batch #: 256  of 300 sample #: 199 reconstruction error: 0.080036\n",
      "Epoch: 0 batch #: 257  of 300 sample #: 199 reconstruction error: 0.088868\n",
      "Epoch: 0 batch #: 258  of 300 sample #: 199 reconstruction error: 0.088239\n",
      "Epoch: 0 batch #: 259  of 300 sample #: 199 reconstruction error: 0.058411\n",
      "Epoch: 0 batch #: 260  of 300 sample #: 199 reconstruction error: 0.093781\n",
      "Epoch: 0 batch #: 261  of 300 sample #: 199 reconstruction error: 0.036558\n",
      "Epoch: 0 batch #: 262  of 300 sample #: 199 reconstruction error: 0.067469\n",
      "Epoch: 0 batch #: 263  of 300 sample #: 199 reconstruction error: 0.099701\n",
      "Epoch: 0 batch #: 264  of 300 sample #: 199 reconstruction error: 0.086079\n",
      "Epoch: 0 batch #: 265  of 300 sample #: 199 reconstruction error: 0.071534\n",
      "Epoch: 0 batch #: 266  of 300 sample #: 199 reconstruction error: 0.038130\n",
      "Epoch: 0 batch #: 267  of 300 sample #: 199 reconstruction error: 0.058808\n",
      "Epoch: 0 batch #: 268  of 300 sample #: 199 reconstruction error: 0.026686\n",
      "Epoch: 0 batch #: 269  of 300 sample #: 199 reconstruction error: 0.083501\n",
      "Epoch: 0 batch #: 270  of 300 sample #: 199 reconstruction error: 0.061873\n",
      "Epoch: 0 batch #: 271  of 300 sample #: 199 reconstruction error: 0.048259\n",
      "Epoch: 0 batch #: 272  of 300 sample #: 199 reconstruction error: 0.053403\n",
      "Epoch: 0 batch #: 273  of 300 sample #: 199 reconstruction error: 0.042748\n",
      "Epoch: 0 batch #: 274  of 300 sample #: 199 reconstruction error: 0.048604\n",
      "Epoch: 0 batch #: 275  of 300 sample #: 199 reconstruction error: 0.095824\n",
      "Epoch: 0 batch #: 276  of 300 sample #: 199 reconstruction error: 0.065233\n",
      "Epoch: 0 batch #: 277  of 300 sample #: 199 reconstruction error: 0.071628\n",
      "Epoch: 0 batch #: 278  of 300 sample #: 199 reconstruction error: 0.061441\n",
      "Epoch: 0 batch #: 279  of 300 sample #: 199 reconstruction error: 0.054002\n",
      "Epoch: 0 batch #: 280  of 300 sample #: 199 reconstruction error: 0.071657\n",
      "Epoch: 0 batch #: 281  of 300 sample #: 199 reconstruction error: 0.069717\n",
      "Epoch: 0 batch #: 282  of 300 sample #: 199 reconstruction error: 0.115685\n",
      "Epoch: 0 batch #: 283  of 300 sample #: 199 reconstruction error: 0.048742\n",
      "Epoch: 0 batch #: 284  of 300 sample #: 199 reconstruction error: 0.056165\n",
      "Epoch: 0 batch #: 285  of 300 sample #: 199 reconstruction error: 0.063735\n",
      "Epoch: 0 batch #: 286  of 300 sample #: 199 reconstruction error: 0.084089\n",
      "Epoch: 0 batch #: 287  of 300 sample #: 199 reconstruction error: 0.078973\n",
      "Epoch: 0 batch #: 288  of 300 sample #: 199 reconstruction error: 0.037526\n",
      "Epoch: 0 batch #: 289  of 300 sample #: 199 reconstruction error: 0.092965\n",
      "Epoch: 0 batch #: 290  of 300 sample #: 199 reconstruction error: 0.096408\n",
      "Epoch: 0 batch #: 291  of 300 sample #: 199 reconstruction error: 0.090726\n",
      "Epoch: 0 batch #: 292  of 300 sample #: 199 reconstruction error: 0.083968\n",
      "Epoch: 0 batch #: 293  of 300 sample #: 199 reconstruction error: 0.055275\n",
      "Epoch: 0 batch #: 294  of 300 sample #: 199 reconstruction error: 0.087278\n",
      "Epoch: 0 batch #: 295  of 300 sample #: 199 reconstruction error: 0.065448\n",
      "Epoch: 0 batch #: 296  of 300 sample #: 199 reconstruction error: 0.027704\n",
      "Epoch: 0 batch #: 297  of 300 sample #: 199 reconstruction error: 0.105552\n",
      "Epoch: 0 batch #: 298  of 300 sample #: 199 reconstruction error: 0.050852\n",
      "Epoch: 0 batch #: 299  of 300 sample #: 199 reconstruction error: 0.047319\n",
      "Epoch: 0 batch #: 300  of 300 sample #: 199 reconstruction error: 0.084275\n"
     ]
    }
   ],
   "source": [
    "#Parameters\n",
    "alpha = 0.01\n",
    "epochs = 1\n",
    "batchsize = 200\n",
    "weights = []\n",
    "errors = []\n",
    "batch_number = 0\n",
    "K = 1\n",
    "\n",
