exercise3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Programming Exercise 3: Multi-class Classification and Neural Networks"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "%matplotlib inline\n",
    "\n",
    "from scipy.io import loadmat"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1&nbsp;&nbsp;&nbsp;&nbsp;Multi-class Classification\n",
    "\n",
    "##### Problem Statement\n",
    "For this exercise, we will use **logistic regression** and **neural networks** to recognize handwritten digits (from 0 to 9). In this part of the exercise we will extend our previous implementation of logistic regression and apply it to one-vs-all classification.\n",
    "\n",
    "#### 1.1&nbsp;&nbsp;&nbsp;&nbsp;Dataset\n",
    "We are given a dataset in ex3data.mat that contains 5000 training examples of handwritten digits, where each training example is a 20 X 20 pixel grayscale image of the digit. Each pixel is repsented by a floating point number indicating the grayscale intensity at that location.  \n",
    "\n",
    "This 20 by 20 pixel grid is \"unrolled\" into 400-dimensional vector. Each of these training examples become a single row in our dataset. This gives us a 5000 X 400 design matrix X where every row is a training example for a handwritten digit image. The second part of the training set is a 5000-dimnesional vectory y that contains labels for the training set. Labels range from 1 to 10 where 10 reprsents digit '0'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "__header__\n",
      "__version__\n",
      "__globals__\n",
      "X\n",
      "y\n"
     ]
    }
   ],
   "source": [
    "# Loading Mat file\n",
    "mat=loadmat('./ex3data1.mat')\n",
    "print(*mat.keys(),sep='\\n')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TRAINING DATASET SHAPE : 5000 X 401\n"
     ]
    },
    {
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       "       x1   x2   x3   x4   x5   x6   x7   x8   x9  x10  ...  x392  x393  x394  \\\n",
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       "\n",
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       "\n",
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      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Loading data from mat to Dataframe\n",
    "m,n=mat['X'].shape\n",
    "\n",
    "data=pd.DataFrame()\n",
    "for i in range(n):\n",
    "    data[f'x{i+1}']=mat['X'].T[i]\n",
    "\n",
    "# Converting label 10 to label 0\n",
    "data['y']=mat['y']\n",
    "data.loc[data['y']==10,'y']=0\n",
    "\n",
    "print('TRAINING DATASET SHAPE : {0} X {1}'.format(*data.shape))\n",
    "data.sample(5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.2&nbsp;&nbsp;&nbsp;&nbsp;Visualizing the data\n",
    "We will begin by visualizing a subset of the training set. We will randomly select 100 rows from X. This function maps each row to a 20 X 20 pixel image and displays together."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def displayData(X):\n",
    "    m,n=X.shape\n",
    "    width=int(np.sqrt(n))\n",
    "    height=int(n/width)\n",
    "    rows=int(np.floor(np.sqrt(m)))\n",
    "    cols=int(np.ceil(m/rows))\n",
    "    totalWidth=cols+cols*width\n",
    "    displayArray=np.zeros((1,totalWidth))\n",
    "    rowPadding=np.ones((1,totalWidth))\n",
    "    colPadding=np.ones((height,1))\n",
    "    index=0\n",
    "    for i in range(rows):\n",
    "        row=colPadding*0\n",
    "        for j in range(cols):\n",
    "            if index<m:\n",
    "                x=X[index].reshape((width,height)).T\n",
    "                index=index+1\n",
    "            else:\n",
    "                x=np.zeros((width,height)).T\n",
    "            row=np.column_stack((row,x))\n",
    "            if j<cols-1:\n",
    "                row=np.column_stack((row,colPadding))\n",
    "        displayArray=np.row_stack((displayArray,row))\n",
