learning.ipynb

    "### Implementation\n",
    "\n",
    "The implementation of the Naive Bayes Classifier is split in two; Discrete and Continuous. The user can choose between them with the argument `continuous`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Discrete\n",
    "\n",
    "The implementation for discrete values counts how many times each feature value occurs for each class, and how many times each class occurs. The results are stored in a `CountinProbDist` object."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With the below code you can see the probabilities of the class \"Setosa\" appearing in the dataset and the probability of the first feature (at index 0) of the same class having a value of 5. Notice that the second probability is relatively small, even though if we observe the dataset we will find that a lot of values are around 5. The issue arises because the features in the Iris dataset are continuous, and we are assuming they are discrete. If the features were discrete (for example, \"Tall\", \"3\", etc.) this probably wouldn't have been the case and we would see a much nicer probability distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.3333333333333333\n",
      "0.10588235294117647\n"
     ]
    }
   ],
   "source": [
    "dataset = iris\n",
    "\n",
    "target_vals = dataset.values[dataset.target]\n",
    "target_dist = CountingProbDist(target_vals)\n",
    "attr_dists = {(gv, attr): CountingProbDist(dataset.values[attr])\n",
    "              for gv in target_vals\n",
    "              for attr in dataset.inputs}\n",
    "for example in dataset.examples:\n",
    "        targetval = example[dataset.target]\n",
    "        target_dist.add(targetval)\n",
    "        for attr in dataset.inputs:\n",
    "            attr_dists[targetval, attr].add(example[attr])\n",
    "\n",
    "\n",
    "print(target_dist['setosa'])\n",
    "print(attr_dists['setosa', 0][5.0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First we found the different values for the classes (called targets here) and calculated their distribution. Next we initialized a dictionary of `CountingProbDist` objects, one for each class and feature. Finally, we iterated through the examples in the dataset and calculated the needed probabilites.\n",
    "\n",
    "Having calculated the different probabilities, we will move on to the predicting function. It will receive as input an item and output the most likely class. Using the above formula, it will multiply the probability of the class appearing, with the probability of each feature value appearing in the class. It will return the max result."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "setosa\n"
     ]
    }
   ],
   "source": [
    "def predict(example):\n",
    "    def class_probability(targetval):\n",
    "        return (target_dist[targetval] *\n",
    "                product(attr_dists[targetval, attr][example[attr]]\n",
    "                        for attr in dataset.inputs))\n",
    "    return argmax(target_vals, key=class_probability)\n",
    "\n",
    "\n",
    "print(predict([5, 3, 1, 0.1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can view the complete code by executing the next line:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%psource NaiveBayesDiscrete"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Continuous\n",
    "\n",
    "In the implementation we use the Gaussian/Normal distribution function. To make it work, we need to find the means and standard deviations of features for each class. We make use of the `find_means_and_deviations` Dataset function. On top of that, we will also calculate the class probabilities as we did with the Discrete approach."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[5.006, 3.418, 1.464, 0.244]\n",
      "[0.5161711470638634, 0.3137983233784114, 0.46991097723995795, 0.19775268000454405]\n"
     ]
    }
   ],
   "source": [
    "means, deviations = dataset.find_means_and_deviations()\n",
    "\n",
    "target_vals = dataset.values[dataset.target]\n",
    "target_dist = CountingProbDist(target_vals)\n",
    "\n",
    "\n",
    "print(means[\"setosa\"])\n",
    "print(deviations[\"versicolor\"])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "You can see the means of the features for the \"Setosa\" class and the deviations for \"Versicolor\".\n",
    "\n",
    "The prediction function will work similarly to the Discrete algorithm. It will multiply the probability of the class occuring with the conditional probabilities of the feature values for the class.\n",
    "\n",
    "Since we are using the Gaussian distribution, we will input the value for each feature into the Gaussian function, together with the mean and deviation of the feature. This will return the probability of the particular feature value for the given class. We will repeat for each class and pick the max value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "setosa\n"
     ]
    }
   ],
   "source": [
    "def predict(example):\n",
    "    def class_probability(targetval):\n",
    "        prob = target_dist[targetval]\n",
    "        for attr in dataset.inputs:\n",
    "            prob *= gaussian(means[targetval][attr], deviations[targetval][attr], example[attr])\n",
    "        return prob\n",
    "\n",
    "    return argmax(target_vals, key=class_probability)\n",
    "\n",
    "\n",
    "print(predict([5, 3, 1, 0.1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The complete code of the continuous algorithm:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%psource NaiveBayesContinuous"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Examples\n",
    "\n",
    "We will now use the Naive Bayes Classifier (Discrete and Continuous) to classify items:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Discrete Classifier\n",
      "setosa\n",
      "versicolor\n",
      "versicolor\n",
      "\n",
      "Continuous Classifier\n",
      "setosa\n",
      "versicolor\n",
      "virginica\n"
     ]
    }
   ],
   "source": [
    "nBD = NaiveBayesLearner(iris, continuous=False)\n",
    "print(\"Discrete Classifier\")\n",
    "print(nBD([5, 3, 1, 0.1]))\n",
    "print(nBD([6, 5, 3, 1.5]))\n",