    "#creating datasets\n",
    "train_ds = \\\n",
    "    tf.data.Dataset.from_tensor_slices((trX, trY)).batch(batchsize)\n",
    "\n",
    "for epoch in range(epochs):\n",
    "    for batch_x, batch_y in train_ds:\n",
    "        batch_number += 1\n",
    "        for i_sample in range(batchsize):           \n",
    "            for k in range(K):\n",
    "                v0_state = batch_x[i_sample]\n",
    "                h0_state = hidden_layer(v0_state, W, hb)\n",
    "                v1_state = reconstructed_output(h0_state, W, vb)\n",
    "                h1_state = hidden_layer(v1_state, W, hb)\n",
    "\n",
    "                delta_W = tf.matmul(tf.transpose([v0_state]), h0_state) - tf.matmul(tf.transpose([v1_state]), h1_state)\n",
    "                W = W + alpha * delta_W\n",
    "\n",
    "                vb = vb + alpha * tf.reduce_mean(v0_state - v1_state, 0)\n",
    "                hb = hb + alpha * tf.reduce_mean(h0_state - h1_state, 0) \n",
    "\n",
    "                v0_state = v1_state\n",
    "\n",
    "            if i_sample == batchsize-1:\n",
    "                err = error(batch_x[i_sample], v1_state)\n",
    "                errors.append(err)\n",
    "                weights.append(W)\n",
    "                print ( 'Epoch: %d' % epoch, \n",
    "                       \"batch #: %i \" % batch_number, \"of %i\" % int(60e3/batchsize), \n",
    "                       \"sample #: %i\" % i_sample,\n",
    "                       'reconstruction error: %f' % err)\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's take a look at the errors at the end of each batch:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "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 matrix $W$ after training?\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-0.28       -0.44999984 -0.28       ... -0.20000002 -0.42999986\n",
      "  -0.23000003]\n",
      " [-0.21000002 -0.41999987 -0.22000003 ... -0.29999998 -0.5199998\n",
      "  -0.20000002]\n",
      " [-0.18       -0.3999999  -0.12999998 ... -0.21000002 -0.43999985\n",
      "  -0.18      ]\n",
      " ...\n",
      " [-0.22000003 -0.43999985 -0.20000002 ... -0.29999998 -0.5099998\n",
      "  -0.17      ]\n",
      " [-0.20000002 -0.44999984 -0.14999999 ... -0.21000002 -0.45999983\n",
      "  -0.25000003]\n",
      " [-0.20000002 -0.34999993 -0.19000001 ... -0.28       -0.44999984\n",
      "  -0.24000004]]\n"
     ]
    }
   ],
   "source": [
    "print(W.numpy()) # a weight matrix of shape (50,784)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<a id=\"ref5\"></a>\n",
    "<h3>Learned features</h3> \n"
   ]
  },
  {
   "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.\n"
   ]
  },
  {
   "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 transforms the <b>uw</b> (with one flattened image per row of size 784), into an array (of size $28\\times28$) in which images are reshaped and laid out like tiles on a floor.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1800x1800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "utils.tile_raster_images(X=W.numpy().T, img_shape=(28, 28), tile_shape=(5, 10), tile_spacing=(1, 1))\n",
    "import matplotlib.pyplot as plt\n",
    "from PIL import Image\n",
    "%matplotlib inline\n",
    "image = Image.fromarray(utils.tile_raster_images(X=W.numpy().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. \n"
   ]
  },
  {
   "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.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from PIL import Image\n",
    "image = Image.fromarray(utils.tile_raster_images(X =W.numpy().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:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--2023-05-15 16:50:01--  https://ibm.box.com/shared/static/vvm1b63uvuxq88vbw9znpwu5ol380mco.jpg\n",
      "Resolving ibm.box.com (ibm.box.com)... 74.112.186.144\n",
      "Connecting to ibm.box.com (ibm.box.com)|74.112.186.144|:443... connected.\n",
      "HTTP request sent, awaiting response... 301 Moved Permanently\n",
      "Cookie coming from ibm.box.com attempted to set domain to box.net\n",
      "Location: /public/static/vvm1b63uvuxq88vbw9znpwu5ol380mco.jpg [following]\n",
      "--2023-05-15 16:50:01--  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",
      "Cookie coming from ibm.box.com attempted to set domain to box.net\n",
      "Location: https://ibm.ent.box.com/public/static/vvm1b63uvuxq88vbw9znpwu5ol380mco.jpg [following]\n",
      "--2023-05-15 16:50:02--  https://ibm.ent.box.com/public/static/vvm1b63uvuxq88vbw9znpwu5ol380mco.jpg\n",
      "Resolving ibm.ent.box.com (ibm.ent.box.com)... 74.112.186.144\n",
      "Connecting to ibm.ent.box.com (ibm.ent.box.com)|74.112.186.144|:443... connected.\n",
      "HTTP request sent, awaiting response... 302 Found\n",
      "Cookie coming from ibm.ent.box.com attempted to set domain to box.net\n",
      "Location: https://public.boxcloud.com/d/1/b1!hEdqfLnzT_HAbjGQbijaH6Rr4I2K5aXjuYeR7KCcIwAae-YS4PPg0kp3dDAaMZDhIXheJI2JIa7MtDnCG0ISc2npA4gOFosZVUBClrOUdI13VrZp5VYFfk5ZeRFCUgveB8ikrI2zphQPMse0s-p2JM7cYsk4dzBlFsYP-kvoutYoES5-PxZUZBZ92zdJXFZ5Qn17H8ugmmK5cFLjVnkmHKQFFGWZzIRp6EeN3ZW6bR9o_X3qMOeQGlz50ScytitTHenDmfvg1JlkoZKLtjEdUQU6eBrNU-JvAJx0HuLhl73vPMtRKXZhqqG047XU1JC-_wBn1pH2m34gk0WwJi5Ltj1kYhfOYgj3jD3iGSXhGtlhH1PEIYi4L5-0xT3Hmpr611Dt3GKcot7EU54WoqQQJfEBcURaNNvyyP7r72WK0cKEsrw83W0ow9zHwL1zllVc8iZnUeaOtseCiZMhurH6eZetr66UxLG6AVWJTrouEeJeyTvaQnb0Jkg_w5zF01yMrosCAnGAgiER3psQeCYXvyuu_E9GMcYFwrhZ3qhhP2Q6NFi5-8jrfG7606U5BPeICoaxTE6crSW3TTmJU8VmwQVWJ7UCPMD9OssecD_kguNX4pj69zrGrFTuRhWnWuulQeGHjK4B9yrzCi3_PlgTecm8WFKbsqnZKrVuffdtJBclDZ4pNwnnlAvBEi1nMLlzekaMn7vtT7LbWtCS63EBEhVahk1EG85-urR3AQ0SWyhlW-gcbsoAh0-IMtCDL0x9wYOlnxzRcw1oMWq4Jy6-8GQix7XbqkJAAH6_OTO0aX5LDZ_5iDk0xWch4RrW5kc1D7d581NbE4hXKgp8CgWitOWycKs8uUiWEYNlBLBIIIN9nIvbYr2XrrJe3gZLdGsJzuRtIaZx8plHhRCxoIq2TWahIUf9BUSqAoDAChSo-KYURa3S2KsHvd7qI8MrKOHkg3Fw3_Dna0kCeMZNpuin1VytzHQMaPvn4ODJ4vaLUSkQE8PZjA0wZPssotKqBZjGwMVqk9jL5e-t9M08uugGBqlOYjuVOWhNlFOVrX5f0YFwXh3monNA180JUNCj4E6uyIJBuMRM5FftYoEMUkc6Zhq0lROc6wQG7G1BgS-0D93th_Z_royAcwle5_A_mSgKeVSN4BTHf55e85zYEWT-PWUELWgXWWgm3yRDUb8jHnERXRZPn1etFl-rywIrB8jLnKDzceeLG2AbiUTz6OD3gHVIkasA0mFfzzSOBUdP7GN7XhPh2LzgPVueyF3LoRkKH25fQu4TbEbyySB2kvrvLXSpN-jFbAbjLour4dVipyd9HuPDII782r01diXyhV-xQnzhgSAlgAqkWkreMiviqptCsNDU2po2kRGQQ-WmfWWtOQdyKRpINI949ZAP9oEEmaD_BEcIoEtPl6UU1RUhIRTVn0f6V8M9-xXVSA../download [following]\n",
      "--2023-05-15 16:50:02--  https://public.boxcloud.com/d/1/b1!hEdqfLnzT_HAbjGQbijaH6Rr4I2K5aXjuYeR7KCcIwAae-YS4PPg0kp3dDAaMZDhIXheJI2JIa7MtDnCG0ISc2npA4gOFosZVUBClrOUdI13VrZp5VYFfk5ZeRFCUgveB8ikrI2zphQPMse0s-p2JM7cYsk4dzBlFsYP-kvoutYoES5-PxZUZBZ92zdJXFZ5Qn17H8ugmmK5cFLjVnkmHKQFFGWZzIRp6EeN3ZW6bR9o_X3qMOeQGlz50ScytitTHenDmfvg1JlkoZKLtjEdUQU6eBrNU-JvAJx0HuLhl73vPMtRKXZhqqG047XU1JC-_wBn1pH2m34gk0WwJi5Ltj1kYhfOYgj3jD3iGSXhGtlhH1PEIYi4L5-0xT3Hmpr611Dt3GKcot7EU54WoqQQJfEBcURaNNvyyP7r72WK0cKEsrw83W0ow9zHwL1zllVc8iZnUeaOtseCiZMhurH6eZetr66UxLG6AVWJTrouEeJeyTvaQnb0Jkg_w5zF01yMrosCAnGAgiER3psQeCYXvyuu_E9GMcYFwrhZ3qhhP2Q6NFi5-8jrfG7606U5BPeICoaxTE6crSW3TTmJU8VmwQVWJ7UCPMD9OssecD_kguNX4pj69zrGrFTuRhWnWuulQeGHjK4B9yrzCi3_PlgTecm8WFKbsqnZKrVuffdtJBclDZ4pNwnnlAvBEi1nMLlzekaMn7vtT7LbWtCS63EBEhVahk1EG85-urR3AQ0SWyhlW-gcbsoAh0-IMtCDL0x9wYOlnxzRcw1oMWq4Jy6-8GQix7XbqkJAAH6_OTO0aX5LDZ_5iDk0xWch4RrW5kc1D7d581NbE4hXKgp8CgWitOWycKs8uUiWEYNlBLBIIIN9nIvbYr2XrrJe3gZLdGsJzuRtIaZx8plHhRCxoIq2TWahIUf9BUSqAoDAChSo-KYURa3S2KsHvd7qI8MrKOHkg3Fw3_Dna0kCeMZNpuin1VytzHQMaPvn4ODJ4vaLUSkQE8PZjA0wZPssotKqBZjGwMVqk9jL5e-t9M08uugGBqlOYjuVOWhNlFOVrX5f0YFwXh3monNA180JUNCj4E6uyIJBuMRM5FftYoEMUkc6Zhq0lROc6wQG7G1BgS-0D93th_Z_royAcwle5_A_mSgKeVSN4BTHf55e85zYEWT-PWUELWgXWWgm3yRDUb8jHnERXRZPn1etFl-rywIrB8jLnKDzceeLG2AbiUTz6OD3gHVIkasA0mFfzzSOBUdP7GN7XhPh2LzgPVueyF3LoRkKH25fQu4TbEbyySB2kvrvLXSpN-jFbAbjLour4dVipyd9HuPDII782r01diXyhV-xQnzhgSAlgAqkWkreMiviqptCsNDU2po2kRGQQ-WmfWWtOQdyKRpINI949ZAP9oEEmaD_BEcIoEtPl6UU1RUhIRTVn0f6V8M9-xXVSA../download\n",
      "Resolving public.boxcloud.com (public.boxcloud.com)... 74.112.186.128\n",
