Digit Classification.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Recognizing handwritten digits with machine learning\n",
    "\n",
    "The University of California Irvines' [Optical Recognition of Handwritten Digits](http://archive.ics.uci.edu/ml/datasets/Optical+Recognition+of+Handwritten+Digits) dataset provides the perfect opportunity to practice multiclass classification. It contains almost 1,800 scanned and normalized handwritten digits, each an 8x8 array of numbers from 0 to 16. Let's use logistic regression to make predictions from the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "digits.images: (1797, 8, 8)\n",
      "digits.target: (1797,)\n"
     ]
    }
   ],
   "source": [
    "from sklearn import datasets\n",
    "\n",
    "digits = datasets.load_digits()\n",
    "print('digits.images: ' + str(digits.images.shape))\n",
    "print('digits.target: ' + str(digits.target.shape))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's what the first digit looks like in numerical form."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.,  0.,  5., 13.,  9.,  1.,  0.,  0.],\n",
       "       [ 0.,  0., 13., 15., 10., 15.,  5.,  0.],\n",
       "       [ 0.,  3., 15.,  2.,  0., 11.,  8.,  0.],\n",
       "       [ 0.,  4., 12.,  0.,  0.,  8.,  8.,  0.],\n",
       "       [ 0.,  5.,  8.,  0.,  0.,  9.,  8.,  0.],\n",
       "       [ 0.,  4., 11.,  0.,  1., 12.,  7.,  0.],\n",
       "       [ 0.,  2., 14.,  5., 10., 12.,  0.,  0.],\n",
       "       [ 0.,  0.,  6., 13., 10.,  0.,  0.,  0.]])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "digits.images[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here's how it looks to the eye."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x124d3238550>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.tick_params(axis='both', which='both', bottom=False, top=False, left=False, right=False, labelbottom=False, labelleft=False)\n",
    "plt.imshow(digits.images[0], cmap=plt.cm.gray_r)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It's obviously a 0, but we can confirm that from its label."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "digits.target[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot the first 50 images and show the corresponding labels."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x504 with 50 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(5, 10, figsize=(12, 7), subplot_kw={'xticks': [], 'yticks': []})\n",
    "\n",
    "for i, ax in enumerate(axes.flat):\n",
    "    ax.imshow(digits.images[i], cmap=plt.cm.gray_r)\n",
    "    ax.text(0.45, 1.05, str(digits.target[i]), transform=ax.transAxes)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Classification models work best with balanced datasets. Plot the distribution of the samples."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([178., 182., 177., 183., 181., 182., 181., 179., 174., 180.]),\n",
       " array([0. , 0.9, 1.8, 2.7, 3.6, 4.5, 5.4, 6.3, 7.2, 8.1, 9. ]),\n",
       " <BarContainer object of 10 artists>)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "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": [
    "plt.xticks([])\n",
    "plt.hist(digits.target, rwidth=0.9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The datatset is pretty well balanced, so let's split the data and train a logistic-regression model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "LogisticRegression(max_iter=5000)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "from sklearn.model_selection import train_test_split\n",
    "\n",
    "x_train, x_test, y_train, y_test = train_test_split(digits.data, digits.target, test_size=0.2, random_state=0)\n",
    "\n",
    "model = LogisticRegression(max_iter=5000)\n",
    "model.fit(x_train, y_train)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use the `score` method to quantify the model's accuracy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9583333333333334"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.score(x_test, y_test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Print a classification report."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "              precision    recall  f1-score   support\n",
      "\n",
      "           0       1.00      1.00      1.00        27\n",
      "           1       0.91      0.89      0.90        35\n",
      "           2       0.97      0.97      0.97        36\n",
      "           3       0.97      1.00      0.98        29\n",
      "           4       0.97      1.00      0.98        30\n",
      "           5       0.97      0.93      0.95        40\n",
      "           6       0.98      0.98      0.98        44\n",
      "           7       1.00      0.97      0.99        39\n",
      "           8       0.92      0.92      0.92        39\n",
      "           9       0.91      0.95      0.93        41\n",
      "\n",
      "    accuracy                           0.96       360\n",
      "   macro avg       0.96      0.96      0.96       360\n",
      "weighted avg       0.96      0.96      0.96       360\n",
      "\n"
     ]
    }
   ],
   "source": [
    "from sklearn.metrics import classification_report\n",
    "\n",
    "y_predicted = model.predict(x_test)\n",
    "print(classification_report(y_test, y_predicted))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use a confusion matrix to see how the model performs on the test dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[27,  0,  0,  0,  0,  0,  0,  0,  0,  0],\n",
       "       [ 0, 31,  0,  0,  0,  0,  1,  0,  2,  1],\n",
       "       [ 0,  0, 35,  1,  0,  0,  0,  0,  0,  0],\n",
       "       [ 0,  0,  0, 29,  0,  0,  0,  0,  0,  0],\n",
       "       [ 0,  0,  0,  0, 30,  0,  0,  0,  0,  0],\n",
       "       [ 0,  0,  0,  0,  0, 37,  0,  0,  0,  3],\n",
       "       [ 0,  1,  0,  0,  0,  0, 43,  0,  0,  0],\n",
       "       [ 0,  0,  0,  0,  1,  0,  0, 38,  0,  0],\n",
       "       [ 0,  2,  1,  0,  0,  0,  0,  0, 36,  0],\n",
       "       [ 0,  0,  0,  0,  0,  1,  0,  0,  1, 39]], dtype=int64)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import confusion_matrix\n",
    "\n",
    "confusion_matrix(y_test, y_predicted)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pick one of the digits from the dataset and plot it to see what it looks like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x124d58f46d0>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.tick_params(axis='both', which='both', bottom=False, top=False, left=False, right=False, labelbottom=False, labelleft=False)\n",
    "plt.imshow(digits.images[100], cmap=plt.cm.gray_r)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pass it to the model and see what digit the model predicts it is."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "4"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.predict([digits.data[100]])[0]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What probabilities did the model predict for each possible digit?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[6.27529405e-11, 4.82484422e-09, 9.28625450e-21, 3.17137774e-22,\n",
       "        9.99999988e-01, 1.00117785e-15, 7.34878841e-09, 1.60279468e-10,\n",
       "        2.72962050e-12, 4.88479346e-22]])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.predict_proba([digits.data[100]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What is the probability that the digit is a 4?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9999999876006042"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.predict_proba([digits.data[100]])[0][4]"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
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