notebooks/01-nn-handwriting-recognition.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Handwritten digit recognition MNIST dataset\n",
    "\n",
    "The [MNIST](http://yann.lecun.com/exdb/mnist/) dataset contains 60,000 images each 28x28 pixels of handwritten digits with correct labels. There are additional 10,000 images of test set. \n",
    "\n",
    "**What we will learn?**\n",
    "- Nearest neighbor (NN) algorithm of classification\n",
    "- Various distance functions\n",
    "- K-nearest neighbors (KNN)\n",
    "- Principle component analysis (PCA)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import io, gzip \n",
    "from urllib.request import urlopen\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt \n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# load images\n",
    "def mnist_images(url):  \n",
    "    with gzip.open(io.BytesIO(urlopen(url).read()), 'rb') as f:\n",
    "        data = np.frombuffer(f.read(), np.uint8, offset=16)\n",
    "        # consult http://yann.lecun.com/exdb/mnist/ for details \n",
    "    data = data.reshape(-1,784)\n",
    "    return data/256  # we are using int8, squared distance could be large\n",
    "\n",
    "# load image labels\n",
    "def mnist_labels(url):        \n",
    "    with gzip.open(io.BytesIO(urlopen(url).read()), 'rb') as f:\n",
    "        data = np.frombuffer(f.read(), np.uint8, offset=8)\n",
    "    return data\n",
    "\n",
    "# plot/view a specific image\n",
    "def mnist_view(im):\n",
    "    plt.axis('off')\n",
    "    plt.imshow(im.reshape((28,28)), cmap=plt.cm.gray, origin='upper')\n",
    "    plt.show()\n",
    "    return\n",
    "\n",
    "# calculate squared distance\n",
    "def dist(x1, x2):\n",
    "    return np.sum(np.square(x1-x2))\n",
    "\n",
    "# find nearest neighbor \n",
    "def find_nn(x):\n",
    "    dist_vec = [dist(x, train_data[i,]) for i in range(len(train_labels))]\n",
    "    print(\"Index: \", np.argmin(dist_vec))\n",
    "    return train_labels[np.argmin(dist_vec)]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "train_data = mnist_images('https://pranabdas.github.io/drive/datasets/mnist-handwritten-digits/train-images-idx3-ubyte.gz')\n",
    "test_data    = mnist_images('https://pranabdas.github.io/drive/datasets/mnist-handwritten-digits/t10k-images-idx3-ubyte.gz')\n",
    "train_labels = mnist_labels('https://pranabdas.github.io/drive/datasets/mnist-handwritten-digits/train-labels-idx1-ubyte.gz')\n",
    "test_labels  = mnist_labels('https://pranabdas.github.io/drive/datasets/mnist-handwritten-digits/t10k-labels-idx1-ubyte.gz')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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": [
    "# view a sample data\n",
    "mnist_view(train_data[50,:]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Label: 3\n"
     ]
    }
   ],
   "source": [
    "# print the corresponding label \n",
    "print(\"Label:\", train_labels[50])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Index:  57158\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "find_nn(test_data[100, :])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAOcAAADnCAYAAADl9EEgAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMywgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/Il7ecAAAACXBIWXMAAAsTAAALEwEAmpwYAAAGl0lEQVR4nO3dT4jN+x/H8XP8GUpjQ11Ks5QVFspC/qw0kprNmBKWQikS2dmJBVkojSmysJidJVMiScqfLC1kQaKURoqh4fxW97ea8z6/+Wde4/d4LO+r772fm573W/fTOafZarUaQJ4Fc30AYGLihFDihFDihFDihFCLqrHZbPpfuTDLWq1Wc6K/7s0JocQJocQJocQJocQJocQJocQJocQJocQJocQJocQJocQJocQJocQJocQJocrPc/LnnT17ttwPHjxY7gMDA+X+7NmzSZ+JueHNCaHECaHECaHECaHECaHECaFcpcyBHTt2tN0OHTpUPvvt27dy37RpU7m7Spk/vDkhlDghlDghlDghlDghlDghlDghVLPVav8rf34CcGq6u7vL/c2bN223mzdvls+eOXOm3Ks/z0aj0fj161e58+f5CUCYZ8QJocQJocQJocQJocQJocQJoXyecxYcOXKk3MfGxtpuFy9eLJ8dHx+f0pmYf7w5