ang-ex3.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multi-class Classification & Neural Networks"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multi-class Classifier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.optimize import minimize\n",
    "from scipy.io import loadmat # To load .mat files.\n",
    "from scipy.special import expit \n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Data\n",
    "There are 5000 images, each represented by a 20 pixel by 20 pixel matrix unrolled in to a vector of 400 elements.\n",
    "Since the datafile was in matlab native format the zero digit was mapped to 10. We will remap it back to zero here."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "datafile = os.path.join('data', 'ex3data1.mat')\n",
    "data = loadmat(datafile)\n",
    "X, y = data.get('X'), data.get('y')\n",
    "y[y==10] = 0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {},
   "outputs": [],
   "source": [
    "m, n = X.shape\n",
    "k, l = y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5000, 400, 5000, 1)"
      ]
     },
     "execution_count": 133,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m, n, k, l"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 155,
   "metadata": {},
   "outputs": [],
   "source": [
    "# It will be better to have the shape of y be (k, ), \n",
    "# since then we will be able to use the codes from the \n",
    "# previous exercise without modification.\n",
    "\n",
    "# Note to self: It is generally a good idea to check \n",
    "# the dimensions of the data at the beginning.\n",
    "\n",
    "y = y.flatten()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Visualization of data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x1440 with 25 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "nrows = 25\n",
    "\n",
    "def row_to_square(X_row):\n",
    "    return np.reshape(X_row, (20, 20)).T\n",
    "\n",
    "# Choose nrows random rows of X.\n",
    "indices = np.random.randint(m, size=nrows)\n",
    "X_sel = X[indices, :]\n",
    "\n",
    "fig, ax = plt.subplots(1, nrows, figsize=(20, 20))\n",
    "\n",
    "for i in range(nrows):\n",
    "    ax[i].imshow(row_to_square(X_sel[i, :]), cmap='gray')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Cost function and gradient\n",
    " We will always use the regularized cost function and its gradient. They will reduce to the non-regularized versions when the regulator is 0."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 203,
   "metadata": {},
   "outputs": [],
   "source": [
    "def cost_function(theta, x, y, regulator=0):\n",
    "    m = y.size\n",
    "    hypothesis = expit(np.dot(x, theta))\n",
    "    term1 = -y * np.log(hypothesis)\n",
    "    term2 = -(1 - y) * np.log(1 - hypothesis)\n",
    "    cost = np.sum(term1 + term2) / m\n",
    "    theta2 = regulator * np.sum(theta ** 2) / (2*m)\n",
    "    return cost + theta2\n",
    "\n",
    "def gradient(theta, x, y, regulator=0):\n",
    "    m, n = x.shape\n",
    "    hypothesis = expit(np.dot(x, theta))\n",
    "    grad = (1. / m) * np.sum((hypothesis - y)[:, None] * x, axis=0)\n",
    "    reg_theta = np.ones(n) * regulator / m\n",
    "    reg_grad = grad + reg_theta\n",