      "Connecting to public.boxcloud.com (public.boxcloud.com)|74.112.186.128|: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  --.-KB/s    in 0.002s  \n",
      "\n",
      "2023-05-15 16:50:03 (13.3 MB/s) - ‘destructed3.jpg’ saved [24383/24383]\n",
      "\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<PIL.JpegImagePlugin.JpegImageFile image mode=RGB size=181x181 at 0x7F1CA349C810>"
      ]
     },
     "execution_count": 35,
     "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 neural net:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "tags": []
   },
   "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\n",
    "\n",
    "sample_case = tf.cast(sample_case, dtype=tf.float32)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Feed the sample case into the network and reconstruct the output:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability nodes in hidden layer: tf.Tensor(\n",
      "[[3.0982494e-06 4.4438243e-04 1.0780488e-05 4.9522993e-18 1.0000000e+00\n",
      "  2.8264790e-06 4.2186606e-08 9.9999571e-01 9.0414667e-01 6.8117739e-13\n",
      "  6.3512943e-13 1.0000000e+00 6.0230196e-03 1.9590259e-03 1.0000000e+00\n",
      "  1.7421420e-10 2.4550927e-06 2.0560115e-15 2.3976167e-08 9.9697459e-01\n",
      "  2.2476790e-08 8.9458940e-11 2.5396737e-11 8.1829530e-01 9.9945688e-01\n",
      "  9.9998939e-01 4.2150474e-01 4.5056259e-12 6.3738090e-12 8.6009502e-04\n",
      "  8.8218381e-05 8.9210474e-08 9.9751848e-01 5.4501469e-11 8.8544693e-06\n",
      "  1.0000000e+00 1.0000000e+00 4.8251336e-09 9.9864674e-01 1.3607177e-01\n",
      "  4.1196598e-13 2.6587605e-02 9.9998462e-01 9.9999934e-01 7.8577995e-03\n",
      "  9.8953724e-01 6.9420445e-01 8.9719714e-07 9.9993312e-01 9.3137729e-01]], shape=(1, 50), dtype=float32)\n",
      "activated nodes in hidden layer: tf.Tensor(\n",
      "[[0. 0. 0. 0. 1. 0. 0. 1. 1. 0. 0. 1. 0. 0. 1. 0. 0. 0. 0. 1. 0. 0. 0. 1.\n",
      "  1. 1. 0. 0. 0. 0. 0. 0. 1. 0. 0. 1. 1. 0. 1. 0. 0. 0. 1. 1. 0. 1. 1. 0.\n",
      "  1. 1.]], shape=(1, 50), dtype=float32)\n",
      "tf.Tensor(\n",
      "[[1.22844183e-04 1.45584345e-04 2.62618065e-04 2.17229128e-04\n",
      "  1.22844183e-04 1.34527683e-04 1.54584646e-04 1.07868902e-04\n",
      "  1.25259161e-04 1.18027507e-04 1.35749578e-04 1.64180994e-04\n",
      "  1.50740147e-04 1.66803598e-04 1.14108967e-04 1.19593038e-04\n",
      "  1.96486712e-04 8.23449445e-05 1.69217587e-04 2.15023756e-04\n",
      "  1.41292810e-04 1.41322613e-04 1.70916319e-04 1.96486712e-04\n",
      "  2.10791826e-04 1.35749578e-04 1.29163265e-04 1.15690353e-04\n",
      "  1.65820122e-04 1.65790319e-04 1.22844300e-04 1.50024891e-04\n",
      "  1.20941731e-04 2.15947628e-04 1.46150589e-04 1.13675800e-04\n",
      "  1.63704157e-04 1.92314386e-04 2.11536884e-04 4.12583351e-04\n",
      "  2.98619270e-04 3.37928534e-04 2.92688608e-04 2.24381685e-04\n",
      "  4.40567732e-04 2.70158052e-04 1.85757875e-04 3.01688910e-04\n",
      "  2.65449286e-04 9.91469569e-05 1.40756369e-04 1.83463097e-04\n",
      "  1.57773495e-04 1.24067068e-04 1.04680919e-04 1.34527683e-04\n",
      "  1.22844300e-04 7.83289215e-05 1.57296658e-04 1.71065331e-04\n",
      "  1.72644854e-04 9.85809747e-05 1.71959400e-04 3.78876925e-04\n",
      "  2.20924616e-04 1.65104866e-04 1.60276890e-04 9.79033066e-05\n",
      "  8.93822071e-05 1.63167715e-04 2.77847052e-04 2.37733126e-04\n",
      "  2.86757946e-04 2.66373158e-04 6.30263312e-05 4.51107662e-05\n",
      "  3.28213173e-05 1.09239976e-04 2.77787447e-04 1.47312880e-04\n",
      "  1.84118748e-04 1.05845087e-04 1.21621830e-04 1.42723322e-04\n",
      "  1.59323215e-04 1.79588795e-04 2.02208757e-04 2.11417675e-04\n",
      "  1.36792660e-04 1.63346529e-04 2.82943249e-04 1.04075400e-04\n",
      "  6.55982294e-05 1.68591738e-04 1.75684690e-04 2.96443701e-04\n",
      "  3.49491835e-04 1.18175149e-03 9.47833061e-04 1.12619996e-03\n",
      "  1.78864598e-03 9.45985317e-04 1.08760595e-03 5.07175922e-04\n",
      "  1.43498182e-04 1.58607960e-04 2.11179256e-04 3.35425138e-04\n",
      "  2.62379646e-04 2.26527452e-04 8.63025198e-05 1.38550997e-04\n",