    "        if i<rows-1:\n",
    "            displayArray=np.row_stack((displayArray,rowPadding))\n",
    "    displayArray=np.row_stack((displayArray,rowPadding*0))\n",
    "    plt.imshow(displayArray,cmap='gray')\n",
    "    plt.axis('off')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "displayData(data.sample(100).iloc[:,:-1].values)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.3&nbsp;&nbsp;&nbsp;&nbsp;Vectorizing Logistic Regression\n",
    "We will be using mutiple one-vs-all logistic regression models to build multi-class classifier. Since there are 10 classes, we wil need to train 10 separate logistic regression. To make this training efficient, it is important to ensure that our code is well vectorized. In this section, we will implement a vectorized version of logistic regression that does not employ any for loops.\n",
    "\n",
    "**Formulae :**\n",
    "\n",
    "$$ h_\\theta(x)=g(\\theta^Tx) $$\n",
    "$$ g(z)=\\frac{1}{1+e^{-z}} $$\n",
    "$$ J(\\theta)= \\frac{-1}{m}\\sum_{i=0}^m[y^{(i)}log(h_\\theta(x^{(i)}))+(1-y^{(i)})log(1-h_\\theta(x^{(i)})]+\\frac{\\lambda}{2m}\\sum_{j=1}^n\\theta_j^2$$\n",
    "$$ \\theta_j:=\\theta_j-\\frac{\\alpha}{m}(\\sum_{i=0}^m(h_\\theta(x^{(i)})-y^{(i)})x_j^{(i)}+\\lambda\\sum_{j=1}^n\\theta_j) $$\n",
    "\n",
    "**From the previous notebook [Exercise-2](https://nbviewer.jupyter.org/github/rj425/ML-Coursera/blob/master/Exercise-2/ex2.ipynb), all these functions are already vectorized.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(z):\n",
    "    sigma=1/(1+np.exp(-z))\n",
    "    return sigma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict(X,theta):\n",
    "    '''Predicts by applying logistic function on linear model'''\n",
    "    z=np.dot(X,theta.T)\n",
    "    h=sigmoid(z)\n",
    "    return h"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def computeCost(h,y):\n",
    "    '''Computes the cost using Cross Entropy function'''\n",
    "    m=y.shape[0]\n",
    "    J=(-1/m)*np.sum(np.multiply(y,np.log(h))+np.multiply(1-y,np.log(1-h)))\n",
    "    return J"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def regularizedGradientDescent(X,y,theta,alpha,lmbda,iterations):\n",
    "    '''Minimizes the cost function using Gradient Descent Optimization Algorithm'''\n",
    "    m=X.shape[0]\n",
    "    jHistory=[]\n",
    "    for i in range(iterations):\n",
    "        h=predict(X,theta)\n",
    "        # Computing cost\n",
    "        J=computeCost(h,y)\n",
    "        # Adding the regularized term\n",
    "        J=J+(lmbda/(2*m))*np.sum(np.power(theta[:,1:],2))\n",
    "        jHistory.append(J)\n",
    "        # Parameters update rule\n",
    "        gradient=(alpha/m)*(np.dot((h-y).T,X))\n",
    "        # Adding the regularized term\n",
    "        gradient=gradient+(alpha/m)*lmbda*np.column_stack((np.zeros((1,1)),theta[:,1:]))\n",
    "        theta=theta-gradient\n",
    "    return (theta,jHistory)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.4&nbsp;&nbsp;&nbsp;&nbsp;One-vs-all Classification\n",
    "In this part of the exercise, **we will implement One-vs-all classification by training multiple logistic regression classifiers, one for each of K classes in our dataset.**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def oneVsAll(X,Y,alpha,lmbda,iterations):\n",
    "    '''Returns all the classifier parameters in a matrix with shape of classes X features'''\n",
    "    m,n=X.shape\n",
    "    # Initializing theta\n",
    "    intialTheta=np.zeros(shape=(1,n))\n",
    "    labels=np.unique(Y)\n",
    "    thetas=np.zeros(shape=(len(labels),n))\n",
    "    i=0\n",
    "    print('Training classifiers...\\n')\n",
    "    for label in labels:\n",
    "        y=np.zeros(shape=(m,1))\n",
    "        y[Y==label]=1\n",
    "        theta,jHistory=regularizedGradientDescent(X,y,intialTheta,alpha,lmbda,iterations)\n",
