MNIST Dataset Digit Recognition.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.image as mpimg\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>label</th>\n",
       "      <th>pixel0</th>\n",
       "      <th>pixel1</th>\n",
       "      <th>pixel2</th>\n",
       "      <th>pixel3</th>\n",
       "      <th>pixel4</th>\n",
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       "      <th>pixel8</th>\n",
       "      <th>...</th>\n",
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       "      <th>pixel780</th>\n",
       "      <th>pixel781</th>\n",
       "      <th>pixel782</th>\n",
       "      <th>pixel783</th>\n",
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       "  </thead>\n",
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       "<p>5 rows × 785 columns</p>\n",
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      ],
      "text/plain": [
       "   label  pixel0  pixel1  pixel2  pixel3  pixel4  pixel5  pixel6  pixel7  \\\n",
       "0      1       0       0       0       0       0       0       0       0   \n",
       "1      0       0       0       0       0       0       0       0       0   \n",
       "2      1       0       0       0       0       0       0       0       0   \n",
       "3      4       0       0       0       0       0       0       0       0   \n",
       "4      0       0       0       0       0       0       0       0       0   \n",
       "\n",
       "   pixel8    ...     pixel774  pixel775  pixel776  pixel777  pixel778  \\\n",
       "0       0    ...            0         0         0         0         0   \n",
       "1       0    ...            0         0         0         0         0   \n",
       "2       0    ...            0         0         0         0         0   \n",
       "3       0    ...            0         0         0         0         0   \n",
       "4       0    ...            0         0         0         0         0   \n",
       "\n",
       "   pixel779  pixel780  pixel781  pixel782  pixel783  \n",
       "0         0         0         0         0         0  \n",
       "1         0         0         0         0         0  \n",
       "2         0         0         0         0         0  \n",
       "3         0         0         0         0         0  \n",
       "4         0         0         0         0         0  \n",
       "\n",
       "[5 rows x 785 columns]"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.read_csv('../Datasets/mnist_train.csv')\n",
    "df.head(n=5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(42000, 785)\n",
      "(42000, 784)\n"
     ]
    }
   ],
   "source": [
    "data = df.values\n",
    "X = data[:,1:]\n",
    "Y = data[:,0]\n",
    "\n",
    "\n",
    "print(data.shape)\n",
    "print(X.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# just to visualize ith test image\n",
    "#plt.imshow(df[2311].reshape((28, 28)))\n",
    "#plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "#g = sns.countplot(df)\n",
    "\n",
    "#df.value_counts()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#df.isnull().any().describe()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0xb5d8e50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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Zr3PphyP8gJg4wg8IivADQRF+ICjCDwRF+IGgCD8QFOEHgiL8QFD/B9W7WUKQsGuLAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xb629710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x17d1330>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x18a2fb0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "for i in range(4):\n",
    "    plt.imshow(X[i].reshape(28,28),cmap='gray')\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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MijhxmJlZEScOMzMr4sRhZmZFnDjMzKyIE4eZmRVx4jAzsyJOHGZmVsSJw8zMijhxmJlZ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\nJw4zMyvixGFmZkX+P8mrlg942Ur3AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x173b79c4860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.hist(df[\"label\"])\n",
    "plt.title(\"Frequency Histogram of Numbers in Training Data\")\n",
    "plt.xlabel(\"Number Value\")\n",
    "plt.ylabel(\"Frequency\")\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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PTdD31TwI12PAUCp7wH7RUQBc+cSfG/zXAsoBz1/fivgU59frl0SCkyWHs9Q4QKxfkM3+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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x173dc0791d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import math\n",
    "# plot the first 25 digits in the training set. \n",
    "f, ax = plt.subplots(5, 5)\n",
    "# plot some 4s as an example\n",
    "for i in range(1,26):\n",
    "    # Create a 1024x1024x3 array of 8 bit unsigned integers\n",
    "    data = df.iloc[i,1:785].values #this is the first number\n",
    "    nrows, ncols = 28, 28\n",
    "    grid = data.reshape((nrows, ncols))\n",
    "    n=math.ceil(i/5)-1\n",
    "    m=[0,1,2,3,4]*5\n",
    "    ax[m[i-1], n].imshow(grid)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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