MNIST_KNN.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# MNIST KNN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "df_train = pd.read_csv(\"dataset/MNIST/train.csv\")\n",
    "df_test = pd.read_csv(\"dataset/MNIST/test.csv\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# training image data\n",
    "X = np.array(df_train)[:, 1:]\n",
    "\n",
    "# image label\n",
    "Y = np.array(df_train)[:, 0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[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]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAPsAAAD4CAYAAAAq5pAIAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjAsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+17YcXAAALi0lEQVR4nO3dX4hc5R3G8eeJtRdGxaTaEJIQjYSCFBrLEgoJxWLVNDcxN2ouSkqEFVFQ6EWDvahQBCnVXgZWjKYlVYp/MGghplGSFopklTTZJNWkIWJCTJAgRrywur9ezImscefM7pxz5kzz+35gmJn3nZnz42yevOffzOuIEIBL35y2CwAwGIQdSIKwA0kQdiAJwg4k8a1BLsw2h/6BhkWEp2uvNLLbXmP7XdvHbG+u8lkAmuV+z7PbvkzSe5Juk3RS0j5JGyLicMl7GNmBhjUxsq+UdCwijkfE55Kel7SuwucBaFCVsC+S9MGU5yeLtq+xPWp73PZ4hWUBqKjxA3QRMSZpTGIzHmhTlZH9lKQlU54vLtoADKEqYd8nabntG2x/W9I9knbUUxaAuvW9GR8RX9h+UNJOSZdJ2hoRh2qrDECt+j711tfC2GcHGtfIRTUA/n8QdiAJwg4kQdiBJAg7kARhB5Ig7EAShB1IgrADSRB2IAnCDiRB2IEkCDuQBGEHkiDsQBKEHUiCsANJEHYgCcIOJEHYgSQIO5DEQKdsxuCtX7++tP+FF14o7b/uuutK+8+dOzfrmtAORnYgCcIOJEHYgSQIO5AEYQeSIOxAEoQdSILz7Je4kZGR0v5es/jefffdpf1btmyZdU1oR6Ww2z4h6bykLyV9ERHl/7IAtKaOkf0nEfFRDZ8DoEHsswNJVA17SHrd9tu2R6d7ge1R2+O2xysuC0AFVTfjV0fEKdvflbTL9r8jYu/UF0TEmKQxSbJdfjQIQGMqjewRcaq4PyvpZUkr6ygKQP36DrvtubavuvBY0u2SJuoqDEC93Os8a9c32svUGc2lzu7AnyPisR7vYTN+wFatWlXa/8Ybb5T2b9++vbR/06ZNs64JzYoIT9fe9z57RByX9IO+KwIwUJx6A5Ig7EAShB1IgrADSRB2IIm+T731tTBOvQ2dgwcPlvYvXry4tL/Xqb3Dhw/PuiZU0+3UGyM7kARhB5Ig7EAShB1IgrADSRB2IAnCDiTBT0mj1NVXX13a32tKZwwPRnYgCcIOJEHYgSQIO5AEYQeSIOxAEoQdSILz7ChlT/vV6K/cf//9pf179uypsxxUwMgOJEHYgSQIO5AEYQeSIOxAEoQdSIKwA0lwnh2lBjmvAJrVc2S3vdX2WdsTU9rm295l+2hxP6/ZMgFUNZPN+GclrbmobbOk3RGxXNLu4jmAIdYz7BGxV9K5i5rXSdpWPN4m6c6a6wJQs3732RdExOni8YeSFnR7oe1RSaN9LgdATSofoIuIKJuwMSLGJI1JTOwItKnfU29nbC+UpOL+bH0lAWhCv2HfIWlj8XijpFfqKQdAU2Zy6u05Sf+U9D3bJ23fK+lxSbfZPirpp8VzAEOs5z57RGzo0nVrzbUAaBCXywJJEHYgCcIOJEHYgSQIO5AEYQeSIOxAEoQdSIKwA0kQdiAJwg4kQdiBJAg7kARhB5Ig7EAShB1IgrADSRB2IAnCDiRB2IEkCDuQBFM2o9ScOYwHlwr+kkAShB1IgrADSRB2IAnCDiRB2IEkCDuQBOfZUWpycrLtElCTmczPvtX2WdsTU9oetX3K9v7itrbZMgFUNZPN+GclrZmm/Q8RsaK4/bXesgDUrWfYI2KvpHMDqAVAg6ocoHvQ9oFiM39etxfZHrU9bnu8wrIAVNRv2LdIulHSCkmnJT3R7YURMRYRIxEx0ueyANSgr7BHxJmI+DIiJiU9JWllvWUBqFtfYbe9cMrT9ZImur0WwHDoeZ7d9nOSbpF0re2Tkn4j6RbbKySFpBOS7muwRgA16Bn2iNgwTfPTDdQCoEFcLgskQdiBJAg7kARhB5Ig7EASfMX1EnfNNdeU9l9xxRWVPn/nzp2V3o/BYWQHkiDsQBKEHUiCsANJEHYgCcIOJEHYgSQ4z36JW7FiRWn/0qVLK33+8ePHK70fg8PIDiRB2IEkCDuQBGEHkiDsQBKEHUiCsANJcJ49Odul/XPmMB5cKvhLAkkQdiAJwg4kQdiBJAg7kARhB5Ig7EASnGdPLiJK+ycnJ0v7ly1bVtq/Z8+eWdeEZvQc2W0vsf2m7cO2D9l+qGifb3uX7aPF/bzmywXQr5lsxn8h6ZcRcZOkH0l6wPZNkjZL2h0RyyXtLp4DGFI9wx4RpyPineLxeUlHJC2StE7StuJl2yTd2VSRAKqb1T677esl3SzpLUkLIuJ00fWhpAVd3jMqabT/EgHUYcZH421fKelFSQ9HxCdT+6JzlGfaIz0RMRYRIxExUqlSAJXMKOy2L1cn6Nsj4qWi+YzthUX/QklnmykRQB16bsa78x3IpyUdiYgnp3TtkLRR0uPF/SuNVIihdscdd5T2P/PMMwOqBL3MZJ99laSfSzpoe3/R9og6If+L7XslvS/prmZKBFCHnmGPiH9I6vYLB7fWWw6ApnC5LJAEYQeSIOxAEoQdSIKwA0nwFddL3Mcff1za/9lnn5X2z507t85y0CJGdiAJwg4kQdiBJAg7kARhB5Ig7EAShB1IgvPsl7j9+/eX9r/22mul/XfdVf7N5YmJiVnXhHYwsgNJEHYgCcIOJEHYgSQIO5AEYQeSIOxAEu41ZW+tC7MHtzAgqYiY9tegGdmBJAg7kARhB5Ig7EAShB1IgrADSRB2IImeYbe9xPabtg/bPmT7oaL9UdunbO8vbmubLxdAv3peVGN7oaSFEfGO7askvS3pTnXmY/80In4/44VxUQ3QuG4X1cxkfvbTkk4Xj8/bPiJpUb3lAWjarPbZbV8v6WZJbxVND9o+YHur7Xld3jNqe9z2eKVKAVQy42vjbV8paY+kxyLiJdsLJH0kKST9Vp1N/U09PoPNeKBh3TbjZxR225dLelXSzoh4cpr+6yW9GhHf7/E5hB1oWN9fhLFtSU9LOjI16MWBuwvWS+JnRoEhNpOj8asl/V3SQUmTRfMjkjZIWqHOZvwJSfcVB/PKPouRHWhYpc34uhB2oHl8nx1IjrADSRB2IAnCDiRB2IEkCDuQBGEHkiDsQBKEHUiCsANJEHYgCcIOJEHYgSQIO5BEzx+crNlHkt6f8vzaom0YDWttw1qXRG39qrO2pd06Bvp99m8s3B6PiJHWCigxrLUNa10StfVrULWxGQ8kQdiBJNoO+1jLyy8zrLUNa10StfVrILW1us8OYHDaHtkBDAhhB5JoJey219h+1/Yx25vbqKEb2ydsHyymoW51frpiDr2ztiemtM23vcv20eJ+2jn2WqptKKbxLplmvNV11/b05wPfZ7d9maT3JN0m6aSkfZI2RMThgRbShe0TkkYiovULMGz/WNKnkv54YWot27+TdC4iHi/+o5wXEb8aktoe1Syn8W6otm7TjP9CLa67Oqc/70cbI/tKScci4nhEfC7peUnrWqhj6EXEXknnLmpeJ2lb8XibOv9YBq5LbUMhIk5HxDvF4/OSLkwz3uq6K6lrINoI+yJJH0x5flLDNd97SHrd9tu2R9suZhoLpkyz9aGkBW0WM42e03gP0kXTjA/Nuutn+vOqOED3Tasj4oeSfibpgWJzdShFZx9smM6dbpF0ozpzAJ6W9ESbxRTTjL8o6eGI+GRqX5vrbpq6BrLe2gj7KUlLpjxfXLQNhYg4VdyflfSyOrsdw+TMhRl0i/uzLdfzlYg4ExFfRsSkpKfU4rorphl/UdL