    "print(nBD([7, 3, 6.5, 2]))\n",
    "\n",
    "\n",
    "nBC = NaiveBayesLearner(iris, continuous=True)\n",
    "print(\"\\nContinuous Classifier\")\n",
    "print(nBC([5, 3, 1, 0.1]))\n",
    "print(nBC([6, 5, 3, 1.5]))\n",
    "print(nBC([7, 3, 6.5, 2]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice how the Discrete Classifier misclassified the second item, while the Continuous one had no problem."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Perceptron Classifier\n",
    "\n",
    "### Overview\n",
    "\n",
    "The Perceptron is a linear classifier. It works the same way as a neural network with no hidden layers (just input and output). First it trains its weights given a dataset and then it can classify a new item by running it through the network.\n",
    "\n",
    "Its input layer consists of the the item features, while the output layer consists of nodes (also called neurons). Each node in the output layer has *n* synapses (for every item feature), each with its own weight. Then, the nodes find the dot product of the item features and the synapse weights. These values then pass through an activation function (usually a sigmoid). Finally, we pick the largest of the values and we return its index.\n",
    "\n",
    "Note that in classification problems each node represents a class. The final classification is the class/node with the max output value.\n",
    "\n",
    "Below you can see a single node/neuron in the outer layer. With *f* we denote the item features, with *w* the synapse weights, then inside the node we have the dot product and the activation function, *g*."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![perceptron](images/perceptron.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implementation\n",
    "\n",
    "First, we train (calculate) the weights given a dataset, using the `BackPropagationLearner` function of `learning.py`. We then return a function, `predict`, which we will use in the future to classify a new item. The function computes the (algebraic) dot product of the item with the calculated weights for each node in the outer layer. Then it picks the greatest value and classifies the item in the corresponding class."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%psource PerceptronLearner"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that the Perceptron is a one-layer neural network, without any hidden layers. So, in `BackPropagationLearner`, we will pass no hidden layers. From that function we get our network, which is just one layer, with the weights calculated.\n",
    "\n",
    "That function `predict` passes the input/example through the network, calculating the dot product of the input and the weights for each node and returns the class with the max dot product."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example\n",
    "\n",
    "We will train the Perceptron on the iris dataset. Because though the `BackPropagationLearner` works with integer indexes and not strings, we need to convert class names to integers. Then, we will try and classify the item/flower with measurements of 5, 3, 1, 0.1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n"
     ]
    }
   ],
   "source": [
    "iris = DataSet(name=\"iris\")\n",
    "iris.classes_to_numbers()\n",
    "\n",
    "perceptron = PerceptronLearner(iris)\n",
    "print(perceptron([5, 3, 1, 0.1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The correct output is 0, which means the item belongs in the first class, \"setosa\". Note that the Perceptron algorithm is not perfect and may produce false classifications."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Neural Network\n",
    "\n",
    "### Overview\n",
    "\n",
    "Although the Perceptron may seem like a good way to make classifications, it is a linear classifier (which, roughly, means it can only draw straight lines to divide spaces) and therefore it can be stumped by more complex problems. We can extend Perceptron to solve this issue, by employing multiple layers of its functionality. The construct we are left with is called a Neural Network, or a Multi-Layer Perceptron, and it is a non-linear classifier. It achieves that by combining the results of linear functions on each layer of the network.\n",
    "\n",
    "Similar to the Perceptron, this network also has an input and output layer. However it can also have a number of hidden layers. These hidden layers are responsible for the non-linearity of the network. The layers are comprised of nodes. Each node in a layer (excluding the input one), holds some values, called *weights*, and takes as input the output values of the previous layer. The node then calculates the dot product of its inputs and its weights and then activates it with an *activation function* (sometimes a sigmoid). Its output is fed to the nodes of the next layer. Note that sometimes the output layer does not use an activation function, or uses a different one from the rest of the network. The process of passing the outputs down the layer is called *feed-forward*.\n",
    "\n",
    "After the input values are fed-forward into the network, the resulting output can be used for classification. The problem at hand now is how to train the network (ie. adjust the weights in the nodes). To accomplish that we utilize the *Backpropagation* algorithm. In short, it does the opposite of what we were doing up to now. Instead of feeding the input forward, it will feed the error backwards. So, after we make a classification, we check whether it is correct or not, and how far off we were. We then take this error and propagate it backwards in the network, adjusting the weights of the nodes accordingly. We will run the algorithm on the given input/dataset for a fixed amount of time, or until we are satisfied with the results. The number of times we will iterate over the dataset is called *epochs*. In a later section we take a detailed look at how this algorithm works.\n",
    "\n",
    "NOTE: Sometimes we add to the input of each layer another node, called *bias*. This is a constant value that will be fed to the next layer, usually set to 1. The bias generally helps us \"shift\" the computed function to the left or right."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![neural_net](images/neural_net.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implementation\n",