      "  2.37643719e-04 2.08854675e-04 1.41888857e-04 1.50918961e-04\n",
      "  2.33530998e-04 6.86198473e-04 5.95152378e-04 5.79774380e-04\n",
      "  4.42802906e-04 8.76337290e-04 1.55925751e-03 3.21784616e-03\n",
      "  3.76033783e-03 7.88137317e-03 2.13529170e-02 5.81859648e-02\n",
      "  4.14452255e-02 1.97549164e-02 1.91928446e-02 8.53839517e-03\n",
      "  2.18722224e-03 1.97851658e-03 3.12206149e-03 4.52440977e-03\n",
      "  1.69003010e-03 4.75496054e-04 1.25676394e-04 1.12911497e-04\n",
      "  2.54869461e-04 1.50024891e-04 2.80380249e-04 3.27885151e-04\n",
      "  5.89787960e-04 5.44250011e-04 1.15647912e-03 5.26905060e-03\n",
      "  8.37659836e-03 1.29459202e-02 6.04752302e-02 6.97268844e-02\n",
      "  3.91281664e-01 6.61941767e-01 8.07901561e-01 8.53737831e-01\n",
      "  7.78009415e-01 7.00342357e-01 4.67214108e-01 2.09283799e-01\n",
      "  1.40934259e-01 7.32059181e-02 3.52505445e-02 6.85995817e-03\n",
      "  2.78559327e-03 9.34660435e-04 2.64674425e-04 1.52289867e-04\n",
      "  1.07868902e-04 1.68353319e-04 1.53213739e-04 5.51521778e-04\n",
      "  1.78655982e-03 1.94135308e-03 6.15978241e-03 1.19587481e-02\n",
      "  1.86510682e-02 1.94535881e-01 6.49095118e-01 8.16264272e-01\n",
      "  9.39554870e-01 9.76199090e-01 9.64333117e-01 9.58674908e-01\n",
      "  9.38338280e-01 9.33214664e-01 8.82574677e-01 8.17984700e-01\n",
      "  6.97712779e-01 2.60923386e-01 6.60022199e-02 3.25520039e-02\n",
      "  4.57048416e-03 1.17859244e-03 7.75307417e-04 1.54703856e-04\n",
      "  2.54034996e-04 1.40041113e-04 4.12493944e-04 1.29303336e-03\n",
      "  4.12985682e-03 6.59301877e-03 8.84094834e-03 4.56732213e-02\n",
      "  1.57861888e-01 3.83201867e-01 7.32272625e-01 9.12208915e-01\n",
      "  9.60179448e-01 9.16011214e-01 7.21092939e-01 8.27533424e-01\n",
      "  5.22908807e-01 5.42051673e-01 7.46871769e-01 9.18501794e-01\n",
      "  9.45250034e-01 4.49046820e-01 1.14220411e-01 1.45037770e-02\n",
      "  1.84193254e-03 3.51160765e-04 4.17441130e-04 1.51604414e-04\n",
      "  1.91926956e-04 2.16394663e-04 4.75853682e-04 1.32191181e-03\n",
      "  5.53944707e-03 1.80399120e-02 2.35297680e-02 1.42523915e-01\n",
      "  1.67089224e-01 5.20724714e-01 7.76944160e-01 7.29285777e-01\n",
      "  5.44030309e-01 2.64406264e-01 1.28759980e-01 6.39154315e-02\n",
      "  3.52836251e-02 7.26621151e-02 2.95499563e-01 8.90867770e-01\n",
      "  9.38922882e-01 5.96570671e-01 1.21246874e-01 6.94522262e-03\n",
      "  1.29017234e-03 3.91960144e-04 3.09228897e-04 1.75237656e-04\n",
      "  1.59621239e-04 1.18802993e-04 1.82420015e-04 1.16315484e-03\n",
      "  2.87368894e-03 1.33359134e-02 2.11273730e-02 8.99889469e-02\n",
      "  2.11050242e-01 2.45989710e-01 2.42488325e-01 3.23899090e-01\n",
      "  8.31000209e-02 1.85974538e-02 4.71216440e-03 4.43145633e-03\n",
      "  4.96280193e-03 4.64612544e-02 2.28816003e-01 8.36814642e-01\n",
      "  9.03275251e-01 7.65911222e-01 1.51252747e-01 9.11077857e-03\n",
      "  2.64456868e-03 5.66810369e-04 4.83393669e-04 1.10493515e-04\n",
      "  1.71512365e-04 1.42514706e-04 3.18855047e-04 6.76900148e-04\n",
      "  2.34934688e-03 5.31262159e-03 1.31152868e-02 4.31436300e-02\n",
      "  3.85551751e-02 2.98192799e-02 1.07360452e-01 2.55286098e-02\n",
      "  8.46812129e-03 4.35686111e-03 3.25939059e-03 7.91907310e-03\n",
      "  3.46772969e-02 2.96709120e-01 8.15600932e-01 9.31604862e-01\n",
      "  8.40487123e-01 4.10793066e-01 8.84932876e-02 9.44316387e-03\n",
      "  2.17363238e-03 5.57214022e-04 3.48776579e-04 1.46180391e-04\n",
      "  1.60604715e-04 1.73598528e-04 2.75522470e-04 5.78284264e-04\n",
      "  2.40069628e-03 6.76637888e-03 8.50319862e-03 6.54631853e-03\n",
      "  1.11094415e-02 8.26811790e-03 1.20851696e-02 7.97024369e-03\n",
      "  1.68879628e-02 1.70195103e-02 1.06638640e-01 2.20456392e-01\n",
      "  5.31571567e-01 8.43107462e-01 8.95601273e-01 7.24745095e-01\n",
      "  4.38499749e-01 7.64561892e-02 1.95772350e-02 4.47651744e-03\n",
      "  1.88913941e-03 7.36176968e-04 1.94102526e-04 9.25492786e-05\n",