    "    reg_grad[0] = grad[0]\n",
    "    return reg_grad"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### One vs All classifier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "metadata": {},
   "outputs": [],
   "source": [
    "def optimize_theta(theta, x, y, regulator=0):\n",
    "    result = minimize(cost_function, theta, \n",
    "                      args=(x, y, regulator), jac=gradient,\n",
    "                      method='CG', options={\"maxiter\":400})\n",
    "    return result.x\n",
    "\n",
    "def compute_theta(x, y, num_labels, regulator=0):\n",
    "    m, n = x.shape\n",
    "    x = np.insert(x, 0, 1, axis=1)\n",
    "    initial_theta = np.zeros(n+1)\n",
    "    all_theta = np.zeros((n+1, num_labels))\n",
    "    for label in np.arange(num_labels):\n",
    "        outcome = (y == label).astype(int)\n",
    "        all_theta[:, label] = optimize_theta(initial_theta, x, outcome, regulator)\n",
    "    return all_theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {},
   "outputs": [],
   "source": [
    "num_labels = np.unique(y).size\n",
    "regulator = 0.1\n",
    "theta = compute_theta(X, y, num_labels, regulator)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 199,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(401, 10)"
      ]
     },
     "execution_count": 199,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 200,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict_one_v_all(theta, x):\n",
    "    x = np.insert(x, 0, 1, axis=1)\n",
    "    prbbls = np.dot(x, theta)\n",
    "    return np.argmax(prbbls, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 201,
   "metadata": {},
   "outputs": [],
   "source": [
    "predictions = predict_one_v_all(theta, X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 202,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9644"
      ]
     },
     "execution_count": 202,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(predictions == y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thus the classifier predicts the training data with 96% accuracy."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Neural Networks"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Classify the same data using a pretrained neural network. The network has three layers, with one hidden. The hidden layer has 25 units and the output layer has 10 units, corresponding to the ten digits."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "metadata": {},
   "outputs": [],
   "source": [
    "input_layer_size = 400 # Each image consists of 20 x 20 pixels\n",
    "hidden_layer_size = 25\n",
    "num_labels = 10\n",
    "\n",
    "weightsfile = os.path.join('data', 'ex3weights.mat')\n",
    "weights = loadmat(weightsfile)\n",
    "\n",
    "theta1 = weights.get('Theta1')\n",
    "theta2 = weights.get('Theta2')\n",
    "theta2 = np.roll(theta2, 1, axis=0) # From matlab indexing to python indexing"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 205,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(25, 401)"
      ]
     },
     "execution_count": 205,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta1.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 206,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10, 26)"
