Chapter05/Exercise5.02/Exercise5.02.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Exercise 5.02: Logistic Regression as a Classifier - 2 Class Classifier"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import struct\n",
    "import numpy as np\n",
    "import gzip\n",
    "import urllib.request\n",
    "import matplotlib.pyplot as plt\n",
    "from array import array\n",
    "from sklearn.linear_model import LogisticRegression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Prepare the MNIST data for training\n",
    "The following 4 cells will download the save the MNIST training data to file.  Once you have run these cells once successfully you can delete or comment them out.\n",
    "\n",
    "Download the image files"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "request = urllib.request.urlopen('http://yann.lecun.com/exdb/mnist/train-images-idx3-ubyte.gz')\n",
    "\n",
    "with open('../Datasets/train-images-idx3-ubyte.gz', 'wb') as f:\n",
    "    f.write(request.read())\n",
    "\n",
    "request = urllib.request.urlopen('http://yann.lecun.com/exdb/mnist/t10k-images-idx3-ubyte.gz')\n",
    "\n",
    "with open('../Datasets/t10k-images-idx3-ubyte.gz', 'wb') as f:\n",
    "    f.write(request.read())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Download the label files"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "request = urllib.request.urlopen('http://yann.lecun.com/exdb/mnist/train-labels-idx1-ubyte.gz')\n",
    "\n",
    "with open('../Datasets/train-labels-idx1-ubyte.gz', 'wb') as f:\n",
    "    f.write(request.read())\n",
    "\n",
    "request = urllib.request.urlopen('http://yann.lecun.com/exdb/mnist/t10k-labels-idx1-ubyte.gz')\n",
    "\n",
    "with open('../Datasets/t10k-labels-idx1-ubyte.gz', 'wb') as f:\n",
    "    f.write(request.read())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "ls: *.gz: No such file or directory\r\n"
     ]
    }
   ],
   "source": [
    "!ls *.gz # or !dir *.gz for windows"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load the downloaded data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "with gzip.open('../Datasets/train-images-idx3-ubyte.gz', 'rb') as f:\n",
    "    magic, size, rows, cols = struct.unpack(\">IIII\", f.read(16))\n",
    "    img = np.array(array(\"B\", f.read())).reshape((size, rows, cols))\n",
    "\n",
    "with gzip.open('../Datasets/train-labels-idx1-ubyte.gz', 'rb') as f:\n",
    "    magic, size = struct.unpack(\">II\", f.read(8))\n",
    "    labels = np.array(array(\"B\", f.read()))\n",
    "\n",
    "with gzip.open('../Datasets/t10k-images-idx3-ubyte.gz', 'rb') as f:\n",
    "    magic, size, rows, cols = struct.unpack(\">IIII\", f.read(16))\n",
    "\n",
    "    img_test = np.array(array(\"B\", f.read())).reshape((size, rows, cols))\n",
    "\n",
    "with gzip.open('../Datasets/t10k-labels-idx1-ubyte.gz', 'rb') as f:\n",
    "    magic, size = struct.unpack(\">II\", f.read(8))\n",
    "    labels_test = np.array(array(\"B\", f.read()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Visualise a sample of the data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 10 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(10):\n",
    "    plt.subplot(2, 5, i + 1)\n",
    "    plt.imshow(img[i], cmap='gray');\n",
    "    plt.title(f'{labels[i]}');\n",
    "    plt.axis('off')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Construct a Logistic Model to Classify Digits 0  - 9\n",
    "\n",
    "In this model as we are predicting classes 0 - 9 we will require images from all available data.  However given the extremely large dataset we will need to sample only a small amount of the original MNIST set due to limited system requirements and anticipated training time.  We will select 2000 samples at random:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "samples_0_1 = np.where((labels == 0) | (labels == 1))[0]\n",
    "images_0_1 = img[samples_0_1]\n",
    "labels_0_1 = labels[samples_0_1]\n",
    "\n",
    "samples_0_1_test = np.where((labels_test == 0) | (labels_test == 1))\n",
    "images_0_1_test = img_test[samples_0_1_test].reshape((-1, rows * cols))\n",
    "labels_0_1_test = labels_test[samples_0_1_test]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Visualising the selected information:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "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": [
    "sample_0 = np.where((labels == 0))[0][0]\n",
    "plt.imshow(img[sample_0], cmap='gray');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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": [
    "sample_1 = np.where((labels == 1))[0][0]\n",
    "plt.imshow(img[sample_1], cmap='gray');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In order to provide the image information to the Logistic model we must first flatten the data out so that each image is 1 x 784 pixels in shape."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(12665, 784)"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "images_0_1 = images_0_1.reshape((-1, rows * cols))\n",
    "images_0_1.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's construct the model, use the sklearn LogisticRegression API and call the fit function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
       "                   intercept_scaling=1, l1_ratio=None, max_iter=100,\n",
       "                   multi_class='warn', n_jobs=None, penalty='l2',\n",
       "                   random_state=None, solver='liblinear', tol=0.0001, verbose=0,\n",
       "                   warm_start=False)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = LogisticRegression(solver='liblinear')\n",
    "model.fit(X=images_0_1, y=labels_0_1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Determine the score against the training set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.score(X=images_0_1, y=labels_0_1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Display the first two predictions for the Logistic model against the training data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1], dtype=uint8)"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.predict(images_0_1) [:2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Examine the corresponding predicted probabilities for the first two training samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[9.99999999e-01, 9.89532857e-10],\n",
       "       [4.56461358e-09, 9.99999995e-01]])"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.predict_proba(images_0_1)[:2]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compare the performance against the test set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9995271867612293"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.score(X=images_0_1_test, y=labels_0_1_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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