Handwritten-Digit-Recognition.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "2d0a9d99-7263-4465-a4da-94e0585e5029",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "from sklearn.datasets import load_digits"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "4a213d3a-92c0-4ef6-bc94-4a698412a7f5",
   "metadata": {},
   "outputs": [],
   "source": [
    "digits = load_digits()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "219c8004-bf6b-47ea-87bb-45a4dd802220",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "['DESCR', 'data', 'feature_names', 'frame', 'images', 'target', 'target_names']"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "dir(digits)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "bd0f2410-6b8b-4442-8fa4-35cec59d6a8f",
   "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": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "digits.data[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "b1fa684f-b7cb-4d2a-b5d2-5c7dd7e83ce0",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 480x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 480x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 480x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 480x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 480x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.gray()\n",
    "for i in range(5):\n",
    "    plt.matshow(digits.images[i])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "aef6dd62-7685-45e5-886b-ed46954fdb63",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4])"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "digits.target[0:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "ad3c1618-791a-4118-8bad-5c7cebf18874",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "1f61eb53-089e-4bed-ad0c-615a9360be94",
   "metadata": {},
   "outputs": [],
   "source": [
    "X_train, X_test, y_train, y_test = train_test_split(digits.data, digits.target, test_size=0.2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "61116655-d9b7-45ed-9578-a4b37251b28f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1437"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(X_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "1b65080f-ac1b-4ab4-a0bb-e80fd4f0053e",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "360"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(X_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "00304973-d128-459c-93cc-40677539e100",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.linear_model import LogisticRegression\n",
    "model = LogisticRegression()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "3cb90ff2-0f74-45d9-ba2d-b094eeb10e9c",
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Python\\Lib\\site-packages\\sklearn\\linear_model\\_logistic.py:460: ConvergenceWarning: lbfgs failed to converge (status=1):\n",
      "STOP: TOTAL NO. of ITERATIONS REACHED LIMIT.\n",
      "\n",
      "Increase the number of iterations (max_iter) or scale the data as shown in:\n",
      "    https://scikit-learn.org/stable/modules/preprocessing.html\n",
      "Please also refer to the documentation for alternative solver options:\n",
      "    https://scikit-learn.org/stable/modules/linear_model.html#logistic-regression\n",
      "  n_iter_i = _check_optimize_result(\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<style>#sk-container-id-1 {color: black;}#sk-container-id-1 pre{padding: 0;}#sk-container-id-1 div.sk-toggleable {background-color: white;}#sk-container-id-1 label.sk-toggleable__label {cursor: pointer;display: block;width: 100%;margin-bottom: 0;padding: 0.3em;box-sizing: border-box;text-align: center;}#sk-container-id-1 label.sk-toggleable__label-arrow:before {content: \"▸\";float: left;margin-right: 0.25em;color: #696969;}#sk-container-id-1 label.sk-toggleable__label-arrow:hover:before {color: black;}#sk-container-id-1 div.sk-estimator:hover label.sk-toggleable__label-arrow:before {color: black;}#sk-container-id-1 div.sk-toggleable__content {max-height: 0;max-width: 0;overflow: hidden;text-align: left;background-color: #f0f8ff;}#sk-container-id-1 div.sk-toggleable__content pre {margin: 0.2em;color: black;border-radius: 0.25em;background-color: #f0f8ff;}#sk-container-id-1 input.sk-toggleable__control:checked~div.sk-toggleable__content {max-height: 200px;max-width: 100%;overflow: auto;}#sk-container-id-1 input.sk-toggleable__control:checked~label.sk-toggleable__label-arrow:before {content: \"▾\";}#sk-container-id-1 div.sk-estimator input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-label input.sk-toggleable__control:checked~label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 input.sk-hidden--visually {border: 0;clip: rect(1px 1px 1px 1px);clip: rect(1px, 1px, 1px, 1px);height: 1px;margin: -1px;overflow: hidden;padding: 0;position: absolute;width: 1px;}#sk-container-id-1 div.sk-estimator {font-family: monospace;background-color: #f0f8ff;border: 1px dotted black;border-radius: 0.25em;box-sizing: border-box;margin-bottom: 0.5em;}#sk-container-id-1 div.sk-estimator:hover {background-color: #d4ebff;}#sk-container-id-1 div.sk-parallel-item::after {content: \"\";width: 100%;border-bottom: 1px solid gray;flex-grow: 1;}#sk-container-id-1 div.sk-label:hover label.sk-toggleable__label {background-color: #d4ebff;}#sk-container-id-1 div.sk-serial::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: 0;}#sk-container-id-1 div.sk-serial {display: flex;flex-direction: column;align-items: center;background-color: white;padding-right: 0.2em;padding-left: 0.2em;position: relative;}#sk-container-id-1 div.sk-item {position: relative;z-index: 1;}#sk-container-id-1 div.sk-parallel {display: flex;align-items: stretch;justify-content: center;background-color: white;position: relative;}#sk-container-id-1 div.sk-item::before, #sk-container-id-1 div.sk-parallel-item::before {content: \"\";position: absolute;border-left: 1px solid gray;box-sizing: border-box;top: 0;bottom: 0;left: 50%;z-index: -1;}#sk-container-id-1 div.sk-parallel-item {display: flex;flex-direction: column;z-index: 1;position: relative;background-color: white;}#sk-container-id-1 div.sk-parallel-item:first-child::after {align-self: flex-end;width: 50%;}#sk-container-id-1 div.sk-parallel-item:last-child::after {align-self: flex-start;width: 50%;}#sk-container-id-1 div.sk-parallel-item:only-child::after {width: 0;}#sk-container-id-1 div.sk-dashed-wrapped {border: 1px dashed gray;margin: 0 0.4em 0.5em 0.4em;box-sizing: border-box;padding-bottom: 0.4em;background-color: white;}#sk-container-id-1 div.sk-label label {font-family: monospace;font-weight: bold;display: inline-block;line-height: 1.2em;}#sk-container-id-1 div.sk-label-container {text-align: center;}#sk-container-id-1 div.sk-container {/* jupyter's `normalize.less` sets `[hidden] { display: none; }` but bootstrap.min.css set `[hidden] { display: none !important; }` so we also need the `!important` here to be able to override the default hidden behavior on the sphinx rendered scikit-learn.org. See: https://github.com/scikit-learn/scikit-learn/issues/21755 */display: inline-block !important;position: relative;}#sk-container-id-1 div.sk-text-repr-fallback {display: none;}</style><div id=\"sk-container-id-1\" class=\"sk-top-container\"><div class=\"sk-text-repr-fallback\"><pre>LogisticRegression()</pre><b>In a Jupyter environment, please rerun this cell to show the HTML representation or trust the notebook. <br />On GitHub, the HTML representation is unable to render, please try loading this page with nbviewer.org.</b></div><div class=\"sk-container\" hidden><div class=\"sk-item\"><div class=\"sk-estimator sk-toggleable\"><input class=\"sk-toggleable__control sk-hidden--visually\" id=\"sk-estimator-id-1\" type=\"checkbox\" checked><label for=\"sk-estimator-id-1\" class=\"sk-toggleable__label sk-toggleable__label-arrow\">LogisticRegression</label><div class=\"sk-toggleable__content\"><pre>LogisticRegression()</pre></div></div></div></div></div>"
      ],
      "text/plain": [
       "LogisticRegression()"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.fit(X_train, y_train)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "c0828fa1-2785-46de-a2f4-0cc871e23791",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9583333333333334"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.score(X_test, y_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "6ddef62a-968b-4567-ada0-468dd2fb998c",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0, 1, 2, 3, 4])"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model.predict(digits.data[0:5])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "23080547-77d0-4979-a7f0-86052bff5dec",
   "metadata": {},
   "outputs": [],
   "source": [
    "#Confusion Matrix \n",
    "y_predicted = model.predict(X_test)\n",
    "from sklearn.metrics import confusion_matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "id": "1c9e5898-9e3c-4989-9d74-1676d0c164f6",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[33,  0,  0,  0,  0,  0,  0,  0,  0,  0],\n",
       "       [ 0, 32,  0,  0,  0,  0,  0,  0,  0,  0],\n",
       "       [ 0,  1, 38,  0,  0,  0,  0,  0,  1,  0],\n",
       "       [ 0,  0,  0, 42,  0,  1,  0,  0,  0,  0],\n",
       "       [ 0,  1,  0,  0, 39,  0,  0,  0,  0,  0],\n",
       "       [ 0,  0,  0,  1,  0, 37,  0,  1,  0,  1],\n",
       "       [ 0,  0,  0,  0,  0,  0, 30,  0,  0,  0],\n",
       "       [ 0,  0,  0,  0,  0,  0,  0, 37,  0,  2],\n",
       "       [ 0,  4,  0,  0,  0,  0,  0,  0, 25,  0],\n",
       "       [ 0,  1,  0,  1,  0,  0,  0,  0,  0, 32]], dtype=int64)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import seaborn as sn \n",
    "plt.figure(figsize = (10,7))\n",
    "sn.heatmap"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "ec08ec47-83e4-49a7-8542-c29bf6e833a5",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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": "3.12.0"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}