2iHipaG593U1X16DWWxth3ydpue0bbH9b0j2SdrRQxzfYnlscOJHtuZJu1/BNRb1D0sbi8UZJr7RYy9cMyzTe3aYZV8vrrvXpzyNi4DdJa9U5Iv8fSb9uo4YudS2T9K/idqjt2iQ9p85m3X/VObZxr6TvSNot6aikv0maP0S1/Umdqb0PqBOshS3VtlqdTfQDkvYXt7Vtr7uSugay3rhcFkiCA3RAEoQdSIKwA0kQdiAJwg4kQdiBJAg7kMT/ADwPlXgkFzeZAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.imshow(X[1000].reshape((28,28)), cmap=\"gray\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(42000,)"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Y.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(42000, 785)"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_train.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(28000, 784)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_test.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "test = np.array(df_test)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "# distance function to calculate the distance between two points in euclidean space having n dimensions(784 in this case)\n",
    "def distance(p1, p2):\n",
    "    return np.sum((p2 - p1)**2)**.5\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# knn function to find the k nearest points to the input point\n",
    "# first we will calc distance from input to each training data point then sort(obv in increasing order) them and take \n",
    "# first k and make predictions based upon them\n",
    "\n",
    "def knn(X , Y, test , k = 500):\n",
    "    # it will have the distance( from the input point ) and label of each point as tuple ie : (distance, label)\n",
    "    d = []\n",
    "    r = X.shape[0]\n",
    "    for i in range(r):\n",
    "        d.append((distance(test, X[i]), Y[i]))\n",
    "        \n",
    "    # l is the list of sorted distance label\n",
    "    l = np.array(sorted(d))[:, 1]\n",
    "    l = l[:k]\n",
    "    u = np.unique(l, return_counts = True)\n",
    "    \n",
    "    # convert the unique labels with their frequency into key value pair\n",
    "    freq_dict = dict()\n",
    "    for i in range(len(u[0])):\n",
    "        freq_dict[u[0][i]] = u[1][i]\n",
    "    \n",
    "    # get the key whose value is maxmimum in the dictionary\n",
    "    pred = int(max(freq_dict, key = freq_dict.get))\n",