    "\n",
    "The `NeuralNetLearner` function takes as input a dataset to train upon, the learning rate (in (0, 1]), the number of epochs and finally the size of the hidden layers. This last argument is a list, with each element corresponding to one hidden layer.\n",
    "\n",
    "After that we will create our neural network in the `network` function. This function will make the necessary connections between the input layer, hidden layer and output layer. With the network ready, we will use the `BackPropagationLearner` to train the weights of our network for the examples provided in the dataset.\n",
    "\n",
    "The NeuralNetLearner returns the `predict` function, which can receive an example and feed-forward it into our network to generate a prediction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%psource NeuralNetLearner"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Backpropagation\n",
    "\n",
    "In both the Perceptron and the Neural Network, we are using the Backpropagation algorithm to train our weights. Basically it achieves that by propagating the errors from our last layer into our first layer, this is why it is called Backpropagation. In order to use Backpropagation, we need a cost function. This function is responsible for indicating how good our neural network is for a given example. One common cost function is the *Mean Squared Error* (MSE). This cost function has the following format:\n",
    "\n",
    "$$MSE=\\frac{1}{2} \\sum_{i=1}^{n}(y - \\hat{y})^{2}$$\n",
    "\n",
    "Where `n` is the number of training examples, $\\hat{y}$ is our prediction and $y$ is the correct prediction for the example.\n",
    "\n",
    "The algorithm combines the concept of partial derivatives and the chain rule to generate the gradient for each weight in the network based on the cost function.\n",
    "\n",
    "For example, if we are using a Neural Network with three layers, the sigmoid function as our activation function and the MSE cost function, we want to find the gradient for the a given weight $w_{j}$, we can compute it like this:\n",
    "\n",
    "$$\\frac{\\partial MSE(\\hat{y}, y)}{\\partial w_{j}} = \\frac{\\partial MSE(\\hat{y}, y)}{\\partial \\hat{y}}\\times\\frac{\\partial\\hat{y}(in_{j})}{\\partial in_{j}}\\times\\frac{\\partial in_{j}}{\\partial w_{j}}$$\n",
    "\n",
    "Solving this equation, we have:\n",
    "\n",
    "$$\\frac{\\partial MSE(\\hat{y}, y)}{\\partial w_{j}} = (\\hat{y} - y)\\times{\\hat{y}}'(in_{j})\\times a_{j}$$\n",
    "\n",
    "Remember that $\\hat{y}$ is the activation function applied to a neuron in our hidden layer, therefore $$\\hat{y} = sigmoid(\\sum_{i=1}^{num\\_neurons}w_{i}\\times a_{i})$$\n",
    "\n",
    "Also $a$ is the input generated by feeding the input layer variables into the hidden layer.\n",
    "\n",
    "We can use the same technique for the weights in the input layer as well. After we have the gradients for both weights, we use gradient descent to update the weights of the network."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Implementation\n",
    "\n",
    "First, we feed-forward the examples in our neural network. After that, we calculate the gradient for each layer weights. Once that is complete, we update all the weights using gradient descent. After running these for a given number of epochs, the function returns the trained Neural Network."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%psource BackPropagationLearner"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n"
     ]
    }
   ],
   "source": [
    "iris = DataSet(name=\"iris\")\n",
    "iris.classes_to_numbers()\n",
    "\n",
    "nNL = NeuralNetLearner(iris)\n",
    "print(nNL([5, 3, 1, 0.1]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The output should be 0, which means the item should get classified in the first class, \"setosa\". Note that since the algorithm is non-deterministic (because of the random initial weights) the classification might be wrong. Usually though it should be correct.\n",
    "\n",
    "To increase accuracy, you can (most of the time) add more layers and nodes. Unfortunately the more layers and nodes you have, the greater the computation cost."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## MNIST Handwritten Digits Classification\n",
    "\n",
    "The MNIST database, available from [this page](http://yann.lecun.com/exdb/mnist/), is a large database of handwritten digits that is commonly used for training and testing/validating in Machine learning.\n",
    "\n",
    "The dataset has **60,000 training images** each of size 28x28 pixels with labels and **10,000 testing images** of size 28x28 pixels with labels.\n",
    "\n",
    "In this section, we will use this database to compare performances of different learning algorithms.\n",
    "\n",
    "It is estimated that humans have an error rate of about **0.2%** on this problem. Let's see how our algorithms perform!\n",
    "\n",
    "NOTE: We will be using external libraries to load and visualize the dataset smoothly ([numpy](http://www.numpy.org/) for loading and [matplotlib](http://matplotlib.org/) for visualization). You do not need previous experience of the libraries to follow along."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Loading MNIST digits data\n",
    "\n",
    "Let's start by loading MNIST data into numpy arrays."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import os, struct\n",
    "import array\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from collections import Counter\n",
    "\n",
    "%matplotlib inline\n",
    "plt.rcParams['figure.figsize'] = (10.0, 8.0)\n",
    "plt.rcParams['image.interpolation'] = 'nearest'\n",
    "plt.rcParams['image.cmap'] = 'gray'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def load_MNIST(path=\"aima-data/MNIST\"):\n",
    "    \"helper function to load MNIST data\"\n",
    "    train_img_file = open(os.path.join(path, \"train-images-idx3-ubyte\"), \"rb\")\n",
    "    train_lbl_file = open(os.path.join(path, \"train-labels-idx1-ubyte\"), \"rb\")\n",