      "  2.46852636e-04 2.56210566e-04 4.44471836e-04 3.37630510e-04\n",
      "  7.45892525e-04 4.08357382e-03 5.20437956e-03 4.06965613e-03\n",
      "  2.31832266e-03 5.62766194e-03 6.81644678e-03 1.95544362e-02\n",
      "  1.08559459e-01 5.61935484e-01 8.00501287e-01 8.70295882e-01\n",
      "  8.87350440e-01 9.01144803e-01 7.13246703e-01 3.55970144e-01\n",
      "  4.48634028e-02 1.73809230e-02 1.20392740e-02 1.63820386e-03\n",
      "  6.84946775e-04 4.01675701e-04 2.26497650e-04 1.26957893e-04\n",
      "  1.48236752e-04 1.53541565e-04 3.48418951e-04 3.58283520e-04\n",
      "  9.77933407e-04 3.02624702e-03 2.43255496e-03 1.70466304e-03\n",
      "  1.35710835e-03 3.32692266e-03 3.21160555e-02 1.74449593e-01\n",
      "  7.20966816e-01 9.71808791e-01 9.84000921e-01 9.67672288e-01\n",
      "  9.35106397e-01 8.24558318e-01 4.58705872e-01 1.41284883e-01\n",
      "  1.13123655e-02 4.16702032e-03 3.13258171e-03 1.52420998e-03\n",
      "  3.60906124e-04 4.66257334e-04 1.80035830e-04 9.60397301e-05\n",
      "  1.59025192e-04 1.57505274e-04 1.44690275e-04 3.31342220e-04\n",
      "  8.45581293e-04 1.97112560e-03 9.28610563e-04 2.23612785e-03\n",
      "  1.80634856e-03 1.06935501e-02 1.18184656e-01 5.82928956e-01\n",
      "  8.78512681e-01 9.69085634e-01 9.67821598e-01 9.35648978e-01\n",
      "  8.47067416e-01 7.06902623e-01 2.53691196e-01 4.69365716e-02\n",
      "  1.00281537e-02 2.68474221e-03 1.64562464e-03 6.78092241e-04\n",
      "  1.69932842e-04 2.82764435e-04 2.02715397e-04 1.06841704e-04\n",
      "  1.69336796e-04 1.70022249e-04 3.39120626e-04 8.31842422e-04\n",
      "  3.32775712e-03 1.81561708e-03 9.05871391e-04 1.13028288e-03\n",
      "  2.04387307e-03 8.63599777e-03 9.21375751e-02 2.79385686e-01\n",
      "  6.56944931e-01 6.90358520e-01 4.64664221e-01 5.46730638e-01\n",
      "  5.76088130e-01 6.30735874e-01 2.32747048e-01 3.11583877e-02\n",
      "  7.23367929e-03 1.40908360e-03 6.60091639e-04 3.72976065e-04\n",
      "  1.70588493e-04 1.41203403e-04 2.69711018e-04 1.04087514e-04\n",
      "  2.40653753e-04 1.49220228e-04 4.68879938e-04 1.63906813e-03\n",
      "  6.62294030e-03 1.68097019e-03 5.82545996e-03 1.66839361e-03\n",
      "  2.37670541e-03 7.03233480e-03 3.27847302e-02 4.88587320e-02\n",
      "  5.08907735e-02 5.09455800e-02 5.04570007e-02 7.53318965e-02\n",
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      "  1.76787376e-04 1.35958195e-04 2.13623047e-04 1.44034624e-04\n",
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      "  3.55717540e-03 9.76428390e-03 6.50528073e-03 1.65004730e-02\n",
      "  1.53958499e-02 1.70025527e-02 1.29118860e-02 3.21172178e-02\n",
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      "  5.28553128e-02 1.42466426e-02 1.53645873e-03 3.99380922e-04\n",
      "  2.05487013e-04 1.14378185e-04 2.21103430e-04 2.33262777e-04\n",
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      "  1.27077699e-02 1.74759924e-02 1.79652572e-02 1.66071951e-02\n",
      "  1.04404002e-01 7.74187446e-01 7.92796731e-01 6.77805424e-01\n",
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      "  3.26305628e-04 3.87430191e-04 2.55018473e-04 2.31444836e-04\n",
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      "  3.34724188e-02 2.76927054e-02 4.53279614e-02 3.04266512e-02\n",
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      "  2.56910443e-01 7.79190540e-01 8.68788838e-01 4.93827075e-01\n",
      "  6.51964247e-02 1.06888115e-02 6.86764717e-04 5.02288342e-04\n",
      "  1.06766820e-03 6.03497028e-04 2.98321247e-04 2.07155943e-04\n",
      "  1.30474567e-04 2.52187252e-04 3.69837880e-03 1.23161495e-01\n",
      "  3.59159052e-01 2.92758226e-01 3.38428736e-01 3.35320652e-01\n",
      "  1.96729004e-01 1.99941128e-01 1.74852669e-01 1.22768015e-01\n",
      "  1.10231251e-01 6.37616217e-02 3.93075943e-02 2.37956136e-01\n",
      "  3.79407823e-01 6.68636382e-01 6.82926893e-01 3.13101768e-01\n",
      "  1.83411837e-02 2.84773111e-03 1.01700425e-03 8.84681940e-04\n",