      ]
     },
     "execution_count": 206,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta2.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Prediction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 223,
   "metadata": {},
   "outputs": [],
   "source": [
    "def predict_nn(theta1, theta2, x):\n",
    "    # Ensure that x is two-dimensional.\n",
    "    if x.ndim == 1:\n",
    "        x = x[None]\n",
    "    a1 = np.insert(x, 0, 1, axis=1)\n",
    "    z2 = np.dot(theta1, a1.T)\n",
    "    a2 = expit(z2)\n",
    "    a2 = np.insert(a2, 0, 1, axis=0)\n",
    "    z3 = np.dot(theta2, a2)\n",
    "    a3 = expit(z3.T)\n",
    "    return np.argmax(a3, axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 224,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9752"
      ]
     },
     "execution_count": 224,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(predict_nn(theta1, theta2, X) == y)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Thus the network predicts the data with 97.5% accuracy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 228,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 144x144 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 144x144 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 144x144 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 144x144 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
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      "text/plain": [
       "<Figure size 144x144 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 144x144 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAJIAAACaCAYAAABCKBHjAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4wLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvqOYd8AAAC+1JREFUeJztnXmMVeUZh58fM4B0pARkEWURhShUU2ItbSJBmmKLFqpNIwFrxChuCWlFbUvrAqWY4oaNoTZ1oYLGraQoJi4IdUmqSUVSrSICJSwD4yAFzUCxbG//uIf2Muc7M9e539zLvfM+yeSe8573nO899/7mO99+ZGY4TrF0KncATnXgQnKi4EJyouBCcqLgQnKi4EJyouBCykPSKZJMUm2y/6KkqSVId7akx9s7nfak4oQkaZOkfZL2SGqU9EdJx7dHWmZ2gZktKjCmce0RQ0Z6X5L0gKSdkj6T9Eap0s6i4oSUMNHMjgfOBr4O3NrcQTkq9f5a40GgFzA8+ZxR3nAqV0gAmNk24EXgTABJr0m6Q9JfgX8Dp0rqIekRSQ2StkmaK6km8a+RdE/yn70R+F7+9ZPrTcvbv1rSh5KaJK2RdLakx4BBwPNJLvmzxPebkt6U9KmkdyWNzbvOEEmvJ9d5Behd6D1LOh34PnCNmX1iZofM7J02fYExMbOK+gM2AeOS7YHAB8Cvk/3XgC3AV4BaoDPwLPAHoA7oC/wNuDbxvw5Ym1ynF/AqYEBt3vWmJduXANvI5YAChgKDm8eU7J8M/Au4kNw/6/nJfp/k+FvAfKArMAZoAh7PO/894NKM+78c+AdwH7Az2f5h2X+XcgfQRiHtAT4FNgMPAN3yfvg5eb79gP8cOZ7YpgCvJtt/Aa7LO/adFoT0MvCT1sSd7P8ceKyZz8vAVHK510GgLu/YE/lCauX+f5nEOBvoApyXfB/Dy/m71FKZXGxmKzKObc3bHkwuV2qQdMTWKc/npGb+m1tIcyDwzwLjGwxcImlinq0zuRzvJGC3me1tlu7AAq+9DzgAzDWzg8Drkl4l90/wYYHXiE6lCqkl8oczbCWXI/VOvvTmNHD0DziohetuBU4rIM0jvo+Z2dXNHSUNBnpKqssT06DANbJ4r0C/klLRhe3WMLMGYDlwr6QvS+ok6TRJ5yUuzwA/ljRAUk9gZguXexi4WdLXkhrh0EQUAI3AqXm+jwMTJX03KdAfJ2mspAFmthlYBfxKUhdJo4GJFM4b5MqBv5BUK+lcYCy5R2fZqGohJVxOriyxBtgNLAH6J8ceIvcDvAusBv6cdREz+xNwB7nyTBO5Qnyv5PBvgFuTGtrNZrYVuIhceeYTcjnUT/n/930p8A1gFzALWJyflqQPJP0oI44DybUvBD5L7uFyM1tbwHfRbigpwDlOUXSEHMkpAS4kJwpFCUnSeEkfSdogqaWCqlPltLmMlHQzrCPXalsPvA1MMbM1LZxjnTp1nEzw8OHDKVul3f/hw4d3mlmf1vyKaUcaBWwws40Akp4iV5vIFFKnTp2oq6srIsljk5BgAPbt25eydevWLeh7rAqsqamppUba/1FM9CdzdKtwfWJzOiDF5EgK2FLPSUnXANck20Uk5xzLFCOkeo7uXhgAbG/uZGYPkhs/Q01NjTdaVSnFCOltYJikIeSGV0