hands-on/020_mnist_data_exploration_complete.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# MNIST: learning to recognize handwritten digits"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dataset exploration"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before starting a machine learning or data science task, it is always useful to familiarize yourself with the data set and its context."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Required imports"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2018-07-17T05:07:22.409259Z",
     "start_time": "2018-07-17T05:07:22.244395Z"
    }
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Using TensorFlow backend.\n"
     ]
    }
   ],
   "source": [
    "from tensorflow import keras\n",
    "from collections import Counter\n",
    "from keras.datasets import mnist\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Obtaining the dataset"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In Keras' datasets module we have a handle to the MNIST dataset we want to use in this notebook.  Download the training and test set for this data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "(x_train, y_train), (x_test, y_test) = mnist.load_data()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dimensions and types"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Determine the shape and type of the training and the test set."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((60000, 28, 28), dtype('uint8'), (60000,), dtype('uint8'))"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_train.shape, x_train.dtype, y_train.shape, y_train.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "((10000, 28, 28), dtype('uint8'), (10000,), dtype('uint8'))"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_test.shape, x_test.dtype, y_test.shape, y_test.dtype"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The training set has 60,000 examples, the test set 10,000.  The input is a 28 $\\times$ 28 matrix of unsigned 8-bit integers, the output a single unsigned 8-bit integer."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Data semantics"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    " Each input represents a scanned grayscale image of a handwritten digit, the output is the corresponding integer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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": [
    "frame = plt.gca()\n",
    "frame.axes.get_xaxis().set_visible(False)\n",
    "frame.axes.get_yaxis().set_visible(False)\n",
    "plt.imshow(x_train[0], cmap='gray');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x216 with 35 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "rows = 5\n",
    "cols = 7\n",
    "figure, axes = plt.subplots(rows, cols, figsize=(5, 3))\n",
    "plt.subplots_adjust(wspace=0.1, hspace=0.1)\n",
    "for img_nr in range(rows*cols):\n",
    "    row = img_nr//cols\n",
    "    col = img_nr % cols\n",
    "    axes[row, col].get_xaxis().set_visible(False)\n",
    "    axes[row, col].get_yaxis().set_visible(False)\n",
    "    axes[row, col].imshow(x_train[img_nr], cmap='gray')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[5, 0, 4, 1, 9, 2, 1],\n",
       "       [3, 1, 4, 3, 5, 3, 6],\n",
       "       [1, 7, 2, 8, 6, 9, 4],\n",
       "       [0, 9, 1, 1, 2, 4, 3],\n",
       "       [2, 7, 3, 8, 6, 9, 0]], dtype=uint8)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "y_train[:rows*cols].reshape(rows, cols)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So this proves that I'm certainly not the only one cursed with bad handwriting."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Data distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "An important question is whether all digits are represented in the training and test set, and what the distribution is.  This may have an impact on the accuracy of the trained model."
   ]
  },
  {
   "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": [
    "distr = Counter(y_train)\n",
    "figure, axes = plt.subplots()\n",
    "axes.set_xticks(list(distr.keys()))\n",
    "axes.bar(list(distr.keys()), list(distr.values()));"
   ]
  },
  {
   "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": [
    "distr = Counter(y_test)\n",
    "figure, axes = plt.subplots()\n",
    "axes.set_xticks(list(distr.keys()))\n",
    "axes.bar(list(distr.keys()), list(distr.values()));"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Although some digits like 1 are overrepresented, and others, e.g., 5 are underrepresented, the distribution seems to be reasonably uniform, and it is likely no special care needs to be taken."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.10.9"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}