Recognizing handwritten digits on MNIST Dataset using KNN(K Nearest Neighbours).ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "c6b88e90",
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "ad40922d",
   "metadata": {},
   "outputs": [],
   "source": [
    "df=pd.read_csv('C:/DigitRecognizer.csv')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "3038b495",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(42000, 785)\n"
     ]
    }
   ],
   "source": [
    "print(df.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "0de2df3a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(42000, 785)\n"
     ]
    }
   ],
   "source": [
    "print(df.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "2847b381",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Index(['label', 'pixel0', 'pixel1', 'pixel2', 'pixel3', 'pixel4', 'pixel5',\n",
      "       'pixel6', 'pixel7', 'pixel8',\n",
      "       ...\n",
      "       'pixel774', 'pixel775', 'pixel776', 'pixel777', 'pixel778', 'pixel779',\n",
      "       'pixel780', 'pixel781', 'pixel782', 'pixel783'],\n",
      "      dtype='object', length=785)\n"
     ]
    }
   ],
   "source": [
    "print(df.columns)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "b52e9ec5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   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  pixel779  \\\n",
      "0       0  ...         0         0         0         0         0         0   \n",
      "1       0  ...         0         0         0         0         0         0   \n",
      "2       0  ...         0         0         0         0         0         0   \n",
      "3       0  ...         0         0         0         0         0         0   \n",
      "4       0  ...         0         0         0         0         0         0   \n",
      "\n",
      "   pixel780  pixel781  pixel782  pixel783  \n",
      "0         0         0         0         0  \n",
      "1         0         0         0         0  \n",
      "2         0         0         0         0  \n",
      "3         0         0         0         0  \n",
      "4         0         0         0         0  \n",
      "\n",
      "[5 rows x 785 columns]\n"
     ]
    }
   ],
   "source": [
    "print(df.head())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "f66c33d7",
   "metadata": {},
   "outputs": [],
   "source": [
    "data=df.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "c12e9001",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(42000, 785)\n"
     ]
    }
   ],
   "source": [
    "print(data.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "4d5a38f7",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "<class 'numpy.ndarray'>\n"
     ]
    }
   ],
   "source": [
    "print(type(data))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "23e111e3",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(42000, 784) (42000,)\n"
     ]
    }
   ],
   "source": [
    "x=data[:,1:]\n",
    "y=data[:,0]\n",
    "print(x.shape, y.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "a6a6e3ca",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 0 0 ... 0 0 0]\n",
      " [0 0 0 ... 0 0 0]\n",
      " [0 0 0 ... 0 0 0]\n",
      " ...\n",
      " [0 0 0 ... 0 0 0]\n",
      " [0 0 0 ... 0 0 0]\n",
      " [0 0 0 ... 0 0 0]]\n"
     ]
    }
   ],
   "source": [
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "6806de26",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1 0 1 ... 7 6 9]\n"
     ]
    }
   ],
   "source": [
    "print(y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "aa5c0cd8",
   "metadata": {},
   "outputs": [],
   "source": [
    "split=int(0.8*x.shape[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "fd8c4c11",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "33600\n"
     ]
    }
   ],
   "source": [
    "print(split)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "594afe83",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_train=x[:split,:]\n",
    "y_train=y[:split]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "41f27b1e",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_test=x[split:,:]\n",
    "y_test=y[split:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "47c9219c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(33600, 784) (33600,)\n"
     ]
    }
   ],
   "source": [
    "print(x_train.shape,y_train.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "c69b5781",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(8400, 784) (8400,)\n"
     ]
    }
   ],
   "source": [
    "print(x_test.shape,y_test.shape)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cb0d9708",
   "metadata": {},
   "source": [
    "# Visualising some samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "c9cde260",
   "metadata": {},
   "outputs": [],
   "source": [
    "def drawImage(sample):\n",
    "    img=sample.reshape((28,28));\n",
    "    plt.imshow(img,cmap='gray');\n",
    "    plt.show();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "77e7df09",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3\n"
     ]
    }
   ],
   "source": [
    "drawImage(x_train[90]);\n",
    "print(y_train[90]);"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "af771d51",
   "metadata": {},
   "source": [
    "# KNN ALGORITHM"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "73f71664",
   "metadata": {},
   "outputs": [],
   "source": [
    "def dist(x1,x2):\n",
    "    return np.sqrt(sum((x1-x2)**2))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "77fbeb4d",
   "metadata": {},
   "outputs": [],
   "source": [
    "def knn(X,Y,queryPoint,k=5):\n",
    "    \n",
    "    vals = []\n",
    "    m = X.shape[0]\n",
    "    \n",
    "    for i in range(m):\n",
    "        d = dist(queryPoint,X[i])\n",
    "        vals.append((d,Y[i]))\n",
    "        \n",
    "    \n",
    "    vals = sorted(vals)\n",
    "    vals = vals[:k]\n",
    "    \n",
    "    vals = np.array(vals)\n",
    "    \n",
    "    \n",
    "    new_vals = np.unique(vals[:,1],return_counts=True)\n",
    "#     print(new_vals)\n",
    "    \n",
    "    index = new_vals[1].argmax()\n",
    "    pred = new_vals[0][index]\n",
    "    \n",
    "    return pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "2ff65148",
   "metadata": {},
   "outputs": [],
   "source": [
    "pred= knn(x_train, y_train, x_test[25])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "f3f1b0c5",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8.0\n"
     ]
    }
   ],
   "source": [
    "print(pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "ae11a65a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "drawImage(x_test[25])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "bf52509d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "8\n"
     ]
    }
   ],
   "source": [
    "print(y_test[25])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "bcabe587",
   "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": "3.9.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}