wm12Jb1Rw8mO6y69MnXBadNm1ayrZ48eKAJ2zfnvofpKam5gtGVz7aLCQzOyhpOrkuhhpgoZl9EC0yp6IoqvffzF4AXogUi1PBHJt1TqficCE5UXAhOVGoxhGS0Qh1Hx06dChlmzRpUvD82267LWVbtmxZ0Le+vj5lq6Ram+dIThRcSE4UXEhOFFxIThS8sE24UA3h4SFjxoxJ2W688cbg+WvWpEfU7Nq1K+hb6R3aniM5UXAhOVFwITlRcCE5UXAhOVHwWhvZg/ePO+64lC1UQ+vRo0fw/Ntvvz1la2hoCPpWUndICM+RnCi4kJwouJCcKBRVRpK0idwSL4eAg2Z2ToygnMojRmH7W2a2M8J1SkKoYB0qVAPMnJlezmD06NEp28MPPxw8f8mSJSlb1oxa7yJxHIoXkgHLJb2TzKh1OijFPtrONbPtkvoCr0haa2ZHvc7Ap2x3DIrKkcxse/K5A1hKboWS5j4Pmtk5ZnaOC6l6abOQJNVJ6n5km9w6z+/HCsypLIp5tPUDlia5TC3whJm9FCWqdiQ0dz9UEwO4/vrrU7ZVq1albHfffXfw/P3796dsld4VkkUxc/83Al+NGItTwXj134mCC8mJggvJiULVjkcKTa0G6N69e8o2Z86coO+ePXtSttmzZ6dsjY2NwfNDXS9ZM1ZClYDa2vDPcyw2o3iO5ETBheREwYXkRMGF5ETBheREoSpqbaGaUFbN5sorr0zZRowYEfRdsGBByrZ69eqUrUuXLsHzQ4PosnyHDh2asm3cuLHg65a7Juc5khMFF5ITBReSEwUXkhOFqihsHzhwIGU744wzgr6h94M0NTUFfZ9++umC0soaYxTynT59etD3sssuS9nmzZsX9F26dGnKVu7ZKZ4jOVFwITlRcCE5UXAhOVFotbAtaSEwAdhhZmcmtl7A08ApwCZgkpntbr8wc2SN5QmN25k8eXLQd9iwYSnb/Pnzg75r165N2UKF1549ewbPv+KKK1K2GTNmBH1DayzNmjUr6BuagLB169aAZ+kmGxSSIz0KjG9mmwmsNLNhwMpk3+nAtCqkZOZs88WhLwIWJduLgIsjx+VUGG1tR+pnZg0AZtaQTNkO4lO2Owbt3iDpb9nuGLS11tYoqT9A8rkjXkhOJdLWHGkZMBWYl3w+Fy2iFsiqtXXr1i1lGzduXNA3VBO7//77C44h9Hi+6qqrgr633HJLyrZixYqg7/Dhw1O2E088MegbqiVu2bIl6FsqWs2RJD0JvAWcLqle0lXkBHS+pPXA+cm+04FpNUcysykZh74dORangvGWbScKLiQnChU1HimrsN27d++UrW/fcNPW5s2bU7bQuCGAzz//PGW74YYbUrabbropeP769etTtpUrVwZ9zzrrrJQta/B/6DUUWeORSoXnSE4UXEhOFFxIThRcSE4UXEhOFCqq1pZVM/n4449Ttg0bNgR9R41KLQUe7MoAePPNN1O2UHdI165dg+efcMIJKVtooa4ssmaR7NiR7tos92q5niM5UXAhOVFwITlRcCE5UVBWt0N7UFNTY3V1dW0+PyvW0HpBEyZMCPreeeedKduAAQOCvqFXQHTu3DllyxpCHLJnzfaYO3duyvb8888Hfffu3ZuytVcXSVNT0zuFvBnUcyQnCi4kJwouJCcKLiQnCoWM2V4oaYek9/NssyVtk/T35O/C9g3TOdYppIvkUWABsLiZ/T4zuyd6RC3wRWpHy5cvD/qGamJDhgwJ+o4cOTJl69WrV0shHsXu3enlEO66666g77p161K2UA0Ryj+ILURbp2w7zlEUI+3pkt5LHn3h5TjITdmWtErSqlK2WTmlpa1C+j1wGjASaADuzXL0t2x3DNokJDNrNLNDZnYYeIjAa9qdjkWbxiNJ6n9kNRLgB5T5Ne2hwmfoRXoAL72UfhF4qIsly17s4zlr7FKWvVIoZMW2J4GxQG9J9cAsYKykkYCRW7Ht2naM0akA2jpl+5F2iMWpYI69BgmnInEhOVFwITlRqKhZJF+ErDarrG4Hpzg8R3Ki4EJyouBCcqLgQnKi4EJyouBCcqLgQnKi4EJyouBCcqLgQnKi4EJyouBCcqLgQnKi4EJyouBCcqJQ0oW2JH0CHHkZSG9gZ8kSLx3Vdl+DzaxPa04lFdJRCedm3ra6ElilUa331Rr+aHOi4EJyolBOIT1YxrTbk2q9rxYpWxnJqS780eZEoeRCkjRe0keSNkiaWer0Y5KxLGIvSa9IWp98Zq4dVU2UVEiSaoDfARcAI4ApkkaUMobIPAqMb2abCaw0s2HAymS/6il1jjQK2GBmG81sP/AUcFGJY4hGxrKIFwGLku1FwMUlDapMlFpIJwP571CoT2zVRL8ja0cln+HXfVcZpRZSaB61VxurgFILqR4YmLc/ANhe4hjam0ZJ/SG3sh2Qft1jFVJqIb0NDJM0RFIXYDKwrMQxtDfLgKnJ9lTguTLGUjJK3iCZvCXgt0ANsNDM7ihpABHJXxYRaCS3LOKzwDPAIGALcImZVf065d6y7UTBW7adKLiQnCi4kJwouJCcKLiQnCi4kJwouJCcKLiQnCj8F0x/fdXTz6CuAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 144x144 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 144x144 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 144x144 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 144x144 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "indices = np.random.randint(m, size=10)\n",
    "\n",
    "for index in indices:\n",
    "    fig = plt.figure(figsize=(2, 2))\n",
    "    predicted_value = predict_nn(theta1, theta2, X[index, :])\n",
    "    plt.imshow(row_to_square(X[index, :]), cmap='gray')\n",
    "    fig.suptitle('Predicted: %d' %predicted_value)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}