      "  2.49382854e-03 7.71760941e-04 6.01410866e-04 1.76012516e-04\n",
      "  1.55419111e-04 1.78754330e-04 3.51130962e-03 1.26173705e-01\n",
      "  3.60777497e-01 5.43475568e-01 6.30137444e-01 5.66200376e-01\n",
      "  5.21526694e-01 1.83763891e-01 3.16011369e-01 2.67755330e-01\n",
      "  2.01005459e-01 1.25227898e-01 1.94931358e-01 1.43294930e-01\n",
      "  5.40521622e-01 6.50925875e-01 2.73198754e-01 4.05721366e-02\n",
      "  7.82665610e-03 1.29514933e-03 6.57826662e-04 1.80283189e-03\n",
      "  2.00086832e-03 1.02707744e-03 3.57538462e-04 2.23428011e-04\n",
      "  1.33693218e-04 1.94787979e-04 2.56928802e-03 2.81822085e-02\n",
      "  4.50981110e-01 5.67242265e-01 7.63654351e-01 8.62650275e-01\n",
      "  5.50130069e-01 4.05740589e-01 4.18742955e-01 4.81850833e-01\n",
      "  3.83863121e-01 3.22231203e-01 2.49776602e-01 2.84700841e-01\n",
      "  3.70730400e-01 2.20483810e-01 1.06880248e-01 2.16012299e-02\n",
      "  5.77467680e-03 1.27598643e-03 1.13144517e-03 2.30386853e-03\n",
      "  1.33377314e-03 7.04020262e-04 7.71189516e-05 1.46180391e-04\n",
      "  1.01587255e-04 1.86920166e-04 4.61369753e-04 1.07416511e-02\n",
      "  1.58470690e-01 5.78036368e-01 8.60349596e-01 9.05345201e-01\n",
      "  7.61188745e-01 6.78812265e-01 6.29251361e-01 6.21671438e-01\n",
      "  4.69822884e-01 4.99311924e-01 4.42850381e-01 3.95377845e-01\n",
      "  1.27918959e-01 5.35416901e-02 3.43501866e-02 1.48070157e-02\n",
      "  4.97072935e-03 1.32474303e-03 6.35355711e-04 6.73800707e-04\n",
      "  5.67734241e-04 2.22682953e-04 2.14606524e-04 1.79648399e-04\n",
      "  1.83254480e-04 1.27881765e-04 2.38329172e-04 1.46737695e-03\n",
      "  1.80826783e-02 1.41378552e-01 3.87527764e-01 5.23037374e-01\n",
      "  6.57625020e-01 6.13942444e-01 3.56862992e-01 3.35341960e-01\n",
      "  1.98223293e-01 6.10933900e-02 5.73782027e-02 4.00795043e-02\n",
      "  4.70950902e-02 2.45716870e-02 1.19875968e-02 7.05397129e-03\n",
      "  1.12539530e-03 5.54710627e-04 4.24176455e-04 2.30520964e-04\n",
      "  4.03612852e-04 1.97052956e-04 1.08714099e-04 1.26630068e-04\n",
      "  1.50024891e-04 1.08953027e-04 1.29669905e-04 1.64002180e-04\n",
      "  4.44859266e-04 1.32316351e-03 4.31597233e-03 2.31043696e-02\n",
      "  3.54812443e-02 2.15242505e-02 1.69878602e-02 1.54633820e-02\n",
      "  6.97493553e-03 5.60501218e-03 4.68289852e-03 9.19231772e-03\n",
      "  5.74618578e-03 2.23776698e-03 1.93712115e-03 7.25626945e-04\n",
      "  2.03669071e-04 3.04073095e-04 2.20686197e-04 1.99317932e-04\n",
      "  1.66326761e-04 2.10195780e-04 1.18337906e-04 1.26630068e-04\n",
      "  1.54584646e-04 1.45584345e-04 1.13399481e-04 1.71035528e-04\n",
      "  1.81436539e-04 4.94122505e-04 6.34163618e-04 8.72552395e-04\n",
      "  9.45776701e-04 5.94973564e-04 6.42925501e-04 2.90572643e-04\n",
      "  2.49117613e-04 1.07372151e-04 7.65775039e-05 1.72674656e-04\n",
      "  1.79588795e-04 2.07394361e-04 2.86906958e-04 2.83837318e-04\n",
      "  1.98066235e-04 2.22712755e-04 8.77633865e-05 1.58786774e-04\n",
      "  1.05563129e-04 1.17851596e-04 1.76101923e-04 2.15023756e-04\n",
      "  1.13399583e-04 1.51574612e-04 1.54584646e-04 1.79648399e-04\n",
      "  1.28597021e-04 1.33752823e-04 2.27987766e-04 1.73002481e-04\n",
      "  4.26322222e-04 3.55482101e-04 4.96476889e-04 3.97413969e-04\n",
      "  2.53260136e-04 2.16513872e-04 1.66922808e-04 2.19583511e-04\n",
      "  3.37779522e-04 3.89456749e-04 3.10748816e-04 9.04538465e-05\n",
      "  1.05629399e-04 1.26093626e-04 3.82542610e-04 1.42514706e-04\n",
      "  1.11154077e-04 1.41292810e-04 1.72585249e-04 1.57773495e-04]], shape=(1, 784), dtype=float32)\n"
     ]
    }
   ],
   "source": [
    "hh0_p = tf.nn.sigmoid(tf.matmul(sample_case, W) + hb)\n",
    "hh0_s = tf.round(hh0_p)\n",
    "\n",
    "print(\"Probability nodes in hidden layer:\" ,hh0_p)\n",
    "print(\"activated nodes in hidden layer:\" ,hh0_s)\n",
    "\n",
    "# reconstruct\n",
    "vv1_p = tf.nn.sigmoid(tf.matmul(hh0_s, tf.transpose(W)) + vb)\n",
    "\n",