    "    \n",
    "    accuracy = int(freq_dict[pred])\n",
    "    \n",
    "    percentage_accuracy = int((accuracy/k)*100)\n",
    "    \n",
    "    print(\"I can say with %d%% of accurancy that test input is %d\" %(percentage_accuracy, pred))\n",
    "    \n",
    "    return freq_dict\n",
    "\n",
    "\n",
    "    \n",
    "    \n",
    "    \n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "I can say with 96% of accurancy that test input is 3\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{3.0: 483, 5.0: 12, 8.0: 1, 9.0: 4}"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "knn(X, Y, test[1134])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "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.imshow(test[1134].reshape(28, 28), cmap = \"gray\");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.image as img \n",
    "import cv2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# reading the following images and storing them into a list\n",
    "img_name = [\"zero\", \"one\", \"two\", \"three\", \"four\", \"five\", \"six\", \"seven\", \"eight\"]\n",
    "abs_path = \"dataset/MNIST/\"\n",
    "grid = []\n",
    "for each in img_name:\n",
    "    grid.append(img.imread(abs_path + each + \".jpg\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "# convert the rgb into gray code resulting 3D matrix into 2D\n",
    "for i in range(len(grid)):\n",
    "    grid[i] = cv2.cvtColor(grid[i], cv2.COLOR_RGB2GRAY)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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XfGBQ1+FCbduh97Nc2hvI3jylxiHbpxSsJovDLA3gqLWRWRGmpzUCZK2vZPH4+hYtzGPHjgEAPv744/G62JjjdTVLNXokfh/7jWTnntXSNDg6EiGENKT3Fqe9gQwfDzFK8U+yPGRpIzGG5fU16+Weezig0TJjHh9w4DlYrPratWsADluM9rftm/0uYr3PvBWzNP02+x3N6nXS4iSEkIb03uI0miTLkuXHEt1jTCzzHnwMiywfXjP7O9ZJb3GaNWiWo+/YYMRYp7dKY7uHt07bat+gxUkIIQ3hg5MQQhrSS1fdB5vN9M8aD4zoomfHk8XjdYljEJi75V06a1iI6WZ+f7J4soYfq5Mx2T3D19HYjz1zvUupifZ8YOMQIYR0TC8tzuwNZGRvkmiFMlF6Ocm0Kw0ftrm5CYBew7LjNTSNzSOwupkNPVeqp3Z85m0Yti5LVZoVWpyEENKQzi1OETn0Bord5rI3kL1dStaH7Z/tE9MSsnEf4+AD2fh+cR9/rju9G2fU1SwBW1fyBGxbdnwc5KNEpmuJqKdPe2GMtD187DrGKOvEOLNzRS+jpL0/d2nc3ibQ4iSEkIbwwUkIIQ25rasuIs8B+EcAH6jqX1brTgD4NwCnAfw3gEdV9U91LjjJ3Y5uWynNICO6dp7oCvp97LrRNfMpTHXc+L4xD129PtEVysIc0Z3399XSkeLvpdQIkGkfXcFSKpovWwwh9Ym2tZ2VzC2+6667AABXrlwBcFiXOOZm1rgTex557aM7vqjGoecBPBzWPQ3gZVV9AMDL1XfSL54HdR0qz4Pazpea04qeBvBr9/08gFPV36cAnK95niPTdY5GIx2NRuMpOeN3ALq+vq7r6+u6urqqq6urura2Nl7iOe37rVu3xsuNGzf0xo0b420rKyvjxdZtbGzoxsZGuk/c1y9ZeQvL64ueInZeut5u6lXTy+7X7e6Z7W9k++zs7OjOzs5YH/t9+CXq2YKGS69rW9rOcD8mLru7u7q7u3tE57q6xHq+vb2t29vb6fGZ5m3V12lb1U+q6sXq7/cBnJy0Y1fTyJJWoK7DpZa21LUeM6cjqaq9ASZtH083WlkFh+KCMf4RR08BynPJWCzK9okjQwMHMY4szmbEGJgvV4yr+dSHoSZfN9FVRFRVD8WpYgpYFguOevjjrTtl3NdrEbvdleLilQWVpsZksbBJMdYhUNI26trG9fyUzv7+A+U2gpgqWJUPwIFmpRHdbV9fX9vq/DJtq/ofRORUVZBTAD5opTRk0VDX4UJtW2Rai/NFAI8DeKb6/Gmdg1QVN2/ePPQGipaiWR/eKtza2gJwMGq0f2vYOjve3kSZZWF4KzF22bJtpWRob9n0ufU1YSpdjcz6LiU4x3vmPQu7r6WODZFsMAnT0c7ty2jnLo3pOBBdgRm1nYXMYzRLs9Rl0u591mJux3vP1IjjcfrjOxuPU0R+COCXAD4rIhdE5OvYv/kPicg7AL5UfSc9groOF2o7f25rcarqYxM2fbHlspAOoa7DhdrOn4WMjpS5P+ZCHT9+HADw0UcfjbfFhgJ/vCXSxkRY72rbubNgcXQj4viPHnM7fUD7Tu+jbsS+6pn769cDR10x73bZOhsByX4D/vionb++/W37ZCED2yfr2MC+6vPB6lccsSxzp7Nwif0dp/71ddKOy0JHFvaLz5SmsMslIYQ0pHOLM6YjxUm5vKVpWJA3SxWKFk2pMSILQJtFY28y28feTMDB26l0zgE1IkxFTEeKIw5l9+fSpUsAyiN2273PRvz2jYz+PJ5o+Za6XPa1++yyk03EVvLUoqWZ/XbM0sxmfIgNxX6fWS3NcRlbOQshhNxBdG5x7u7uHnoDxelB7e2SpQOV4k5x8vpsfD6zRi2FyW+L+DdTKWn2Trc0PVmaVpwryFt1MRk6u5fRE/DE2LU/ftIYrNnvwtYxxtkddq+zsXZLMUojep/+eRGnFZ6HlrQ4CSGkIXxwEkJIQxYydUYWLI54073OcPcxsJ+d17vovjzA0cYMb97HNKbS2H93MqWwRRaCKTGp0S377XDyveUmC6HE+po18pTCdlbfYv3158pcdE4PTAghC6Jzi1NVD6WRxBSfmNjqiaM+t0lplPcYwLYUJiC3YgkhB3iPIFqRWSpaTCMqNe7E8QYy7JkC5M+VaaDFSQghDenc4hyNRsVRaOyNUEo/aRM7p73VYkJ+hrcy52kFEzIEsq64dVKEYsqSP1ccl9OnD8bUs7asTA8tTkIIaUjnFufe3l46AIe9XczSy0aAj2P4tYnFLTOrNrbEeWuYidKElMm8x1infKt6HEM1I3qGvot0kxkBpqXOeJz3i8grIvK2iLwlIk9W60+IyEsi8k71ec9MJSGdQl2HCXXthjqu+i6Ab6vqGQBfAPANETkDTjfad6jrMKGuHVBnIOOLAC5Wf18RkXMA7gPwCIC/r3Y7C+A/ADxV56LevZ002VqW0GrmeZv9wyclT2fhBGMI/dPnoStZPMuoazaGQQl7FsRR0YCj46zGY/z+masex3edlkYxThE5DeBBAK+C040OBuo6TKjrHGkwwf1xAG8A+Kfq+6Ww/U91J7i3ieJXVlZ0fX1d19fXa00QHyejn+di18qut7q6Ol6ySe8Ly8QJ7he1tKnrPO5/SReji98DdW1nuXXrlt66dWtc760e+X1Go5GORqNi3bLzZMR6WqrL0+paKx1JRNYAvADgB6r6k2o1pxvtOdR1mFDX+XNbV132Aw3fB3BOVb/nNk093aiPPVhswuKYFp/QJI4Yx3Zsg+w6wOHRxa28lg7l4691EuaXkXnoShbPMurqU40mjZubdcss1XOrizbGbkbWfTq2qUxLnRjn3wL4ZwC/EpH/qtZ9F/sC/LiaevQ9AI/OVBLSNdR1mFDXDqjTqv4LAJMe/ZxutKdQ12FCXbuh855DKysrxYx+M8FLUxy0OSVvPGd0JTKyidwIITlZfbV6VmeajMyNt+Ptu08fjD2H5jGOBPuqE0JIQzq3OCdZi/GNk+3XpqU56Zx13k60MueD9zJio11pVB1O0dw/TKs6I55lusZ62vWYEbQ4CSGkIZ1bnIRMIvMo4ijgfvT9mK6SxcUJmQe0OAkhpCG0OMnS4AdziPPO2KcffT/GNmllkq6gxUkIIQ3hg5MQQhpCV50sDT41xdxwaxTyDT+GuejWIYFpYqQraHESQkhDurY4/wjgavXZNz6J2cv96TYKsoS0rmtMei41/MxoaVLXybC+TkC67m0hIq+r6uc6vWgL9LXcXdHX+9PXcndFX+/PvMtNV50QQhrCBychhDRkEQ/OZxdwzTboa7m7oq/3p6/l7oq+3p+5lrvzGCchhPQduuqEENIQPjgJIaQhnT04ReRhETkvIu+KyNNdXbcpInK/iLwiIm+LyFsi8mS1/oSIvCQi71Sf9yy6rMtCH7Slrs2hroXrdhHjFJERgN8AeAjABQCvAXhMVd+e+8UbUs05fUpV3xSRuwC8AeArAL4G4ENVfab6Ed2jqk8tsKhLQV+0pa7NoK5lurI4Pw/gXVX9raruAPgRgEc6unYjVPWiqr5Z/X0FwDkA92G/vGer3c5iXxzSE22pa2Ooa4GZHpwNTPn7APzOfb9QrVtqROQ0gAcBvArgpKperDa9D+Dkgoo1dxq6aL3T9k7VFRh2ne1S16kfnJUp/68A/gHAGQCPiciZtgq2aETkOIAXAHxLVS/7bbof3xhkHhd1HaauwLC17VxXVZ1qAfA3AH7uvn8HwHdK+1aFv5OX/5n2fne1NNHV7d/ZPRSR8dLFdYai65R1dtH1ZdHLRF1nGR0pM+X/Ou4kIk8AeALAX81wrUNkUyyUpo+1/etMRTpn3lt0AWrQVNe5EnW178DRKWL95G1ao9Gz9Luw69SZLhr90BWooW1XurZVJ22c1tLoWdnzoiYTdZ37sHKq+iyAZ0XkywD+vY1z+n9+fX0dALCzs3Pou3+A2v5xXzI9pisAVJbZzPiHoulnn3W08w/LOnOtx0rkK1jNB+bgmIeuTWcfjQ9Vf3zctqh5pmZpHPo9gPvd909V61JU9WczXIt0RyNdSa+gti0xy4PzNQAPiMhnRGQdwFcBvNhOscgCoa7Dhdq2xNSuuqruisg3sd/oMwLwnKq+1VrJCvhYVnTdSq6cd8VIziJ19eGV6JKZrsePHx/vYyO/2z7+dxFZW1sDkLvgtm0JYuBzZVHaZu50vNdeO9tmvwF//KS4tg/JWMjHjsvmsqoTAy8xU4yzcr/pgg8M6jpcqG079HKWy1IjwObmJgDg+vXr433MojALZYZWNtIRsbXU9P3oo4+O7GOYzsBRz8PO4/cx6yWzQjlzZntkjX7RKvRWpdVp08rXZcO2ZVk02bq24ehIhBDSkF5anB5785iFYW8nb41Ei4JW5nKSpQOZjvbpvQ2zUsx6yeLbMY3Jax+9E/+boaXZHiWrMHoNwIHGpov3Euy4UrrY9vY2AODq1atHtpnms+pLi5MQQhrSe4vTLAl7c9WxJv1bbtbWNdIeJe1MpywWZlZI1qpuvw+zSr32ZtHYcYtKph46pR5dMYad4T2JSR1esv3N8vTnbsuToMVJCCEN4YOTEEIa0ktXvZRSkiXNlgYAIcuDbxwyraJL5hsF/O8AOKx5bHQwt9y7djG847fRbW8P7yrffffdAIDLly8f2WbEkEuWPrixsQEAuHHjxpF9TDv7rfh0qNYGF5npaEIIuQPppcWZpSJk6SpGqfGAjUPLQ9Y1LpKNtJNZEbFjxLFjxwAAH3/88Xgfs1jNaskanvj7aJdoaWY6xzSxzDo0zbJRs+z4LNWp1C23CbQ4CSGkIZ1bnCsrK2n8qDQGn+2fDVpqby47rhQzqZN2kl0jWh9ZjJW0yyTLYNrYdUw9Ag60oycyX+rUF1/fY0cGr08cYDo735///OcjxxltdX6hxUkIIQ3hg5MQQhpyW1ddRJ4D8I8APlDVv6zWnQDwbwBOA/hvAI+q6p/qXHCSmxzdYO8qmRlvLlmpv7J9Zi5Z5n5Fd8/2yQLLlgLhR2uJaRF9oW1d2yAbRac0ZUZs9MvSmYzsdxd/D9l4rX0c12DZtPXu9CRXPdMnG0M1phhlzwSj1Dg0ayimjsX5PICHw7qnAbysqg8AeLn6TvrF86CuQ+V5UNv5UnNa0dMAfu2+nwdwqvr7FIDzNc+jAHRlZWW8rK+v6/r6eqMpWz1xGtfStK51rrW2tqZra2vFfVZXV8dLnXK75fUup4PtWtc2l6iD6Xr8+PHx0uR89nvLKP3W+qhrW9q2peXu7u6RxfQ4duyYHjt2LK1ftk9JT9Pp5s2b48X2GY1GOhqN5lJfp21VP6mqF6u/3wdwctKOXU03SlqBug6XWtpS13rMnI5kVl9h+5HpRktziMSRoWtcH8DRdCbffS523/PE9KMsRaXhHNuDYBpd22RStzs/Arztk436H1PPsnEc7TeSpaANWfOStvPQ1ceOo67WIcHHI+ukl5VGxiqNlFaae6oJ07aq/0FETgFA9fnBTKUgywJ1HS7UtkWmtThfBPA4gGeqz582uqhrPY0WYjbOnq2zt4t/k5jFaW+QbMZCe+OVxvCLSfJ23uzcQ7RCKmbSdVZKcwZlVoj9jkpjLHodgYMsiIwsE2NALEzbbDzObDAeI3af9r8L2z8+E6xLrd8na1VvS9fbWpwi8kMAvwTwWRG5ICJfx/7Nf0hE3gHwpeo76RHUdbhQ2/lzW4tTVR+bsOmLLZeFdAh1HS7Udv503ld9NBodcrvMnI4mtP9upr652NkoOFmA318zHmfEqTfseO/S2TVKk0dFl5A0J9M8BvqzCd3sd+G1j41BsSEoO7eHoyO1R3YP7Z7HMVWBow0+PmwTG2+zsJvpar+VeYRd2OWSEEIa0rnFube3d8iai10Vs3ETjVKqUgw2lywL3zh1/PjxQ+WwN5nfJ+ItZlok88Hua9Sz5DVkx0e8heLTlwDgE5/4xPjvS5cuNSwxqYPdc6vnmU6xO2WWGlhqzC2lMrbVRZoWJyGENKRzi1NEijEHszSzARfsuMyanNT5Hzgat/RvG3tjZYOLGKUBBRgLa48608hm2pfizFFfb2XGuLa3Mtuam4Yc1sU6K0StvCAJD4sAAAYpSURBVPamZ5Mpv/3xsfOD9zLaGoyHFichhDSED05CCGlI5666G3mlyLQukpn53tW365mZnk3LUbqurcvccrsOpx6enex3Ed01r1fpNxL7RGfhoVIjAl309shCW/F7Npaqhci8Fln6UiSGdbLGw1mhxUkIIQ3p5fTAmdURk6CzCd2yJHl708V9Slaph5Zme2QjwMcUsqzRzzTM+iaTxZPpYvWtNLpRrJPA5LpYmvbXW7OcrI0QQhZELy1On0CfjbMI5Gkrhn/rxBha6c1lVq2/FtOQ2iPrihvHXfREXeuO4Uq6JUs1Mg9ia2sLQHks1VKM1LZl3kpp5KVZfyu0OAkhpCF1Zrm8H8D/w/5Q+wrgWVX9v4ucNS+zTKy1zeIZ3iqNSfWZxVl6A8XxPH3LXl/HbVxGXTOiLtkAK1kM7U61PpdRV69ZtBhtLNXMQ4wxbH981Nw/E2L2S5YcPyt1LM5dAN9W1TMAvgDgGyJyBpw1r+9Q12FCXTvgtg9OVb2oqm9Wf18BcA7AfQAeAXC22u0sgK/Mq5CkfajrMKGu3dCocUhETgN4EMCraDAjYttk6QlxVCU/ulJ00b25Hvuxm+udpTMZ2YRf80iy7Ypl0TUL8Bumgb/PTSf2u9NYFl19fYmNflkHEtPz7rvvBgBcvnz5yDlLaUXWH96u68/dVjpS7QeniBwH8AKAb6nq5TAgw8RZ8zjd6HJDXYcJdZ0zNSe3XwPwcwD/sgwT3JeWzc1N3dzcTCevj99XVlbGk9bXOfeUk9rXmuB+Ecsy67qxsaEbGxvj79evX9fr16+PNch0sGP8cR0t1LWwrK2tjZfd3V3d3d3Vvb093dvbUyPTVUSOLLEu7+zs6M7Ozrge+7psx/ht8fhpda0zWZsA+D6Ac6r6PbfJZs0DFjAjIpkN6jpMqGs3iN4mgVtE/g7AfwL4FQALJn0X+3GTHwP4CwDvYT+94cPbnKt8sZr49ISYKmT4FIhsgAgj68oHHMRJgKMjhfvrZ0m6Bd5Q1c/V2XHeLKOuntgxwe6vv/em8RLEl6lrQ0xHq1s+lGB1L0s3m1TfsjSjFqbznqhrnVkufwFgUvITZ83rKdR1mFDXbmDPIUIIaUgv+6r7lII4eo6Z8FkKRNZzKI7Okk2xEHsieDehpotOapCNYhOngeW97zexDppb7utbHDe3lBqY9SSK0wL7qTPaCuvQ4iSEkIb00uLMKI2LWSdB2t5kdaaaZcL1fCglJ2e69HWcgDuZqLF9rzOyewlfJ2P95AjwhBCyBPDBSQghDeGDkxBCGsIHJyGENIQPTkIIaQgfnIQQ0hA+OAkhpCF8cBJCSEO6ToD/I4Cr1Wff+CRmL/en2yjIEkJdhwl1ncBth5VrGxF5fVmG4GpCX8vdFX29P30td1f09f7Mu9x01QkhpCF8cBJCSEMW8eB8dgHXbIO+lrsr+np/+lrurujr/ZlruTuPcRJCSN+hq04IIQ3p7MEpIg+LyHkReVdEnu7quk0RkftF5BUReVtE3hKRJ6v1J0TkJRF5p/q8Z9FlXRb6oC11bQ51LVy3C1ddREYAfgPgIQAXALwG4DFVfXvuF2+IiJzC/vzTb4rIXQDeAPAVAF8D8KGqPlP9iO5R1acWWNSloC/aUtdmUNcyXVmcnwfwrqr+VlV3APwIwCMdXbsRqnpRVd+s/r4C4ByA+7Bf3rPVbmexLw7pibbUtTHUtUBXD877APzOfb9QrVtqROQ0gAexPyf1SVW9WG16H8DJBRVr2eidttS1FtS1ABuHJiAixwG8AOBbqnrZb9P9+AbTEXoIdR0mXeva1YPz9wDud98/Va1bSkRkDfsi/EBVf1Kt/kMVT7G4ygeLKt+S0RttqWsjqGuBrh6crwF4QEQ+IyLrAL4K4MWOrt0I2Z+o+fsAzqnq99ymFwE8Xv39OICfdl22JaUX2lLXxlDX0nW7SoAXkS8D+D8ARgCeU9X/3cmFGyIifwfgPwH8CoDNM/pd7MdNfgzgLwC8B+BRVf1wIYVcMvqgLXVtDnUtXJc9hwghpBlsHCKEkIbwwUkIIQ3hg5MQQhrCBychhDSED05CCGkIH5yEENIQPjgJIaQhfHASQkhD/j9ldzt/SOHn9wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 9 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# just for the sake of visualization, showing these images into a grid\n",
    "f, axarr = plt.subplots(3,3) # figsize(x, y) for size of each\n",
    "n = 0;\n",
    "for i in range(3):\n",
    "        for j in range(3):\n",
    "            axarr[i, j].imshow(grid[n], cmap = \"gray\")\n",
    "            n = n + 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "# convert each 28x28 image matrix into an array\n",
    "\n",
    "for i in range(len(grid)):\n",
    "    grid[i] = grid[i].flatten()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(784,)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "grid[6].shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "I can say with 96% of accurancy that test input is 1\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "{1.0: 483, 2.0: 2, 3.0: 2, 4.0: 1, 5.0: 5, 6.0: 3, 7.0: 2, 9.0: 2}"
      ]
     },
     "execution_count": 38,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "knn(X, Y, grid[1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.6.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}