Chapter05/Activity5.02/Activity5.02.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Activity 5.02: K-NN Multiclass Classifier\n",
    "\n",
    "This activity uses the K-NN model to classify the MNIST dataset.\n",
    "\n",
    "Import the following packages"
   ]
  },
  {
   "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.neighbors import KNeighborsClassifier as KNN"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Load the MNIST data into memory\n",
    "\n",
    "1. Training images"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "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",
    "\n",
    "    img = np.array(array(\"B\", f.read())).reshape((size, rows, cols))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "2. Training labels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "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()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "3. Test images"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "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))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "4. Test labels"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "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": 6,
   "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 K Nearest Neighbours Classification Model\n",
    "\n",
    "Construct a KNN classifier, with 3 nearest neighbours to classify the MNIST dataset.  Again to save in processing power randomly sample 5000 images for use in training."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(0)\n",
    "selection = np.random.choice(len(img), 5000)\n",
    "selected_images = img[selection]\n",
    "selected_labels = labels[selection]"
   ]
  },
  {
   "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": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(5000, 784)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "selected_images = selected_images.reshape((-1, rows * cols))\n",
    "selected_images.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Build the 3 neighbour KNN model and fit the data to the model.  **Note: in this activity we are providing 784 features or *dimensions* to the model, not simply 2**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "KNeighborsClassifier(algorithm='auto', leaf_size=30, metric='minkowski',\n",
       "                     metric_params=None, n_jobs=None, n_neighbors=3, p=2,\n",
       "                     weights='uniform')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model = KNN(n_neighbors=3)\n",
    "model.fit(X=selected_images, y=selected_labels)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Determine the score against the training set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9712"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.score(X=selected_images, y=selected_labels)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Display the first two predictions for the Logistic model against the training