    "    test_img_file = open(os.path.join(path, \"t10k-images-idx3-ubyte\"), \"rb\")\n",
    "    test_lbl_file = open(os.path.join(path, 't10k-labels-idx1-ubyte'), \"rb\")\n",
    "    \n",
    "    magic_nr, tr_size, tr_rows, tr_cols = struct.unpack(\">IIII\", train_img_file.read(16))\n",
    "    tr_img = array.array(\"B\", train_img_file.read())\n",
    "    train_img_file.close()    \n",
    "    magic_nr, tr_size = struct.unpack(\">II\", train_lbl_file.read(8))\n",
    "    tr_lbl = array.array(\"b\", train_lbl_file.read())\n",
    "    train_lbl_file.close()\n",
    "    \n",
    "    magic_nr, te_size, te_rows, te_cols = struct.unpack(\">IIII\", test_img_file.read(16))\n",
    "    te_img = array.array(\"B\", test_img_file.read())\n",
    "    test_img_file.close()\n",
    "    magic_nr, te_size = struct.unpack(\">II\", test_lbl_file.read(8))\n",
    "    te_lbl = array.array(\"b\", test_lbl_file.read())\n",
    "    test_lbl_file.close()\n",
    "\n",
    "     #print(len(tr_img), len(tr_lbl), tr_size)\n",
    "     #print(len(te_img), len(te_lbl), te_size)\n",
    "    \n",
    "    train_img = np.zeros((tr_size, tr_rows*tr_cols), dtype=np.int16)\n",
    "    train_lbl = np.zeros((tr_size,), dtype=np.int8)\n",
    "    for i in range(tr_size):\n",
    "        train_img[i] = np.array(tr_img[i*tr_rows*tr_cols : (i+1)*tr_rows*tr_cols]).reshape((tr_rows*te_cols))\n",
    "        train_lbl[i] = tr_lbl[i]\n",
    "        \n",
    "    test_img = np.zeros((te_size, te_rows*te_cols), dtype=np.int16)\n",
    "    test_lbl = np.zeros((te_size,), dtype=np.int8)\n",
    "    for i in range(te_size):\n",
    "        test_img[i] = np.array(te_img[i*te_rows*te_cols : (i+1)*te_rows*te_cols]).reshape((te_rows*te_cols))\n",
    "        test_lbl[i] = te_lbl[i]\n",
    "        \n",
    "    return(train_img, train_lbl, test_img, test_lbl)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The function `load_MNIST()` loads MNIST data from files saved in `aima-data/MNIST`. It returns four numpy arrays that we are going to use to train and classify hand-written digits in various learning approaches."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "train_img, train_lbl, test_img, test_lbl = load_MNIST()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check the shape of these NumPy arrays to make sure we have loaded the database correctly.\n",
    "\n",
    "Each 28x28 pixel image is flattened to a 784x1 array and we should have 60,000 of them in training data. Similarly, we should have 10,000 of those 784x1 arrays in testing data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training images size: (60000, 784)\n",
      "Training labels size: (60000,)\n",
      "Testing images size: (10000, 784)\n",
      "Training labels size: (10000,)\n"
     ]
    }
   ],
   "source": [
    "print(\"Training images size:\", train_img.shape)\n",
    "print(\"Training labels size:\", train_lbl.shape)\n",
    "print(\"Testing images size:\", test_img.shape)\n",
    "print(\"Training labels size:\", test_lbl.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Visualizing MNIST digits data\n",
    "\n",
    "To get a better understanding of the dataset, let's visualize some random images for each class from training and testing datasets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "classes = [\"0\", \"1\", \"2\", \"3\", \"4\", \"5\", \"6\", \"7\", \"8\", \"9\"]\n",
    "num_classes = len(classes)\n",
    "\n",
    "def show_MNIST(dataset, samples=8):\n",
    "    if dataset == \"training\":\n",
    "        labels = train_lbl\n",
    "        images = train_img\n",
    "    elif dataset == \"testing\":\n",
    "        labels = test_lbl\n",
    "        images = test_img\n",
    "    else:\n",
    "        raise ValueError(\"dataset must be 'testing' or 'training'!\")\n",
    "        \n",
    "    for y, cls in enumerate(classes):\n",
    "        idxs = np.nonzero([i == y for i in labels])\n",
    "        idxs = np.random.choice(idxs[0], samples, replace=False)\n",
    "        for i , idx in enumerate(idxs):\n",
    "            plt_idx = i * num_classes + y + 1\n",
    "            plt.subplot(samples, num_classes, plt_idx)\n",
    "            plt.imshow(images[idx].reshape((28, 28)))\n",
    "            plt.axis(\"off\")\n",
    "            if i == 0:\n",
    "                plt.title(cls)\n",
    "\n",
    "\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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oEY2P0GMYgM7R34Qyx3QR2rv66qupXr06ADVr1gSgSJEiABQtWpRff/0VgCee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\nJSIiImJJEykRERERS/8BXiDyuivXR2QAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd8cb45f4e0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# takes 5-10 seconds to execute this\n",
    "show_MNIST(\"training\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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r1syc4GktXuU1J06cYM2aNYAb/HrgwIGMmAFE5hi+/PLLAPTp0yfFc/fcc48J\n2j1+/HiwX5EmXp6noULH6BCq8Y0cORJw3T5Hjx7liiuuAOC3334LxVekQI+hS6jGGBcXB8Dq1asB\nqF69Or///jsAH3zwgXkM4IcffuCBBx7I9HfqcXRQ156iKIqiKEqQZLnyB3Xr1gWge/fugH9l4O+/\n/zay5jXXXGNet3LlSgAWL14cCVNDRp8+fYiPjwcgkgpjIPTt25f/+7//S/d1y5cv56uvvgLgpptu\nApw0bIA8efLQqFEj87sXEbeIzDd/x+G1117jzjvvBKB58+aRMy4T9OrVC4DRo0dTrlw5AI4dO5bm\ne8qXLw9gzrF3330XgK5du6apQCqRp2fPnjz44IMARqWfPn162JQoJXzceOONgKs6/frrr+a+8PPP\nPwOOhwAcD0zZsmUB2L17d2QNzQRNmzYFoEOHDgB07NiRUqVKAY4rE9xSHWPHjo2YXapIKYqiKIqi\nBEmWUaTuueceAF566SUAcufODTixKOfOnQPc1fj48eNN/NDy5csBqF+/fshTfCNFtWrVom1Cqoi6\n5MvPP//M/PnzAZg2bRoAR44c4ejRo4AbZ/Tnn3+meO+zzz4LwG233RYWe4OhVKlSJnYrPRo0aAC4\n8/X1118Pm12hQJS1Cy+8kMmTJwOOspQWJ0+eBNyU+VtvvRVwxnzixIlwmRp2rr32WgAOHTrE4cOH\nARg4cCAAuXLlAlJXhHfs2AHAnDlzAOdvI9elaFCrVi0Ahg4dSoECBQBXtfjf//4XNbvCQevWrXnz\nzTcBN7no559/5u+//wYw16JYnpvgqjRCy5YtUwSUSxzVI488YkoiiPfGq0iS0vz586lXrx7gqqd7\n9+7ll19+AaBMmTIAjBo1CnAUuXfeeSciNmaJhVSDBg149dVXATdA+dChQ4CTqSeuugsvvBBwTiKZ\nUCJh169fnypVqgDw3XffRc74TCBBovXr10/xnFw4ooXcdCpWrGgekwt1u3btzI3FHwcPHkz1ufff\nfz9EFmYe+bvPnj2bQoUKJXnu8OHDKVzE1apVo06dOoCzmAf48ccfATdA1MtcffXVABQvXhzwv9AF\n2L9/P+COqW3bthGwLrTIRqxBgwbGHSubArmO+CIX9vRc6y+88ALg3BQ+++wzwF1cpTXvQ80jjzwC\nwKWXXmq+V45vuBIhIo1czxcvXmyOi7iqfROOHn/8ccDNaJs/f36KY/HXX3+ZRZgXKV++fIrzzNdl\nJyER99/miH5KAAAgAElEQVR/v3ns119/jYhtwVK0aFHADbWpVasWe/bsAeDee+8F4NtvvzUb8NKl\nSwNOBj5Ap06dTFiBtDnasGED27ZtA0IbBqOuPUVRFEVRlCCJaUVKyhq89NJLRon64osvABg2bBiQ\ndKfvu4MWRUpcLX/88UfMBFiK7a1btwYgf/785jlxGUXbTblixQrACTiWYED5+6elRoGrZiWvgQJu\nbSkv0KxZMwBT3gFc90D79u3N30Bo0qQJn3/+OQB58+ZN8hleVaTWrl0LOCnxEmwuP1NTpASpRSQ7\n5Xz58nnefSIuL0mQyExSgCgCRYoUMbvfnDlzAo4bRhIo5Oftt98e9HcFSr9+/QC3jEhCQgLPPPMM\nAP/++2/Yvz/cFCtWzHgn2rVrBzhqobjxZs6cCTjquKhTgqjFtWvXTqEwZsuWjS1btgBuwHO0r7G+\n7Ny5kzNnzgD+E3KeeOIJAAYPHgw4gdmRDMYOBqn7KOfkvn37qFy5MoAZqy9y/xb16fTp06Yc0KxZ\ns8zr5H4pIQihQBUpRVEURVGUIIlJRWr06NGAG+iZI0cOswsZNGgQAP/880+anyEF5y6++GIANm/e\nbNQsLyGxGomJiZw9exZwg3dr165tXif+/SVLlkTYwrT566+/TMp7oDsgqXYu7/NqyrzsTH2Lu4o/\n31eNkqBOf4VIW7ZsCcC4cePM8fUSGzduBGDSpEnm3AoUKaIqzJs3jyZNmoTMtlBzxRVXmMKFcl1I\njW+//RZwr0X+jp387XwVSzmfL7jgAqNYSexguMmRI4dRvaRg8cyZMzNcuFeQjhGhqJAdLO3bt0/y\n/+eff94EHYua9Pfff5syAJIiD26BYMH3etq4cWMAo4A0btzY/C7X2Pj4eKN0eZFWrVrx0UcfASmT\nfp577jlzz/AinTt3NnF8Eu9ctWpVv0pUcsTjUa1aNd56660kzy1cuDAs446ZhZTIcV27djULKAkI\nnDFjBo899hgQWABZ6dKlTYsYCVSbMGFCyG0OBXfccQfgBEBKptBrr70GJB3rK6+8AnhLbgZ47LHH\nzMVu69atab5W6prIItcXya48cuRIaA3MBOLasm3b/N1HjBiR4nWffvopAJdffrlZQMmxkwt248aN\nTfCxF/E9dnJDkcVEoFSqVCmkNoWae+65J8UC6vDhw8btKhmmBw4cMAkpgVzY//jjjxBbGhy9evXi\nqquuAtyEGnH1BUr27NlNVp8EaW/bts24YeTGHQni4uJMhlbVqlWBpEHkskCVukrp4bvIkt/l/OzT\np485dyWIvWjRop5aSMkmQLJqZ8+ezebNmwH3bzB79mzAaUztZWrWrGk2nZKQk179uuTs3bs3xWP/\n/vtvWGotqmtPURRFURQlSDyvSNWoUQNwa13079/fSOKSyhnoLihfvnyAE0gqKdwzZswAMAqVVxB1\nRlSKw4cPGyUuOevXr/erhHiBvXv3MmDAAIB0JVVJA5emm8KpU6eMRCsKoheQEgZFixY1QZwSkJpR\n3njjDd544w3ADQz1Er7nmLjRjxw5wqJFi1K8VtxX4j4SLMsytdyiWUMpIxw4cIBu3boBeEp9CIYL\nLrjA/C5p4eI2SQ9R/Dt37myCf4Xq1aubXp/izo1EKYcqVaoYdVRUBtu2jbt1zJgxmf4OOa8TExPN\nd/jWovISTz75JOAG2cfFxZnOHVLSQvopen0uX3bZZeZ3SYbIKK1atTJJPYLcY0KNKlKKoiiKoihB\n4nlFSnaDDz/8MODsoKSf2SeffJKhz5JUc98q5tOnTwe8t0OWHYTY2bZtWxMPkJyvv/7as6nL586d\nY+LEiQG9VoKykzN69OgUQYNeYN26dQAmkDUzlCxZ0ux+vahI/fPPPybIVlKK33vvPb/HRQqVJo9F\nKFasGLfccgvgxmp4iVWrVpmSIhJIXaVKFebOnQu4Ctv8+fONKhfKFOpwI0pFemTLls2k0MvxEsU7\nV65cJCQkAG5CRY0aNUyMUufOnQG3O0E4WbduXQoVZvTo0SEpnDlv3jwArr/+eiBpQsldd92V6c8P\nB6LWHzhwAHB7Xvoix8mr/fXEa+SbRLBv374MfYZ0GRg9erT5XeKrfvjhh1CYmQJPL6Suvvpq+vbt\nm+SxIUOGZHgBJe4ECcIrXbq0cUl4MVMPUgaNt2jRwoxDEDeS3IBjEUkieOutt4w7U5BgQy/VjgoG\nWWw89dRT5oIsyQGXXnop4N6wABMgmtzFGU1OnjxpEh/keFSpUsVkWPoSaJVvr/HOO++Y2lfiHurc\nubMJOBYaNmxIixYtAPcG7sWMy2CpV69equfctGnTjAtaFlLjx4/noYceAtzq6JFYSAE8/fTTSX6G\ngvbt25vj6juHQ/kdoaZevXqm3ZS/BZTUHpRF4Jo1azzt3kseFhAIUqPtuuuuA5L+HSRRJFzV3NW1\npyiKoiiKEiSeVKSkDsisWbNM4KrUZMloUHiOHDn4+OOPAde1t27duoCbzEYbGX/z5s3NTl+UGmng\nG0gKtleRVOIbb7wxRb0oCXDetGlTxO0KJdJfTX76Y+zYsdx3332AUyYBnNIXkgzhBcR1ILWvNm3a\n5LfvXCwjLg/przdixAiGDx8OuO6B9u3bG3euBGv7BnLHOr5hDlK6QboN7NmzxzwvpSLkeg1Jg4Rj\nDXHrvvrqq0lceeCEkXi5mfPAgQNNiQNRRzt37myurzKHpdl7rly5TAVwL9Xpk7m1e/du46EQ92pq\n94GSJUsC7jnrL8lAVNRwoYqUoiiKoihKkHhSkZKAuLJly5qU+cmTJwOBB3dKPNELL7xgKlBLcPDL\nL7/s6aquvsjqumrVqsZfL92rk/dyi0VEVfOHVB72UhHOcDFo0CB++uknwPXnFytWLJompYoEf7Zp\n08b0tPQtepg8Rkoqe+fKlYuCBQtG0tSgkYDqn3/+2QRQCz179jTqocS6SYHDNm3axKxCLD0xfVVQ\nUVGlj9m5c+dM70Qpa9KkSRNOnz4NBJ+qHk1EtZGuBLZtm7krcVGBJsxEGpmbjRs3NglK4m358MMP\nzeskyFp6zrVv35569eoB3urzKedOkyZNTAywzKnrr7/eJAFUq1YNcJRg6VVZokQJwO1qUrBgQfbs\n2QMQ9j66qkgpiqIoiqIEiRXJzBrLstL8Mkk5lqJZV1xxhcn+kFXp77//nuZ3iBIlcVFNmzY1xeEk\nsySY1Gvbtq30X5X+GANFMg5kt+AbiyJ/p1CnsAYyxlCNT7LUpPyEv47lEouTGhK/EWhhvEgfw2AR\nNWTnzp2mlECgBQ69OEbZ1Q8aNMi0lWnQoEHQn+elMc6fPx9w07UHDx4ccE/JtAjHufjNN9+Y+SRt\nN5YsWWIKy95zzz2AExcm1xYp6Cg9ErNnz25680lsCjhFjsFtG5MeXjiGkjErWbWibNi2beKhMpOp\nF4kxSluYNm3amKy9Xr16pfp6aeXzzDPPGAXuxhtvDPbrwzpG6Q84dOhQAOrWrWuekziwXbt2sXLl\nSsDJugVXicuVK5eJjZK5HQwBnYteWkjJpJV0/rVr15rU4/RccXJSS4VdkTwPHTpEmzZtgIz3BvMl\n0ie+9JsTd6QvycsghIpILqTuvvtuAKZOnZrqa5I3+E3Orl27ANfFuXDhQhYuXJjq53nh4h0I33//\nPeC4cyWoOdDeWF4cY+HChQGnyr0cy4YNGwJuqYeM4KUxSokKCYTdv3+/cZFlhnCci6+99prfchXi\nTpHzLUeOHCboV46X1OPxRfrRvfTSSyYJSDYB6RHtY1ilShVzv7n55pvlu8S2kFxjIzFGcbOfPHnS\ndAFJK/xF7isbNmxg//79QPoNutMiEmOUsgZ16tQxj8mc9e2PKL08JUQCMG7opUuXBvv1AY1RXXuK\noiiKoihB4qlgcwlYFJVs3759ZpeUFvfcc4+pgC47XZEtH330Uc/1REqPuLg4v8GNkyZNioI1oUPc\neQ899JCR0dNKvU3v2FesWBFwU667detmjrXsMrdv3545o4OkePHipkpvRl2wXi6UFwyHDx8GnGMt\nf5PmzZsDwSlSXiJ5mnz+/PmNSuW1sfXu3duo8h06dACckjD+1KbUFBnbtpk5cybguomkknYs0bFj\nR+OOlfuNHEspxhpLlCtXjr179wKYYtPz5s0z6ox4dqSobiwhbrz0guL9KWuZ8UJlBFWkFEVRFEVR\ngsRTipSkRsvOYOnSpZw4cSLF66StiPi4+/TpY/yoUsRRio3FSpkDX9q2bWsK4Anr169n0KBBUbIo\neHLkyGHa/IwcORJwAstFifJVpORYyQ43vVYj/p7fuXMnQNR7D44bN84cQxn30qVLTYB8cvLmzWsC\ndaVcR2JiogmwDDRGKlbwDRyNNerWrWvORVE+hZ9++slzSpSQmJhoYhLlZ7169UywsSjGlStXNu+R\nQF5RdhcvXmx6D8Yiosz07NnTXDfkp/To81fQMRaQWETxzsjP1NixY0fYbYokvm22Io2nFlLJL0B9\n+/Y10pwssgYOHGgqnvrWrnnwwQcBNwMjFhdQElg8bNiwFIuHH3/80dQJiSUuueQSk9GTFsuXLzfH\nzosNijPKkiVLuP3224GkAfVSxyX58S1XrpzJZJPF5YkTJzzbCzIY3n33Xbp37x5tM1Ig592OHTtM\n0sry5cvN85LpNnDgQMBp2pw8y3Tr1q2At/ux+eO7777ju+++A7zZLDvUSLPpMmXKmI2YuNKjeSMO\nFkkemDx5MqVLlwYC63W5atUqkxUX60hl/eTdSr766itTUyrcqGtPURRFURQlSDylSCWnevXqRpGS\nwOPs2bObStey0x8zZozp6hxrHed9EYWtWrVqZhxSPyjcvYLCRXr1OyRt/K233soSSpTgm4LrS9eu\nXYG056mk9j700EOeqjqcWT788EOjSEll4ri4uKgrrc8//zzguEZE+Zbq8g0aNDB12+Li4sx7xNUl\nde6kNl0sBl7/F5Dq5eK29D3/YjG4XJBQltq1a5vyAEOGDAGcjhCiOn311VeAO9a1a9dmmY4RkmyU\nvGvCwoULk/SNDCeqSCmKoiiKogSJpwpyShC5VCi94YYbUrxm1qxZpoLrl19+GWILUycShcckBuOZ\nZ54xOybpaC1/k3ASjiKAZcuWNb0Bffnmm28AuPXWW4HI7OQjWQQwb968Zqf01FNPAU5gciDxC9K/\nTSrxZ4RoFzpMi7x585qYr6uuugpw0rEzOrdDPUaJixo1ahQFChQAnPT45Eix16efftoo4H/99Vcg\nX5FhIlkcNxpEep6uWbMGcIs62rbNJ598ArgxcqHGy+diqPDCGG+77TbAjT+VBLVChQoFXCA2LQIZ\no6dce8eOHQMyV7I+K3DixAlGjBgBYJo0xiq7d+82GZX/JU6ePGkahUrtluuuu860npALutyQfTOh\nAm2zEWucPHnSZB/KQuqJJ56IyCYhLaTC8z333GPqJxUtWjTF68TNLnVtlNhBWvnUrl0bcBZSsklV\nYpvkmx7pDBGKRVSgqGtPURRFURQlSDzl2vMyXpAww426Exx0jOFDSpeIazd//vzGnRYoXh9jKNBz\n0SHUY5SegO3atTPNpcNVskLnqUs4xyjlYmQtIyUuHnjggZB8vvbaUxRFURRFCSOqSAWIF1be4UZ3\nwQ46Rm+jY3TI6uOD8I2xffv2pkyAxOuFmmiPMRLoGB10IRUgOmEcsvr4QMfodXSMDll9fKBj9Do6\nRgd17SmKoiiKogRJRBUpRVEURVGUrIQqUoqiKIqiKEGiCylFURRFUZQg0YWUoiiKoihKkOhCSlEU\nRVEUJUh0IaUoiqIoihIkupBSFEVRFEUJEl1IKYqiKIqiBIkupBRFURRFUYIkRyS/LKuXiYesP8as\nPj7QMXodHaNDVh8f6Bi9jo7RQRUpRVEURVGUINGFlKIoiqIoSpDoQkpRFEVRFCVIdCGlKIryH6Z/\n//7079+fs2fPcvbsWd58881om6QoMYUupBRFURRFUYIkoll7oSIuLg6AQYMGAdC4cWOmTp0KQLFi\nxQCwbSdJYPz48VGwUPFHnjx5AChVqhRXXXUVAG3btgUgb968jBo1CoCNGzdGx8BMcOmllwIwePBg\nAKpWrcro0aMBWL9+PQB//fVXdIxTlFSIj49nxIgRAOTI4dwOzp49G02TlCAZOXIkAI899hgAuXLl\nMtegoUOHRs2u/wIxuZBasmQJAPPnzwecG9S4ceOAlAupVq1aceeddwLw999/R9rUoMiZMyfDhg0D\n4H//+x8Av/32G2XKlImmWUFTo0YNAF555RUAGjZs6Pd17du3T/Jz0aJFEbAuNBQtWhSAnj17AmBZ\nFosXLwacYwcwZcoUFixYAMDPP/8cBStDT+/evQEYOHAgAE2aNGH//v0Z+oz69esD0K9fPwC6dOkS\nQguVtJg2bRr58+cHYN26dYC7GVBiCzmPcubMCbj3QF9KliwJwJNPPskff/wBYBZbZ86ciYSZWRJ1\n7SmKoiiKogRJTCpSTZo0AVz16d577zW/W5ZTO0t2/K1ateLAgQMAXHTRRYD3XSz9+/c3ilRiYiIA\nF1xwAR07dgRg3rx5UbMto1SpUoWlS5cCjksvEMTdF0uKlOzmxT3Su3dvo6y1atUKgFGjRvH0008D\nmJ9PPPFEpE0NKR06dACgXLlyACQkJGT4M2688UYAqlWrFjrDlDRp1qwZ4F5DAaZPnw54//oYKE2b\nNgXggw8+4NSpUwBcffXVAOzcuTNaZoWUKlWqAPDGG2+YcAnh5MmTrFq1CsDcO6ZMmQJA4cKFzeuK\nFy8OwP333x92ezNDhQoVjALerVs3wPEEZMvm6EFyr/z1118BGDJkCLNnz46IbapIKYqiKIqiBInl\nz48ati8LcZl4UTquv/56tmzZArgrVVGkGjVqZNJ5JVYlPj4+w/FSkSyFv3r16hS7C8CMo0ePHpn9\nCr+Eoy1FrVq1+PzzzwE3SWDVqlUmfuiXX34BoHr16ibO5siRIwBcdtllGfmqdIlWOwNRpAYPHkyj\nRo3EFsCJVQBXocoskRxj8eLF2bFjBwB9+/YFyHDqfIkSJdi0aROAUY6vuOKKNN+jbSkcMjO+CRMm\nAPDQQw+ZxwoVKgTA0aNHg/3YgAnnMSxbtizgqsS+6oucfytXrszox2aYcI5RvCsrVqwAoHz58ub8\nkXjhefPmUblyZcCNJ86bN2+Kzzp58iQAt9xyi7mnBkokzkWZow8++KBRvpN9ttiS5PFdu3YxceJE\nAF588cVgvz6wczEWF1Li2mrXrh3gZEX1798fcCeWL+JimTx5MuAE12U0my+SF+8iRYrw559/png8\nFhdSADVr1gScmybAsmXL/L5ObspCVllI+fLqq68C0KtXL8DN6PO3cA6GSIyxYMGCAHz++ecmW7Fu\n3boA7N69O0Of1bFjR+bOnQu4Lr4PP/wwzfd44TimRs6cOc2CpHnz5oDj9pSbe4sWLVK8Z+HChQA8\n8sgj5rFwnYuymZF5V6lSJd555x0A7rjjDsB1kYSTcB7Drl27AvD222+bx+R6KgHZ/uZprly5AGjd\nujUVK1YE4NixY4Dr9gQ3qzG9e2e4xpgjRw6z4JE5tnnzZlq2bAkkdc1KAoe44J977jnACY95+OGH\n5fsBmDlzpknMCpRwHsdOnToBGPdcan/v1BZSvkjIRTBorz1FURRFUZQwEnPB5kOHDjVKlLjz+vfv\n71eJEiTlXFwsgwYN4qOPPgK8mYZ+4sQJ3nrrLQDuuusu87ioFrL7X7t2beSNC4LNmzdH2wRPUKVK\nFaOOyu7pp59+iqZJQSHq75VXXsnjjz8OZFyJEurWrcvevXuB1JVKL9KgQQPAUXTAqRsmj1977bWp\nvk+uN9u3bzfK3i233AIkVaTCRb58+QDXbnAClSEySlQkkPnky++//w6487R48eJcfvnlgKt83H33\n3YCrTPkyadIk83vr1q0B+OSTT0Jmc0YoW7asUaLOnTsHOLb7SxIQF678FBYtWmTmQJs2bQCoXbt2\n2GwOBn+JOK+//jqQ1FUnweaSOCHzWUo9RAJVpBRFURRFUYIkZhQp2QWMGDHCBI1LCm+ggeOywq1T\np44JvhN158SJEyG1NzOcPHnSFB31VaQkPVx2v7GiSCkOHTt2TFEw1vf4eh0JXB0wYAAAx48fNzFf\nmeHLL78E4PTp05n+rHAi8UVdu3blpZdeAtzih8KePXvYvn07gFGVN2zYYAKf//33X8CJvZH3ikoU\nCUQFy8okL+iakJBgFBmJTRw8eLCJW0vOwYMHTQq9P5WmevXqQPQUqdKlS5vfJa40mG4QuXPnDplN\noaZ69eopClBv2bKFBx98EPBfPFTKOEhcmy/Tpk0Dwhdf7PmFlNTJkEBr27bNoiqjmXcifU6dOtVI\nteJqmTlzZkjsDRWyWJQTJdSB116jVq1apjp4rFSgDxSZY4MGDTILKFnIxwq5c+dmzJgxSR679dZb\nzcIgWMqXL+/5ispSmf/ZZ58FnKxfudF+9913gBtmMHz48IA/V4KWI5ElJ4gbSzhw4ABr1qyJ2PeH\nmzx58lCrVq0kjyUmJpogasnay5Url3FlyiJEWlStXLnSbKyff/55wF2AgRuoHy3ETQnO+QNO7b30\nkjTAPf5jxoxJkQGX0Y4E4aRatWpm4yKuu4SEhDSvFeLK83VbC1J7Mlyoa09RFEVRFCVIPK1IxcXF\nmfo64hL56quvMh0gPmXKFLP78KoitXr1agA+++wzIOsrUmXKlDE9v6T6bqwjc1bmcL58+Uyq7muv\nvRY1u4KhZcuWJsnj+++/B8hwzRl/XHfddSbxw4s0aNDA1DyTsgZr1qwxPTC9bHsgnD59msOHD0fb\njJAxb9486tWrl+SxnDlzmuBsYe3atabJ7wcffJDicyRhwNcVdPDgQSAyNajSYseOHcateP311wMw\nd+5co5p9+umngKMwSaN4CdKWxAZfl7QE4Hupx+V7771n3LFSNie18gYyFrHf3+uktEq4UEVKURRF\nURQlSDytSA0aNIibb74ZcNPEQxWcKzEqPXv2DMnnRZJnnnkGcIMdpaJtLCJxUb6prv7Sl2ONYsWK\nmYQBCdL23SlJzJ/0A/NiGQ5fOnToYI7LrbfeGmVrwo/s5Pv27WuUKGH69Ols2LAhGmZlmkBLHEi8\niaiQEqvqO0+lkKd0IvACqfVrFBulV9vChQtNjFpyihUrZuLhsmfPbh4XxUNKDkSLhIQEcx8UT0rz\n5s3NNUW6RQwfPpybbroJ8K82ibdDlCwv9VisXr16iiSMCy64gCJFigCuOli2bFnTIzCt8iESwxg2\nbNuO2D/Azsi/LVu22AkJCXZCQoJdpUoVu0qVKhl6f1r/Jk+ebE+ePNl8fnqvD9cY0/s3adIke9Kk\nScZO33/du3e3u3fvHrLvisb4rr32Wvvaa6+1ExMTzb9Qjysax9B37sq45s6da8+bN8+eN29eiuda\ntWrlyTEOGzbMHjZsmJ2YmGhPnz7dnj59ekjsbNeund2uXTs7MTHRbtasmd2sWTNPHUfLsmzLsux7\n773XPnv2rH327Fnbl3Pnztnnzp2z77zzTvvOO++08+XLZ+fLly+iczWYzy1WrJhdrFgxM45///3X\nrlGjhl2jRg3zmhIlSpjxpcWJEyfsEydO2P369Yv6PJV/u3btMufU6dOn7dOnT9tjx461CxcubBcu\nXDigz+jfv7/5DDlPx44da+fIkcPOkSNH1Mfo+y9btmx2tmzZ7Pvuu88+evSoffTo0STX0uT/ZC7H\nx8eb94Z7ngY7xn379tn79u0zx+DcuXP2tm3b7G3bttkbNmywN2zYYP/2229Jnk/tX7jHqK49RVEU\nRVGUIPGka08CwCtXrmxccKF2fZxfJacawBYLPPbYY0DSPlCxhjSZtm3blHwIdDxSZ2TPnj3hMS4I\nhg4dCjhzV+aWVNb3dUvLHJdaQ2+++aan3HwSwCmugVWrVpmK5hlF3CPZs2cnISEBcMe/d+9eT9ZD\nk2M3efJkE1wsYQYXX3yx+V2On/xfgnljhfz581OqVCkAfvjhB8C5rsgxE1fgCy+8ADjp8+KOF9dL\n06ZNU1TOjhYbN240oQ5ik7gg00PS5qU/HWBcuIMGDQqlmSFDjs+kSZNYvnw54CYqSfKOL1JKoEKF\nCp5PlJAaddLYHfDbtNgLqCKlKIqiKIoSJJ5UpCRt3LKssOzOixUrZoIOvRRg919CdrPSlRxc5SYQ\nHnvsMXMMK1SoEFrjMoGkTVuWZcbjT6WQIFHpUF+sWDEaN24MeEORatGiBeBW/u/fv39AQcUVKlTg\noosuAtxAelFr6tSpw/vvvw9gXvPJJ59kuqhnuBGlRn6CW4hT1FNR7mKR22+/HXCDlEUlBjehZeDA\ngeanHDv5e9SrV89vMHo0EKUzGBYtWgSQpKK2lMmJBeS4+SpRMibp0ypJBBMmTDAV0kVt81qvxREj\nRgBOySNwupuIqu+rYot6KoW6o4EqUoqiKIqiKEHiSUVKsG07QypFoLRv397EQHi9VYesxm+77bYs\n1SdLlBtJLT9z5kySjt7JkV1W3759ARg5cqRJ3/US0oqiTJkyAe3OZf61a9fO7Oq9wJAhQwBMj7hZ\ns2alKAMQHx/PxRdfDDgtKgBq1qxp1MaTJ08CbgHP5557zrSx+OKLLwB3xxxr5MqVK9omBMWhQ4cA\nt4TK448/bpSM+Ph4AJNiDjB+/Pgk7y9evDh333034J672bNn59JLLwWir0gFQ/fu3YGkrUVmzJgB\nOGUSYoH69eubHpjCM888w9ixYwH3XJw7dy7gnK+iMkrPQa+WNZFenF9++aXfWLULLrgAgG+++QZw\ne9FGEk8vpKQKdKiQ3j39+vUzgc2+9Yu8iARKDh8+PEstpOrUqZPk/x9//DE7d+70+9rixYvz8ccf\nA86NWvBijzDpExhov0CZ45ZlmT5gXkDmmvSZS69WmRyL8ePHm8WSv55kkydPTvJ/qcIcTaTC9dSp\nU2hIhIQAACAASURBVNNMXBCXVu/evXnooYcAtwlxrFSql2B/6SHXu3dvChcuDLhNX32RLgPixmvc\nuHGKIObVq1ebhXEsITfgRx99NMVzUu08VpKRBgwYYALJZfE7ZMiQFPaL63PAgAFmkSXneL58+UyP\nwVhC7uvRWEAJ6tpTFEVRFEUJEk8rUrZtm1VmKDpuS6py5cqVTRfsQJWDaNOmTRuWLVsGJA2GjFU6\nd+6c5P8S6AquWiVSdb169VKkvf7666/GZRTLSOVor+18V6xYASR18wgSKH/y5ElzTknV89OnT6f5\nuRIQKgqjFyqEi1vyggsuMBWtJfD2zJkzNGzYEHADj2vWrGlcJTJHJ02aFFGbM8uff/4JQK1atUzC\ngyiivp4Audb4u+ZIt4mePXty5syZsNobDqQKenKX+syZM01/RS9xySWXAHD27FmjEOfNmxdw5zDA\nnDlzAP/XFFEkJ0yYYPrPyfwuWbIkO3bsCJP10SHsFc3Po4qUoiiKoihKkHhSkZKSBNmyZTM+XUnD\nzWi5gtatW5seRBIE26lTp7AEsYeT7du3M3z4cACmTZsGYGIbmjdv7snA69TIkSOHiTcRevXqZYJe\nJXZB+p2BqxxKzMbbb7/N1q1bI2Fu0MjcFXXHd+5KiQ+Ja0hMTPRUnI30r5KfoUaCkmWHHE3mzZsH\nOLFSUoxR+rAdOnTIdJ8XZsyYwbhx4wDYtGlTBC0NPXv27KFJkyaAmwAycOBAU7LCH5KWPmbMGABO\nnToVZitDT4ECBVL0ZhMVcs6cOZ6MFZLrh6/SJLGMuXPnNo/5qvupkStXrpju0RookSpv5MmFlCxy\n5s2bZ1wfkhXSv39/c2Pyh9Tikff169fPTDxx58XaIio15GbcoUOHmFpItWzZ0iwCBd9Aet/FBTiL\nyFq1agFu9kksIJlvQv/+/c0xk2BfGeOWLVv48ccfI2tghLn55ptNlp8XgswFyWBbtWpVimB4cAPt\nJfHjhRdeSNeFGYvIdXX16tVmcemvPpYEnsfiAkp4+OGHTZaa3B+kGbFkNnoNf3OufPnyKR6TLLd1\n69YZ96sgGXqtW7c24RJyPGO1WbzUuvOXnBaprgnq2lMURVEURQkSTypSwsSJE40SJavO5cuXm5Wn\n1OCpVq0alStXBtxVqUh6EyZMYPTo0UDsBJanhgSIythE3ejVq5dJ237uuecAd3flRZYuXWp2Cldf\nfXWK548dOwbAG2+8AcDgwYNjSokSpIq3BCkvX748hdomSRTx8fExPz/To2vXrqY6uvQD8wLixvvs\ns888VSU/Wpw7d85UOxcVv2PHjgC0atWKXbt2Rc22UHH77benCMaWOelbwd7rSLLG2bNnTX/Myy+/\nPMnP1JB7hKjjsaqyyr0kmgk7qkgpiqIoiqIEiRXJVZxlWRn+Muk0LinxgwcPNmm6YvvUqVNNmYSv\nv/7aPAakWWAvI9i2HVB10GDGmFFkd/j6668DbnA2uCpVMH7+QMYYqvG1bNkScOOINm7caBQosV2K\npoaKaB3Dhx9+GHDi9mSeipoqBWFDpUZ5aZ4KEv928OBBU5lYgrWDwYtjDDWRPBejQbSO4cSJEwG3\nQwLA8ePHAUzvuUB6SgZCJMfYvn17c04lLxXjiyjh48aNM4p5ZtRhL5yL4tVYuXJlksf3799vSjxs\n3Lgx6M8P6Fz0+kLKK3hhwiRHgiW7dOliLhASMCruioygF28HHWNokWzM6dOnm2DXzGxwvDjGUKPn\nokOoxygb7YYNG3L06FHArWkntc1Chc5Tl3COUWq/Jc/CPHLkiAn5OXjwYNCfH8gY1bWnKIqiKIoS\nJJ4ONlfSRirYyk9F8SJSx01+Kkq02Lx5MwBXXXWVSQIJtRKlRJbUShx8+umnHD58OCI2qCKlKIqi\nKIoSJBojFSBe8AWHG43LcNAxehsdo0NWHx/oGL2OjtFBFSlFURRFUZQg0YWUoiiKoihKkETUtaco\niqIoipKVUEVKURRFURQlSHQhpSiKoiiKEiS6kFIURVEURQkSXUgpiqIoiqIEiS6kFEVRFEVRgkQX\nUoqiKIqiKEGiCylFURRFUZQg0YWUoiiKoihKkOSI5Jdl9X47kPXHmNXHBzpGr6NjdMjq4wMdo9fR\nMTqoIqUoiqIoihIkupBSFEVRFEUJEl1IKYqiKIqiBIkupBRFURRFUYJEF1KKoiiKoihBogspRVEU\nRVGUIIlo+YNQUaVKFQCeeeYZANq2bUu2bM6acOHChQCMGjUKgPXr15OYmBgFK0ND/fr1AVi6dCln\nz54FoHXr1oAztqzE+PHjAbjxxhsBKFeuHAAHDx40vx87diw6xoWAGjVq0L17dwBq164NQNOmTQH8\nztEOHTqwbNkyAE6cOBEZI5WQM378ePr165fksQsvvJDDhw9HyaLQ8MorrwDO+TplyhQAXnrpJYCY\nH1usUblyZapWrZrksVy5cvHuu+8CYNspqw906NABgPfffz/8BmZxLH9/4LB9WQhqSVSoUMHcXEqX\nLu372UDKCTNo0CDGjRuX2a+NWr2Md955B4DbbrvNPLZy5UoAmjRpAvi/CQdDtGvXfPrpp4C7QGzT\npg3gLJyXLFkCwB133AHA0aNHM/z5kTyGNWrUMMencePGgLMovvjii5N/l9jmzw5z3OfOnRvQ92pd\nF5dgxpgrVy4A6tWrB8Ctt97KqlWrAPdcDPQzihQpAsCYMWO46667krxm6NChjBkzJtXPiPa5mJzi\nxYsDULJkSf73v/8B0K5dO7HDvO7BBx8E4OWXX07z83SeumRmjCImNG/enCuvvDJD712zZg3gbtaD\nQY+jg7r2FEVRFEVRgiTmXHudOnVKokSlx9NPP82PP/4IOO6xWEOUF8uyjGoxbdo0IHRKlFdo0aJF\nkv8vWrQIgM8++4wbbrgBcN263377bWSNC5CRI0cCzs48f/78QNqqk7Bq1SoqV64MOG4fL5Mjh3PZ\neOCBB4xSsXbtWsBxE6Q2zuzZsxvXphzrmjVr0qhRI8Bx4UabmjVrAvDJJ58AkCdPHuNKF2Vq9+7d\nqb4/d+7cRgF/4IEHUjwv5/OECRNCZnM4yJ49OwBdunQBYNKkSQDkzJnTKG7CsmXLmDhxIgCXXXZZ\nBK387yLXmUceeQTAhLakh7hcv//+e7p16xYe4yJAgwYNAKhbty4DBgwAnLkJ8N577wHw4osvsn37\n9ojYo4qUoiiKoihKkMRcjNRvv/1GyZIlUzx+/PjxJD8lPiF79uzs2bMHcGOKfvvttwx/b7R8wWLz\nF198YR7r3LkzAHPmzAnlV3kuLkP4+OOPjYKxefNmABo1apThwPNwHcM6deqwYMECAAoXLgxA3rx5\nfT9Pvt/E2fzxxx8AfP3114Czq3/22WcBuO+++wDYv38/lSpVAuDkyZMB2RKJedqpUycAZs+eneK5\nAgUKmHNQEAVr6NChJr7GF1HiAt09hnOMoiJ+9dVXANSqVcs8J/bVrFmTQoUKAa6KVr16dQB69OhB\n3759U3zuoUOHALj55psBN84xNaJ5LhYvXpzp06cDEB8fn+J5iWF84oknAGfunjt3DnDnfXrzNZLX\n09y5c/N///d/Ab++ZMmSVKtWDYCKFSsCjtoxY8YMAB5++GEgfQU1XGO87LLLzLknSSuB8vHHHwNw\nww03UKZMGQAeeughwBlPWnF7/ojkcaxSpYpJarjmmmsAVzn1x08//cRVV10FZC5ZJ5Axxoxrr2jR\nokDSG5TIlHPmzDHS8i+//AK4QXgDBgwwE6ZHjx4APPXUU5ExOky0bNkSCP1CyqusXbs2iSsIoHz5\n8mZRFW169uxp3M3+3K3//PMP4ATKL168OMlzsshYsGCBcV8Kzz//fMALqEggQalyrvkiLit/G7Oy\nZcsC+F1EgZtU4AV3l7itDhw4kOK5ChUqAI7LWcYkm7JmzZql+pl///03t9xyC5D+AiqaFChQAHA2\nbckzwP79918ABg4caEILEhISUnyGl+arcO7cOXMj7dmzJ+BueAIlMTGR22+/HYD58+cDmM1TpJB7\n2u23306pUqVSPL9jxw7AtU8WHb7I8SlVqhQffPAB4CTGACYrHMjwgiqcyGJ+8uTJXHLJJYC7EX39\n9dfZt28fACVKlABgyJAhAFStWtVkgEv2YrhQ156iKIqiKEqQeF6REiVq3rx5ABQqVMjsfm+99VYg\nqdtLeO655wC4//77jYolO8pYxDfYXBQpkTX97QyzEu+++y6DBg1K8linTp08o0jdd999Rim76KKL\nANi3b59xgUgq+NatW817ZEc5efJkwNl1yfGdOnUqQAr1KtqIoiQB5r689dZbQHASur/PizbffPMN\nAK1atUrxXIsWLYy71t81RZRyCTbfuHEjP//8c7hMDRmy84+Li0vxnKiGK1asiKhNoSAhIcFcP/bu\n3QvApZdemuJ14pJNHkwPjtL6+OOPA9Gru1SsWDEAv2oUYBQzSfzwhyQDzJgxwyhRwrRp09iwYUMo\nTA0J+fLlAzAhD5dccom513fs2BGAI0eOmNcXLFgQcF2vBQoUiNg9XxUpRVEURVGUIPG0ImVZFnfe\neScADRs2NI9LbJA/JUr4888/AcfvK4qUBITGxcWlCIj1KhLEmZCQYFJcJeZL/p/VFSl/8SpeQ+an\nJELcfPPNZu6+8cYbAKxbt84Eh8rrZGds2zaff/45gKmCfebMmcgYHwBNmzalTp06qT6fmXg9CWz2\nAqKOSWHJ9Dh16hSAiTdZsGCBUQQilXqdWSSh4emnnwac+CFR1USRS0vliCWk8rovkjjQu3dvIKki\nJYpHt27d+PDDDyNgYfCIYiXjOXLkiDl+Ui5B4uAqVqzIli1bAExJkh9//NFTMW7ly5cH3Pv2P//8\nY85LOS6FChWif//+gBv/JmM8fvy48WSFG08vpIoXL54i22LRokUmqykQRo4caT5D3C833XRTwFWK\no40Ep27dutXUUIp1unTpYlxgkh2zceNGli9fDmCyLCVI2x+y6PAa4v7q1q2buSCLG0iqZaeGZKKI\nC0EuftFE3DwjRowwbnZ/7Ny50/wuAfTt27cH4NFHHw2jhaFFLtDys2jRomzbtg1wWxhJZwVwNzpp\n1ZbyMkWKFDGBuHLjOnXqlAnSzSoLKH/I9VRutpKx6Yu48by+iALXRsk4nTNnjtn8+NsEybhj5Rgv\nWbLELP5kQ7pgwYJU60ru2LEjYptwde0piqIoiqIEiacVKWmq6ItUKQ+UWbNmpVC1RAVRIoOkGov0\nOnLkSFOF1hdRbiSIXNLhkwdFQsbnQaSQlGhxE0DSXmQSjC11hUS9ueiii0xw5fDhwwFHyZGq35s2\nbQqv4akgLkhf17o/RME4cuQIw4YNA/wft+QsW7YsqLpu4UKCU32DVOVYiWLYokULU+W8T58+gFsS\n4q+//ooZtRscdfiKK65I8lj27NlNqQtRN7Ii4kL3p/RLzahevXpF1Ka0kASqNm3aGPedXD98kd6e\n8tMXCQOZOHGip0oc+EPUXinL0KFDB2OzlB9Jq8tJzZo1zfVYmsOHC1WkFEVRFEVRgsTTlc39VTGv\nXLmyKTwWCCVKlOD3339P8tj+/fsz1K8Pot/lesuWLSl2Trlz5waSFlLLDOGoptyiRQsTTCxpu6+8\n8orZXUk67iWXXGKqSIu6Ua5cuVQ/Nz4+3vRDC5RIHEOJN5H0XHCPzy+//MKsWbMAN6VXVKiXX37Z\nqABSTdmyLG677f/ZO/M4G8v3j7/HnrGLsoWyha8SJfuUkopCsiZLlH2XpIlsRUrZExIRKkLZSbQo\nWSq70kYRlcIgzPz+eH7X/Zwz58zMOWfO8pzper9evUbPWea+5znnee77c13X52oFwLvvvuvT7w/2\nHOU8SUmxj+8tY0nzuXfddVeqRSPeCOV5lPy0tHbrKc0xMTHRJOyKTcm2bdv8HUbYnM1HjRrFsGHD\nPI6LcjFt2jTAVm+CRaSvpw888ID5bEtumDBjxgyT65ie/o+hnKP0c5REa19xdTYPBuE4j2Iw2rRp\nU79fu2fPHsDOjw6EqHc2z5cvn1tYBGyHXX9I/h7iN6GEDqmcePbZZ/nyyy8B98WF4Jqk++abbwIw\nceJEwHbybd26tccNa9SoUWYhuWHDBsAZrsrSNmP37t0mWVzCYocPHzbuu4KE+jp16mTaGsmFo06d\nOvTo0QOwK1TD3dg3VJVnUizgNF8icaaXz5trM1hZEF+8eNEcT+5knzlzZpO0LOG/wYMH8/LLL3t9\nfqQQp3XXRZRUIA4ZMsTMQaqkZEPbpk2bqK4SlorncePGeSygtm/fDsDw4cMd0UA7NST0KA7fcq1M\nCwnjvv322+a7LdcspyKpDhcuXDAtllyR75mEAhs2bGgecy2CCSUa2lMURVEURQkQR4f2/vnnHxP6\nEIoUKcLJkyd9fg9vob1z5875rUpFWoqOttCe7CKKFi3qlnjtD/Ie8fHxxgrBtVRXSvPFHVwUrZQI\n5znMmTMnBQoUAGw3ZV+RRtUTJkygatWqAEyePBmwFL7UVNlgz1GSrqWHpY/vLWNJ8TmrVq0C7DCu\nP4TjPD755JOAFdKcPn06gLHnSC0Bu1ChQsaRvnr16ua4nEdfiwZCHdoTJ/pHHnnEjElsZVxDkXL+\nxZU/Z86cRrlKD+G+nkpStqQDyHcM4NtvvwXsfonioZVewjFHUf6nTJlCu3bt/HqtqKNy/3jsscf8\nLpSI9H3RFfHMWr16tTn26KOPAraCFwi+zFEVKUVRFEVRlABxdI5UMJD+Q9HO4cOHo8qQU6wrpBTe\nH4oVKwZYOyRB3kf61gHkyJEDwCPvyAkkJCQE1HcObOUjJibGqDuuO+hwIqrSpUuXjNP6/PnzAWsH\n6K1Pnow5ec82136Rks/gVKQYQH76ysmTJ43KJspV2bJleeeddwC49dZbAUy/0HAjSnyjRo0AOHbs\nmOmxJ/k2riTPkevWrZsxJo0WsmfPboo1XL9H0t3iueeeA4KnRIUTyfnypkZNnjzZo8ejWMpkyZLF\n5PlJZGPq1KnmOx4uR/BgInMTjhw5Era+iKpIKYqiKIqiBIijFan27dt7rIwHDhxoOnn7grccDOns\nHk1s3LgxoHyScCO7WzE9lYo6X8icOTNglR+DbZdw8uRJkwfliuRq/PTTT4EPOABy584N2D2gjh8/\nHtQWIWICWLVqVaPgSCVjIFWr6UGsRurUqeNzKwlpjSOl1mIM6JozJaXnGY1SpUoZk07JkQOM6ejF\nixcjMi5Bqrak3c/8+fO9KlEp0bJlS9OvzumqolC5cmWv5f5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Lw+kJob4uoNauXQvYFZoS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JZnlCBl6zlz5jSKnLxXtWrV2L9/PwAJCQnBG7gPSBm0K1IMIMTGxvLee+8BsGnTJsCyIklucyAq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\nCQDaL2fACPKUKVPMc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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd8c6dc43c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# takes 5-10 seconds to execute this\n",
