learning.ipynb

    "$$P(X_{1}, X_{2}, ..., X_{n}|Y) = P(X_{1}|Y)*P(X_{2}|Y)*...*P(X_{n}|Y)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Classifying an Item\n",
    "\n",
    "How can we use the above to classify an item though?\n",
    "\n",
    "We have a dataset with a set of classes (**C**) and we want to classify an item with a set of features (**F**). Essentially what we want to do is predict the class of an item given the features.\n",
    "\n",
    "For a specific class, **Class**, we will find the conditional probability given the item features:\n",
    "\n",
    "$$P(Class|F) = \\dfrac{P(F|Class)*P(Class)}{P(F)}$$\n",
    "\n",
    "We will do this for every class and we will pick the maximum. This will be the class the item is classified in.\n",
    "\n",
    "The features though are a vector with many elements. We need to break the probabilities up using the multiplication rule. Thus the above equation becomes:\n",
    "\n",
    "$$P(Class|F) = \\dfrac{P(Class)*P(F_{1}|Class)*P(F_{2}|Class)*...*P(F_{n}|Class)}{P(F_{1})*P(F_{2})*...*P(F_{n})}$$\n",
    "\n",
    "The calculation of the conditional probability then depends on the calculation of the following:\n",
    "\n",
    "*a)* The probability of **Class** in the dataset.\n",
    "\n",
    "*b)* The conditional probability of each feature occuring in an item classified in **Class**.\n",
    "\n",
    "*c)* The probabilities of each individual feature.\n",
    "\n",
    "For *a)*, we will count how many times **Class** occurs in the dataset (aka how many items are classified in a particular class).\n",
    "\n",
    "For *b)*, if the feature values are discrete ('Blue', '3', 'Tall', etc.), we will count how many times a feature value occurs in items of each class. If the feature values are not discrete, we will go a different route. We will use a distribution function to calculate the probability of values for a given class and feature. If we know the distribution function of the dataset, then great, we will use it to compute the probabilities. If we don't know the function, we can assume the dataset follows the normal (Gaussian) distribution without much loss of accuracy. In fact, it can be proven that any distribution tends to the Gaussian the larger the population gets (see [Central Limit Theorem](https://en.wikipedia.org/wiki/Central_limit_theorem)).\n",
    "\n",
    "*NOTE:* If the values are continuous but use the discrete approach, there might be issues if we are not lucky. For one, if we have two values, '5.0 and 5.1', with the discrete approach they will be two completely different values, despite being so close. Second, if we are trying to classify an item with a feature value of '5.15', if the value does not appear for the feature, its probability will be 0. This might lead to misclassification. Generally, the continuous approach is more accurate and more useful, despite the overhead of calculating the distribution function.\n",
    "\n",
    "The last one, *c)*, is tricky. If feature values are discrete, we can count how many times they occur in the dataset. But what if the feature values are continuous? Imagine a dataset with a height feature. Is it worth it to count how many times each value occurs? Most of the time it is not, since there can be miscellaneous differences in the values (for example, 1.7 meters and 1.700001 meters are practically equal, but they count as different values).\n",
    "\n",
    "So as we cannot calculate the feature value probabilities, what are we going to do?\n",
    "\n",
    "Let's take a step back and rethink exactly what we are doing. We are essentially comparing conditional probabilities of all the classes. For two classes, **A** and **B**, we want to know which one is greater:\n",
    "\n",
    "$$\\dfrac{P(F|A)*P(A)}{P(F)} vs. \\dfrac{P(F|B)*P(B)}{P(F)}$$\n",
    "\n",
    "Wait, **P(F)** is the same for both the classes! In fact, it is the same for every combination of classes. That is because **P(F)** does not depend on a class, thus being independent of the classes.\n",
    "\n",
    "So, for *c)*, we actually don't need to calculate it at all."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Wrapping It Up\n",
    "\n",
    "Classifying an item to a class then becomes a matter of calculating the conditional probabilities of feature values and the probabilities of classes. This is something very desirable and computationally delicious.\n",
    "\n",
    "Remember though that all the above are true because we made the assumption that the features are independent. In most real-world cases that is not true though. Is that an issue here? Fret not, for the the algorithm is very efficient even with that assumption. That is why the algorithm is called **Naive** Bayes Classifier. We (naively) assume that the features are independent to make computations easier."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 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": [
    "## Learner Evaluation\n",
    "\n",
    "In this section we will evaluate and compare algorithm performance. The dataset we will use will again be the iris one."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "iris = DataSet(name=\"iris\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Naive Bayes\n",
    "\n",
    "First up we have the Naive Bayes algorithm. First we will test how well the Discrete Naive Bayes works, and then how the Continuous fares."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error ratio for Discrete: 0.033333333333333326\n",
      "Error ratio for Continuous: 0.040000000000000036\n"
     ]
    }
   ],
   "source": [
    "nBD = NaiveBayesLearner(iris, continuous=False)\n",
    "print(\"Error ratio for Discrete:\", err_ratio(nBD, iris))\n",
    "\n",
