Digit Classification with Logistic Regression (Binary).ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy\n",
    "import matplotlib.pyplot as plt\n",
    "from sklearn.datasets import load_digits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "digits = load_digits()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Image data shape (1797, 64)\n",
      "Label data shape (1797,)\n"
     ]
    }
   ],
   "source": [
    "# We see that we have 1797 images, each 8x8=64 pixels\n",
    "print(\"Image data shape\", digits.data.shape)\n",
    "\n",
    "# And we see we have the right number of labels (integers from 0-9)\n",
    "print(\"Label data shape\", digits.target.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x288 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Show a few training images\n",
    "plt.figure(figsize=(20,4))\n",
    "for index, (image,label) in enumerate(zip(digits.data[0:5], digits.target[0:5])):\n",
    "    plt.subplot(1, 5, index + 1)\n",
    "    plt.imshow(numpy.reshape(image, (8,8)), cmap=plt.cm.gray)\n",
    "    plt.title('Training: %i\\n' % label, fontsize=20)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "sklearn.utils.Bunch"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(digits)\n",
    "binary_digits = load_digits()\n",
    "type(binary_digits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 0.,  0.,  5., 13.,  9.,  1.,  0.,  0.,  0.,  0., 13., 15., 10.,\n",
       "       15.,  5.,  0.,  0.,  3., 15.,  2.,  0., 11.,  8.,  0.,  0.,  4.,\n",
       "       12.,  0.,  0.,  8.,  8.,  0.,  0.,  5.,  8.,  0.,  0.,  9.,  8.,\n",
       "        0.,  0.,  4., 11.,  0.,  1., 12.,  7.,  0.,  0.,  2., 14.,  5.,\n",
       "       10., 12.,  0.,  0.,  0.,  0.,  6., 13., 10.,  0.,  0.,  0.])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "binary_digits.data[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x288 with 5 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Now, let's threshold the data\n",
    "threshold = 12\n",
    "#binary_digits = numpy.copy(digits)\n",
    "binary_digits.data[digits.data < threshold] = 0.0\n",
    "binary_digits.data[digits.data > 0.0] = 1.0\n",
    "\n",
    "# Show the same training images after thresholding\n",
    "plt.figure(figsize=(20,4))\n",
    "for index, (image,label) in enumerate(zip(binary_digits.data[0:5], binary_digits.target[0:5])):\n",
    "    plt.subplot(1, 5, index + 1)\n",
    "    plt.imshow(numpy.reshape(image, (8,8)), cmap=plt.cm.gray)\n",
    "    plt.title('Training: %i\\n' % label, fontsize=20)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Split data into training and testing sets\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "x_train, x_test, y_train, y_test = train_test_split(binary_digits.data, binary_digits.target, test_size=0.25, random_state=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import scikit learn logistic regression ML model\n",
    "from sklearn.linear_model import LogisticRegression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(C=1.0, class_weight=None, dual=False, fit_intercept=True,\n",
       "          intercept_scaling=1, max_iter=100, multi_class='ovr', n_jobs=1,\n",
       "          penalty='l2', random_state=None, solver='liblinear', tol=0.0001,\n",
       "          verbose=0, warm_start=False)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a model instance\n",
    "LRmodel = LogisticRegression()\n",
    "\n",
    "# train model and store information learned\n",
    "# x is digit images and y is labels\n",
    "LRmodel.fit(x_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([2])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# predict labels for first test image\n",
    "LRmodel.predict(x_test[0].reshape(1,-1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# get all test predictions\n",
    "predictions = LRmodel.predict(x_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.9022222222222223\n"
     ]
    }
   ],
   "source": [
    "# compute accuracy\n",
    "score = LRmodel.score(x_test, y_test)\n",
    "print(score)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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