    "        thetas[i,:]=theta\n",
    "        print(f'For classifier{label} , J = {jHistory[iterations-1]:.3f}')\n",
    "        i+=1\n",
    "    return thetas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Training classifiers...\n",
      "\n",
      "For classifier0 , J = 0.016\n",
      "For classifier1 , J = 0.023\n",
      "For classifier2 , J = 0.063\n",
      "For classifier3 , J = 0.067\n",
      "For classifier4 , J = 0.046\n",
      "For classifier5 , J = 0.069\n",
      "For classifier6 , J = 0.030\n",
      "For classifier7 , J = 0.042\n",
      "For classifier8 , J = 0.088\n",
      "For classifier9 , J = 0.083\n"
     ]
    }
   ],
   "source": [
    "m=data.shape[0]\n",
    "\n",
    "X=data.values[:,:-1]\n",
    "# Adding intercept term to the design matrix\n",
    "intercept=np.ones(shape=(m,1))\n",
    "X=np.column_stack((intercept,X))\n",
    "y=data['y'].values.reshape((m,1))\n",
    "\n",
    "alpha=1\n",
    "lmbda=0.3\n",
    "iterations=3000\n",
    "\n",
    "thetas=oneVsAll(X,y,alpha,lmbda,iterations)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 1.4.1&nbsp;&nbsp;&nbsp;&nbsp;One-vs-all Prediction\n",
    "After training One-vs-all classifier, we can use it to predict the digit contained in a given image. For each input, we should compute the 'probability' that it belongs to each class using the trained logistic regression classifiers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predictOneVsAll(thetas,X):\n",
    "    '''Predic the label for a trained One-vs-all classifier. The labels are in the range 0 to 9'''\n",
    "    h=predict(X,thetas)\n",
    "    labels=h.argmax(axis=1)\n",
    "    return labels.reshape((X.shape[0],1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "def calculateAccuracy(h,y):\n",
    "    '''Calculates the accuray between the target and prediction'''\n",
    "    m=y.shape[0]\n",
    "    unique,counts=np.unique(h==y,return_counts=True)\n",
    "    dic=dict(zip(unique,counts))\n",
    "    accuracy=(dic[True]/m)*100\n",
    "    return accuracy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TRAINING ACCURACY : 94.16\n"
     ]
    }
   ],
   "source": [
    "h=predictOneVsAll(thetas,X)\n",
    "accuracy=calculateAccuracy(h,y)\n",
    "print(f'TRAINING ACCURACY : {accuracy:.2f}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 2&nbsp;&nbsp;&nbsp;&nbsp;Neural Networks\n",
    "\n",
    "In previous part of the exercise, we implemented multi-class logistic regression to recognize the handwritten digits. **However, logistic regression cannot form more complex hypotheses, as it is only a Linear Classifier.**  \n",
    "\n",
    ">**One may ask why is logistic regression a linear model if it can fit curves to our data??**  \n",
    "That's because the linearity of the model is concerned by the linearity of the parameters $\\theta$. Here the target variable is a function of parameter  ($\\theta$) multiplied by the independent variable ($x_i$). And we can fit the curves to our data using the non linear transformation of independent variables or features but the parameters are still linear.\n",
    "\n",
    "**Non Linear Hypotheses**  \n",
    "If the number of features are large which will ususally be the case, we will move towards the non linear hypotheses for a better fit for the data. So if $n=100$ :\n",
    "- For quadratic hypotheses, $n\\approx5000$ features\n",
    "- For cubic hypotheses, $n\\approx170000$ features  \n",
    "\n",
    "Solving such problems with logistic regression can cause two problems:\n",
    "- Computationally expensive\n",
    "- Time consuming\n",
    "\n",
    "Not a good way to learn complex Non Linear hypthoses when feature space is large. Hence, **Neural Networks**."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.1&nbsp;&nbsp;&nbsp;&nbsp;Model Representation\n",
    "\n",