IZQ4IZQ4IZQ4IZQ4IZQ4IZQ4IZR7zllw+vTpch8cHGy7ffjwYaaPwzzlzQmhxAmhxAmhxAmhxAmhxAmhXKVMQaevvlyyZEm5v3r1aiaPw1/KmxNCiRNCiRNCiRNCiRNCiRNCiRNCueecgt7e3mk9f+fOnRk6CX8zb04IJU4IJU4IJU4IJU4IJU4IJU4I5Z5zCg4fPlzuP378KPdPnz7N5HH4S3lzQihxQihxQihxQihxQihxQihxQij3nBNoNpvlvmLFinK/d+/eTB4nxo4dO8p9YGBgWn//0dHRttvDhw/LZzt9RrbVak3lSHPKmxNCiRNCiRNCiRNCiRNCiRNCiRNCueecwOrVq8t9/fr15X7hwoWZPM6M6urqKvfz58+33Y4fP14++/bt23L/+vXrlJ8/evRo+Wx/f3+5j4yMlHsib04IJU4IJU4IJU4IJU4IJU4I5SplFszlV18uWFD/93ZoaKjcDxw40HbrdJ1x48aNcu/0laGVvr6+ch8cHCz3jRs3lvuXL18meaLZ580JocQJocQJocQJocQJocQJocQJodxzTqCnp2dazz99+nSGTjJ5V65cKfedO3dOee/0lZ+z+fWTd+/eLfelS5eW+7Jly8rdPSfwPxMnhBInhBInhBInhBInhBInhHLPOYF//vlnro/Q1qpVq8p9z5495b5v375yv3///qTP9Cd8//693F+/fl3uW7duLffh4eFJn2m2eXNCKHFCKHFCKHFCKHFCKHFCKHFCKPecE/j58+e0nl+zZk25T+ezg/v37y/3Tvegjx8/nvI/ez7r7u6e6yNMmjcnhBInhBInhBInhBInhBInhBInhHLPOYFHjx6V+8ePH8v98OHD5X7s2LFJn+lfT548KfdFi+o/0u3bt5f7yMjIpM/0J3T691q+fHm5j46OzuBp/gxvTgglTgglTgglTgglTgglTgjlKmUCX79+Lff379+Xe39/f7mfOHGi7TY+Pl4++/nz53L//ft3uS9cuLDcU3W6fur0UblOP1+YyJsTQokTQokTQokTQokTQokTQokTQjVbrVb7sdlsP/4fGxgYKPdbt26V+9WrV9tu0/k4WaPRaFy7dq3cd+/eXe7Xr19vu42NjU3pTP/q9FG8np6ettvQ0FD57K5du8o99acNG41Go9VqNSf6696cEEqcEEqcEEqcEEqcEEqcEEqcEMo95ywYHh4u976+vrbb5cuXy2cvXbpU7p1+XrC3t7fcV65c2XZrNie8jvuvrq6ucl+7dm25b9iwoe128uTJ8tnnz5+XezL3nDDPiBNCiRNCiRNCiRNCiRNCiRNCueecBYsXLy73c+fOtd2OHz9ePtvpO3Nv375d7u/evSv3SnU/22g0Glu2bCn3Tt8de+rUqbbby5cvy2fnM/ecMM+IE0KJE0KJE0KJE0KJE0K5SgmzefPmct+7d2+5b9u2rdzXrVtX7g8ePGi7vXjxonz24cOH5d7p6yk7/Xzh38pVCswz4oRQ4oRQ4oRQ4oRQ4oRQ4oRQ7jlhjrnnhHlGnBBKnBBKnBBKnBBKnBBKnBBKnBBKnBBKnBBKnBBKnBBKnBBKnBBKnBBKnBBKnBBKnBBKnBBKnBBKnBBKnBBKnBBKnBBKnBBKnBBKnBBKnBBKnBBKnBBKnBBKnBBKnBBKnBBKnBBKnBBKnBBKnBBKnBBKnBBKnBBKnBBKnBBKnBBKnBBKnBCq2Wq15voMwAS8OSGUOCGUOCGUOCGUOCGUOCHUfwDseS3N0LWlNQAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mnist_view(test_data[100, :])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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": [
    "mnist_view(train_data[57158, ])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice that in oder to find nearest neighbors we need to go through each training data point. There are better search algorithms to look for nearest neighbors quickly. We can use scikit learn, there are KDTree and BallTree."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.neighbors import BallTree, KDTree\n",
    "\n",
    "ball_tree = BallTree(train_data)\n",
    "kd_tree = KDTree(train_data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_labels[ball_tree.query(test_data[100, :].reshape(1, -1), \\\n",
    "                             k=1, return_distance=False)[0][0]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "train_labels[kd_tree.query(test_data[100, :].reshape(1, -1), k=1, \\\n",
    "                           return_distance=False)[0][0]]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Above two sklearn and our own algorithm would produce same result, but time to find the nearest neighbor is faster in case of KDTree and BallTree."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Let's calculate the precision of nearest neighbor algorithm\n",
    "\n",
    "result = [train_labels[ball_tree.query(test_data[i, :].reshape(1, -1), k=1, \\\n",
    "         return_distance=False)[0][0]] for i in range(len(test_labels))]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Success = 96.91 %\n"
     ]
    }
   ],
   "source": [
    "correct_result = np.equal(result, test_labels)\n",
    "success = float(np.sum(correct_result))/len(test_labels)\n",
    "print('Success =', success*100, '%')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "# np.savetxt('mnist_test_images.gz', test_data, fmt='%d')\n",
    "# tst_l = np.loadtxt('mnist_test_labels.gz')"
   ]
  },
  {
   "cell_type": "code",
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