    "show_MNIST(\"testing\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's have a look at the average of all the images of training and testing data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "classes = [\"0\", \"1\", \"2\", \"3\", \"4\", \"5\", \"6\", \"7\", \"8\", \"9\"]\n",
    "num_classes = len(classes)\n",
    "\n",
    "def show_ave_MNIST(dataset):\n",
    "    if dataset == \"training\":\n",
    "        print(\"Average of all images in training dataset.\")\n",
    "        labels = train_lbl\n",
    "        images = train_img\n",
    "    elif dataset == \"testing\":\n",
    "        print(\"Average of all images in testing dataset.\")\n",
    "        labels = test_lbl\n",
    "        images = test_img\n",
    "    else:\n",
    "        raise ValueError(\"dataset must be 'testing' or 'training'!\")\n",
    "        \n",
    "    for y, cls in enumerate(classes):\n",
    "        idxs = np.nonzero([i == y for i in labels])\n",
    "        print(\"Digit\", y, \":\", len(idxs[0]), \"images.\")\n",
    "        \n",
    "        ave_img = np.mean(np.vstack([images[i] for i in idxs[0]]), axis = 0)\n",
    "        #print(ave_img.shape)\n",
    "        \n",
    "        plt.subplot(1, num_classes, y+1)\n",
    "        plt.imshow(ave_img.reshape((28, 28)))\n",
    "        plt.axis(\"off\")\n",
    "        plt.title(cls)\n",
    "\n",
    "\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average of all images in training dataset.\n",
      "Digit 0 : 5923 images.\n",
      "Digit 1 : 6742 images.\n",
      "Digit 2 : 5958 images.\n",
      "Digit 3 : 6131 images.\n",
      "Digit 4 : 5842 images.\n",
      "Digit 5 : 5421 images.\n",
      "Digit 6 : 5918 images.\n",
      "Digit 7 : 6265 images.\n",
      "Digit 8 : 5851 images.\n",
      "Digit 9 : 5949 images.\n"
     ]
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd8c7dbe5c0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Average of all images in testing dataset.\n",
      "Digit 0 : 980 images.\n",
      "Digit 1 : 1135 images.\n",
      "Digit 2 : 1032 images.\n",
      "Digit 3 : 1010 images.\n",
      "Digit 4 : 982 images.\n",
      "Digit 5 : 892 images.\n",
      "Digit 6 : 958 images.\n",
      "Digit 7 : 1028 images.\n",
      "Digit 8 : 974 images.\n",
      "Digit 9 : 1009 images.\n"
     ]
    },
    {
     "data": {
      "image/png": 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ShfrMZz4DAHjuuefw+OOPA6i3cTablX7LjUuvvPIKAODHP/4xrl27BqCusK6vr0sdW1Wo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\nAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fd8c75960f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "show_ave_MNIST(\"training\")\n",
    "show_ave_MNIST(\"testing\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Testing\n",
    "\n",
    "Now, let us convert this raw data into `DataSet.examples` to run our algorithms defined in `learning.py`. Every image is represented by 784 numbers (28x28 pixels) and we append them with its label or class to make them work with our implementations in learning module."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(60000, 784) (60000,)\n",
      "(60000, 785)\n"
     ]
    }
   ],
   "source": [
    "print(train_img.shape, train_lbl.shape)\n",
    "temp_train_lbl = train_lbl.reshape((60000,1))\n",
    "training_examples = np.hstack((train_img, temp_train_lbl))\n",
    "print(training_examples.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we will initialize a DataSet with our training examples, so we can use it in our algorithms."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# takes ~10 seconds to execute this\n",
    "MNIST_DataSet = DataSet(examples=training_examples, distance=manhattan_distance)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Moving forward we can use `MNIST_DataSet` to test our algorithms."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plurality Learner\n",
    "\n",
    "The Plurality Learner always returns the class with the most training samples. In this case, `1`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    }
   ],
   "source": [
    "pL = PluralityLearner(MNIST_DataSet)\n",
    "print(pL(177))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Actual class of test image: 8\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f79589f7dd8>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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TT07NXVVLjz169OjU3Pfff//U+EOHDi099tVXX52aGy6gI2OMves9yBksADQQWABoILAA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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7958a01e80>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\"Actual class of test image:\", test_lbl[177])\n",
    "plt.imshow(test_img[177].reshape((28,28)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is obvious that this Learner is not very efficient. In fact, it will guess correctly in only 1135/10000 of the samples, roughly 10%. It is very fast though, so it might have its use as a quick first guess."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Naive-Bayes\n",
    "\n",
    "The Naive-Bayes classifier is an improvement over the Plurality Learner. It is much more accurate, but a lot slower."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "7\n"
     ]
    }
   ],
   "source": [
    "# takes ~45 Secs. to execute this\n",
    "\n",
    "nBD = NaiveBayesLearner(MNIST_DataSet, continuous=False)\n",
    "print(nBD(test_img[0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Actual class of test image: 7\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f7958b05278>"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7958e68c88>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\"Actual class of test image:\", test_lbl[0])\n",
    "plt.imshow(test_img[0].reshape((28,28)))"
   ]
  },
  {