    "nBC = NaiveBayesLearner(iris, continuous=True)\n",
    "print(\"Error ratio for Continuous:\", err_ratio(nBC, iris))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The error for the Naive Bayes algorithm is very, very low; close to 0. There is also very little difference between the discrete and continuous version of the algorithm."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## k-Nearest Neighbors\n",
    "\n",
    "Now we will take a look at kNN, for different values of *k*. Note that *k* should have odd values, to break any ties between two classes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error ratio for k=1: 0.0\n",
      "Error ratio for k=3: 0.08666666666666667\n",
      "Error ratio for k=5: 0.1466666666666666\n",
      "Error ratio for k=7: 0.21999999999999997\n"
     ]
    }
   ],
   "source": [
    "kNN_1 = NearestNeighborLearner(iris, k=1)\n",
    "kNN_3 = NearestNeighborLearner(iris, k=3)\n",
    "kNN_5 = NearestNeighborLearner(iris, k=5)\n",
    "kNN_7 = NearestNeighborLearner(iris, k=7)\n",
    "\n",
    "print(\"Error ratio for k=1:\", err_ratio(kNN_1, iris))\n",
    "print(\"Error ratio for k=3:\", err_ratio(kNN_3, iris))\n",
    "print(\"Error ratio for k=5:\", err_ratio(kNN_5, iris))\n",
    "print(\"Error ratio for k=7:\", err_ratio(kNN_7, iris))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice how the error became larger and larger as *k* increased. This is generally the case with datasets where classes are spaced out, as is the case with the iris dataset. If items from different classes were closer together, classification would be more difficult. Usually a value of 1, 3 or 5 for *k* suffices.\n",
    "\n",
    "Also note that since the training set is also the testing set, for *k* equal to 1 we get a perfect score, since the item we want to classify each time is already in the dataset and its closest neighbor is itself."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Perceptron\n",
    "\n",
    "For the Perceptron, we first need to convert class names to integers. Let's see how it performs in the dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Error ratio for Perceptron: 0.31999999999999995\n"
     ]
    }
   ],
   "source": [
    "iris2 = DataSet(name=\"iris\")\n",
    "iris2.classes_to_numbers()\n",
    "\n",
    "perceptron = PerceptronLearner(iris2)\n",
    "print(\"Error ratio for Perceptron:\", err_ratio(perceptron, iris2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The Perceptron didn't fare very well mainly because the dataset is not linearly separated. On simpler datasets the algorithm performs much better, but unfortunately such datasets are rare in real life scenarios."
   ]
  },
  {
   "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": "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": 3,
   "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": 4,
   "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": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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fxo0be20zZ84EoEWLFtnYu+x38sknA/71cMopp3ht1113HQDfffcd4Kc4AlSsWBGAdevW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\nAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f614fccc198>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# takes 5-10 seconds to execute this\n",
    "show_MNIST(train_lbl, train_img)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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bQODOO+8E4LHHHgNyX8jT/Rzs3bs3kD3aI/8ZOHBg1P+7RZc+/fTTwm5OIOwa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\n9ddfH0g91ypwxUKDqeTxkUceG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1T24osvBuL1rxBHLd555x0gXt9Zy8LvIM8880wjjqTy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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f6147f2dc50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# takes 5-10 seconds to execute this\n",
    "show_MNIST(test_lbl, test_img)"
   ]
  },
  {
   "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": 7,
   "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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EmBfUFMR+K/Taaawu5aKWp5qaGgBpmcuRI0dWzjGumO9XnaQVlLLQ8ry09NLq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\npfUISK1KXOXrap/Wt1gJWa5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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f614c36abe0>"
      ]
     },
     "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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GU9N7AwCvvPIKgNTLoyv0sNytxhKHVlG1fIYbNgJ1yxLm2XuhhKtvjbFk6Vpa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\nxxhjjDHGGFMq/h+V5nVldnlnJQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f614d1b6a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "print(\"Average of all images in training dataset.\")\n",
    "show_ave_MNIST(train_lbl, train_img)\n",
    "\n",
    "print(\"Average of all images in testing dataset.\")\n",
    "show_ave_MNIST(test_lbl, test_img)"
   ]
  },
  {
   "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": 8,
   "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": 9,
   "metadata": {
    "collapsed": true
   },
   "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": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    }
   ],
   "source": [
    "pL = PluralityLearner(MNIST_DataSet)\n",
    "print(pL(177))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Actual class of test image: 8\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f614c5b29b0>"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f614c422358>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "print(\"Actual class of test image:\", test_lbl[177])\n",
    "plt.imshow(test_img[177].reshape((28,28)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [