learning_apps.ipynb 197 ko
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{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# LEARNING APPLICATIONS\n",
    "\n",
    "In this notebook we will take a look at some indicative applications of machine learning techniques. We will cover content from [`learning.py`](https://github.com/aimacode/aima-python/blob/master/learning.py), for chapter 18 from Stuart Russel's and Peter Norvig's book [*Artificial Intelligence: A Modern Approach*](http://aima.cs.berkeley.edu/). Execute the cell below to get started:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from learning import *\n",
    "from notebook import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## CONTENTS\n",
    "\n",
    "* MNIST Handwritten Digits\n",
    "    * Loading and Visualising\n",
    "    * Testing"
   ]
  },
  {
   "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.\n",
    "\n",
    "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": 2,
   "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": 3,
   "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 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": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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uiR8XVjYWgrueH3/8sdtnk5jnzJmTtee08bQxT1c4Ik6aNm0KJEfnzz33XAA2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\nTSogEJeXVVqLFiyXw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PTfSlMa97zzzhv2PfXUU0DpKWrx38BKX85Hf6tofmqRJulIjpmZ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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f5317f27400>"
      ]
     },
     "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": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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YKZIjIiIiIiKhEoo5OVZ688wzzwSgd+/ebp/N0xk4cKBrs7tDdnfTZ2VorRye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\nRQBNurmtlhVgkR2ACy64AAi+h/2IkP32LDdWHj8d/3vArLLKKtU+3jI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cAAAg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\n/wGjgMWJk2e4ogAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f53133edbe0>"
      ]
     },
     "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": 6,
   "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 0x7f5316873630>"
      ]
     },
     "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 0x7f5314187400>"
      ]
     },
     "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": 7,
   "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": 8,
   "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": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    }
   ],
   "source": [
    "pL = PluralityLearner(MNIST_DataSet)\n",
    "print(pL(177))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Actual class of test image: 8\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f5313b6d320>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f53114917f0>"
      ]
     },
     "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": [
    "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": 11,
   "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": "markdown",
   "metadata": {},
   "source": [
    "### k-Nearest Neighbors\n",
    "\n",
    "We will now try to classify a random image from the dataset using the kNN classifier."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "5\n"
     ]
    }
   ],
   "source": [
    "# takes ~20 Secs. to execute this\n",
    "kNN = NearestNeighborLearner(MNIST_DataSet, k=3)\n",
    "print(kNN(test_img[211]))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To make sure that the output we got is correct, let's plot that image along with its label."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Actual class of test image: 5\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f53133da7f0>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f53116f9eb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "print(\"Actual class of test image:\", test_lbl[211])\n",
    "plt.imshow(test_img[211].reshape((28,28)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hurray! We've got it correct. Don't worry if our algorithm predicted a wrong class. With this techinique we have only ~97% accuracy on this dataset."
   ]
  }
 ],
 "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": "3.5.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}