    "\n",
    "<table>\n",
    "    <tr>\n",
    "        <td>\n",
    "            <img src=\"images/neuron.png\" width=\"300\">\n",
    "        </td>\n",
    "        <td>\n",
    "            <img src=\"images/nn.png\" width=\"300\">\n",
    "        </td>\n",
    "    </tr>\n",
    "</table>\n",
    "\n",
    "$a_i^{(j)}=$ \"activation\" of unit $i$ in layer $j$  \n",
    "$\\theta^{(j)}=$ matrix of weights controlling function mapping from layer $j$ to layer $j+1$  \n",
    "$g(x)=$ sigmoid activation function  \n",
    "\n",
    "**If network has $s_j$ units in layer $j$, $s_{j+1}$ units in layer $j+1$, then $\\theta^{(j)}$ will be of dimension $s_{j+1}$ X $(s_j+1)$**\n",
    "\n",
    "\n",
    "$$ a^{(2)}_1=g(\\theta_{10}^{(1)}x_0+\\theta_{11}^{(1)}x_1+\\theta_{12}^{(1)}x_2+\\theta_{13}^{(1)}x_3) $$\n",
    "\n",
    "$$ a^{(2)}_2=g(\\theta_{20}^{(1)}x_0+\\theta_{21}^{(1)}x_1+\\theta_{22}^{(1)}x_2+\\theta_{23}^{(1)}x_3) $$\n",
    "\n",
    "$$ a^{(2)}_3=g(\\theta_{30}^{(1)}x_0+\\theta_{31}^{(1)}x_1+\\theta_{32}^{(1)}x_2+\\theta_{33}^{(1)}x_3) $$\n",
    "\n",
    "\n",
    "In this exercise, we will be using the parameters from a neural network that is already trained. Our goal is to implement the **Feed-Forward Progration** algorithm for prediction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "__header__\n",
      "__version__\n",
      "__globals__\n",
      "Theta1\n",
      "Theta2\n"
     ]
    }
   ],
   "source": [
    "# Loading weights\n",
    "weights=loadmat('./ex3weights.mat')\n",
    "print(*weights.keys(),sep='\\n')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The neural network we are about to use has 3 layers - an input layer ($L_1$), a hidden layer ($L_2$) and an output layer ($L_3$). \n",
    "\n",
    "* L1 layer has 400 Neuron units (20 X 20 pixel image) excluding the extra bias unit that always output +1\n",
    "* L2 layer has 25 Neuron units\n",
    "* L3 layer has 10 Neuron Units"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "X : (5000, 401)\n",
      "Theta1 : (25, 401)\n",
      "Theta2 : (10, 26)\n"
     ]
    }
   ],
   "source": [
    "theta1=weights['Theta1']\n",
    "theta2=weights['Theta2']\n",
    "print(f'X : {X.shape}')\n",
    "print(f'Theta1 : {theta1.shape}')\n",
    "print(f'Theta2 : {theta2.shape}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 2.2&nbsp;&nbsp;&nbsp;&nbsp;Feedforward Propogation and Prediction\n",
    "\n",
    "**Vectorized Implementation** for three layered Neural Network:\n",
    "\n",
    "Step 0 : $a^{(1)}=x$  \n",
    "Step 1 : $z^{(2)}=\\theta^{(1)}a^{(1)}$  \n",
    "Step 2 : $a^{(2)}=g(z^{(2)})$  \n",
    "Step 3 : Add $a^{(2)}_0=1$  \n",
    "Step 4 : $z^{(3)}=\\theta^{(2)}a^{(2)}$  \n",
    "Step 5 : $a^{(3)}=g(z^{(3)})$  \n",
    "Step 6 : $h_\\theta(x)=a^{(3)}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predictNN(theta1,theta2,X):\n",
    "    '''Predict the label of an input given a trained neural network'''\n",
    "    m,n=X.shape\n",
    "    # Feed Forward Propogation\n",
    "    a1=X\n",
    "    z2=np.dot(a1,theta1.T)\n",
    "    a2=sigmoid(z2)\n",
    "    a2=np.column_stack((np.ones(shape=(a2.shape[0],1)),a2))\n",
    "    z3=np.dot(a2,theta2.T)\n",
    "    a3=sigmoid(z3)\n",
    "    h=a3\n",
    "    labels=h.argmax(axis=1)\n",
    "    return labels.reshape((m,1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "TRAINING ACCURACY : 97.52\n"
     ]
    }
   ],
   "source": [
    "# Using label 10 for digit 0\n",
    "y=mat['y']\n",
    "\n",
    "h=predictNN(theta1,theta2,X)\n",
    "# Adding one to h because matlab indexing starts from 1 whereas python indexing starts from 0\n",
    "h+=1\n",
    "\n",
    "accuracy=calculateAccuracy(h,y)\n",
    "print(f'TRAINING ACCURACY : {accuracy:.2f}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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