    "print(vv1_p)\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:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "ename": "NameError",
     "evalue": "name 'tile_raster_images' is not defined",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mNameError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m/tmp/ipykernel_68/3803996827.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mimg\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mImage\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfromarray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtile_raster_images\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mvv1_p\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnumpy\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mimg_shape\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m28\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m28\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mtile_shape\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtile_spacing\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m)\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[0m\u001b[1;32m      2\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrcParams\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'figure.figsize'\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;36m4.0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m4.0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0mimgplot\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mimshow\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mimg\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mimgplot\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mset_cmap\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'gray'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mNameError\u001b[0m: name 'tile_raster_images' is not defined"
     ]
    }
   ],
   "source": [
    "img = Image.fromarray(tile_raster_images(X=vv1_p.numpy(), 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": [
    "<hr>\n",
    "\n",
    "## Want to learn more?\n",
    "\n",
    "Also, you can use __Watson Studio__ to run these notebooks faster with bigger datasets.__Watson Studio__ is IBM’s leading cloud solution for data scientists, built by data scientists. With Jupyter notebooks, RStudio, Apache Spark and popular libraries pre-packaged in the cloud, __Watson Studio__ enables data scientists to collaborate on their projects without having to install anything. Join the fast-growing community of __Watson Studio__ users today with a free account at [Watson Studio](https://cocl.us/ML0120EN_DSX).This is the end of this lesson. Thank you for reading this notebook, and good luck on your studies.\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Thanks for completing this lesson!\n",
    "\n",
    "Notebook created by: <a href = \"https://ca.linkedin.com/in/saeedaghabozorgi?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkDL0120ENSkillsNetwork954-2022-01-01\">Saeed Aghabozorgi</a>\n",
    "\n",
    "Updated to TF 2.X by  <a href=\"https://ca.linkedin.com/in/nilmeier?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkDL0120ENSkillsNetwork954-2022-01-01\"> Jerome Nilmeier</a><br />\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### References:\n",
    "https://en.wikipedia.org/wiki/Restricted_Boltzmann_machine  \n",
    "http://deeplearning.net/tutorial/rbm.html  \n",
    "http://www.cs.utoronto.ca/~hinton/absps/netflixICML.pdf<br>\n",
    "http://imonad.com/rbm/restricted-boltzmann-machine/  \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<hr>\n",
    "\n",
    "Copyright &copy; 2018 [Cognitive Class](https://cocl.us/DX0108EN_CC). This notebook and its source code are released under the terms of the [MIT License](https://bigdatauniversity.com/mit-license/?utm_medium=Exinfluencer&utm_source=Exinfluencer&utm_content=000026UJ&utm_term=10006555&utm_id=NA-SkillsNetwork-Channel-SkillsNetworkCoursesIBMDeveloperSkillsNetworkDL0120ENSkillsNetwork954-2022-01-01).\n"
   ]
  }
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