data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAV0AAACmCAYAAAB5qlzZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjEsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy8QZhcZAAAHbklEQVR4nO3dy4vN/x8H8M8Ri0GSS5RrhBllJaVcZmU5IxobIUqsNEpIslD2dopcymUhhkI0VsJfIOMyCwY1iikpxkLN+e2+9evz/kxn5sx5zWfG47F8zvu85910es673p9LpVqtZgDEmDLeCwD4lyhdgEBKFyCQ0gUIpHQBAildgEBTh/thpVJxPRkNVa1WK+Pxe323abSi77adLkAgpQsQSOkCBFK6AIGULkAgpQsQSOkCBFK6AIGULkAgpQsQSOkCBFK6AIGULkAgpQsQSOkCBFK6AIGULkAgpQsQSOkCBFK6AIGGfTElk0dvb28uq1bT72Zcs2ZNo5fDP2jBggW5rL+/Pzk29X3dsGFDcuyvX7/qW1gwO12AQEoXIJDSBQikdAECTciDtDNnziTzPXv25LJt27Ylx37+/HlM11QW+/btS+ZLlizJZX19fQ1eDQyv6DB31apVuaypqSk51kEaAIWULkAgpQsQSOkCBFK6AIFKf/XCokWLctn+/fuTY5ctW5bLTp48mRx74sSJXPb79++RLa6Ejh8/nsynTZsWvBL4f7t37x7vJZSCnS5AIKULEEjpAgRSugCBSn+Qlrr1L3VgVuTw4cPJ/MGDB7msu7u79oWVQEdHRy5bu3ZtcmzR7ZYw1opu121vb695jlevXuWyyXDQnWV2ugChlC5AIKULEEjpAgRSugCBSn/1Qmtr63gvobQ2b9483kuAnGPHjiXzLVu21DxHT09PLhscHBz1msrEThcgkNIFCKR0AQIpXYBApT9I27lz53gvYdJ6+/bteC+BCW7hwoW57ODBg3XPe+fOnbrnKCs7XYBAShcgkNIFCKR0AQIpXYBApbl6YcaMGcl8+vTpdc1b9ODjifRA5NQbkbMsy9ra2uqa9+LFi3V9Hs6fP5/LFi9enBybepD+hQsXkmOfPHlS38JKzE4XIJDSBQikdAECKV2AQKU5SNu6dWsyH8kzOFOeP3+ezF++fFnXvJGK3q46krciQz2am5uT+caNG2ue4/v377mss7Nz1GuaqOx0AQIpXYBAShcgkNIFCKR0AQKV5uqFIpVKpa7PHz16dIxWUj6pv82UKen/o69fv85l7969G/M1MTl1d3cn86Jb1FO6urrGajkTmp0uQCClCxBI6QIEUroAgUpzkLZ27dpknnoG52Q2f/78XNba2pocm/rbDA0NJce2tLTksps3bybH1nvrNRPbgQMHctlInpHb09OTHHv27Nn6FjZJ2OkCBFK6AIGULkAgpQsQqDQHaYcOHWrIvKmDqSzLsi9fvuSypUuXNmQNHR0duazo+cFz587NZevXr697DakXcd64caPueZnY2tvbc9nly5dzWdGdjoODg7ls165dybEDAwMjXN3kZKcLEEjpAgRSugCBlC5AIKULEKg0Vy80yq1bt5L5ixcvctmePXuSY1PPra339uSi5wQ36rbn1FuRL1261JDfRfnMnDkzme/duzeXjeT28lOnTuWy3t7eEa7u32KnCxBI6QIEUroAgZQuQKDSHKQVHSzV+2LK5cuXjyhPSd0CWXSwUM+cWZZlHz9+zGWpQ7AsSx+CFM177969EayOyeb06dPJfMeOHTV9/unTp8n82rVro17Tv8pOFyCQ0gUIpHQBAildgEBKFyBQZbjbTiuVStireN+/f5/MV65cGbWEQo24DbjoNPn69es1/f4sS9/KXHRVxuPHj3NZW1vbMCuMUa1W67s8ZZQiv9vRtm/fnstu376dHDt1av4Cpj9//uSyOXPmJD//9+/fEa7u31H03bbTBQikdAECKV2AQEoXIFBpbgP+9u1bMi/DQVpKX19fLvv69Wty7Llz53JZd3d33Wt4+PBhLjty5Ejd8zIxzJs3L5lfuXIll6UOzLIsy378+JHLUm/zdWA2dux0AQIpXYBAShcgkNIFCKR0AQKV5uqFojfxPnr0KJe1tLTUPG/qyoEsy7KBgYGa50i5ceNGLvv582ddc0KR1JUKXV1dybGzZ8+ued7UlQ7Pnj2r+fOMnJ0uQCClCxBI6QIEUroAgUpzkPbp06dkvm7dulzW0dGRHJt6xm3RYcNk8PLly1zW2dk5Diuh0Zqbm3PZpk2bav58f39/Mr906dKo18To2OkCBFK6AIGULkAgpQsQSOkCBCrN1Qsjcffu3fFeQimk/g5DQ0PjsBLGyqxZs5L51atXa54j9R0ouqrlw4cPNc/L2LDTBQikdAECKV2AQEoXINCEPEiDyaqpqSmZr1ixouY53rx5k8vu378/6jUxtux0AQIpXYBAShcgkNIFCKR0AQK5egFKZHBwMJn39vbmstWrVyfHFr0Bm3Kw0wUIpHQBAildgEBKFyBQJfUG3f9+WKkU/xDGQLVarYzH7/XdptGKvtt2ugCBlC5AIKULEEjpAgRSugCBlC5AIKULEEjpAgRSugCBlC5AIKULEEjpAgRSugCBlC5AIKULEEjpAgRSugCBlC5AIKULEEjpAgRSugCBhn0bMABjy04XIJDSBQikdAECKV2AQEoXIJDSBQj0P27kYlojEpeUAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "model.predict(selected_images)[:2]\n",
    "\n",
    "plt.subplot(1, 2, 1)\n",
    "plt.imshow(selected_images[0].reshape((28, 28)), cmap='gray');\n",
    "plt.axis('off');\n",
    "plt.subplot(1, 2, 2)\n",
    "plt.imshow(selected_images[1].reshape((28, 28)), cmap='gray');\n",
    "plt.axis('off');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Compare the performance against the test set"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9346"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.score(X=img_test.reshape((-1, rows * cols)), y=labels_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How did the performance of the KNN model compare with the logistic regression model?"
   ]
  }
 ],
 "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": "3.7.4"
  }
 },
 "nbformat": 4,
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}