KMEANS.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import random as rd\n",
    "import seaborn as sns\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.DataFrame({\n",
    "    'x': [12,20,28,18,29,33,24,45,45,52,51,52,55,53,55,61,64,69,72],\n",
    "    'y': [39,36,30,52,54,46,55,59,63,70,66,63,58,23,14, 8,19, 7,24]\n",
    "})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1a7f1125f10>"
      ]
     },
     "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": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(df['x'], df['y'], color='k')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Step 1: Choose the number of clusters k\n",
    "The first step in k-means is to pick the number of clusters, k."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(200)\n",
    "k = 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Step 2: Select k random points from the data as centroids\n",
    "Next, we randomly select the centroid for each cluster. Let’s say we want to have 2 clusters, so k is equal to 2 here. We then randomly select the centroid:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{1: [38, 48], 2: [28, 11], 3: [54, 62]}"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "xmin = min(df['x'])\n",
    "xmax = max(df['x'])\n",
    "ymin = min(df['y'])\n",
    "ymax = max(df['y'])\n",
    "centroids = {\n",
    "    i+1: [np.random.randint(xmin, xmax), np.random.randint(ymin,ymax)]\n",
    "    for i in range(k)\n",
    "}\n",
    "centroids"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAT8AAAEzCAYAAABHZATQAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8vihELAAAACXBIWXMAAAsTAAALEwEAmpwYAAAVCElEQVR4nO3dbYydZ33n8e/PSVhwKGBvx5aX4BmQrKQsNAFG2dCsql1MqsC2OG+QgoaVtYo0b9gtVJW6Zi1txQtL0aqq6ItVpRHQWtvZrCCFxo0qiuWCVrtapTgPNEmdrFuYMWlcewgL7NYShfq/L849ycSxPWdmzjn3OXN/P9LoOvc15+Gv8czP99N1XakqJKlrdrRdgCS1wfCT1EmGn6ROMvwkdZLhJ6mTDD9JndRX+CX5tSTPJnkmyUNJXp9kd5KTSc427a5hFytJg7Ju+CV5K/CrwGxVvQu4AbgfOAKcqqoDwKlmW5ImQr+HvTcCb0hyI7ATeBE4BBxvvn8cuG/g1UnSkKwbflX1N8BvAeeA88APq+prwN6qOt885zywZ5iFStIg3bjeE5pzeYeAtwM/AL6U5OP9fkCSeWAe4Oabb37fbbfdtrlKJekaHn/88e9V1dRGXrNu+AEfBL5TVSsASb4M/AJwIcm+qjqfZB9w8WovrqoFYAFgdna2Tp8+vZH6JGldSZY3+pp+zvmdA+5KsjNJgIPAGeAEcLh5zmHgkY1+uCS1Zd09v6p6LMnDwBPAT4En6e3JvRH4YpIH6AXkR4dZqCQNUj+HvVTVbwK/eUX3j+ntBUrSxHGEh6ROMvwkdZLhJ6mTDD9JnWT4Seokw09SJxl+kjrJ8JPUSYafpE4y/CR1kuEnqZMMP0mdZPhJ6iTDT1InGX6SOsnwk9RJhp+kTjL8JHWS4Sepkww/SZ1k+EnqJMNPUicZfpI6yfCT1EmGn6ROWjf8ktya5Kk1Xz9K8qkku5OcTHK2aXeNomBJGoR1w6+qnq+qO6rqDuB9wCXgK8AR4FRVHQBONdtSJywuLjIzM8OOHTuYmZlhcXGx7ZK0QRs97D0I/HVVLQOHgONN/3HgvgHWJY2txcVF5ufnWV5epqpYXl5mfn7eAJwwGw2/+4GHmsd7q+o8QNPuGWRh0rg6evQoly5delXfpUuXOHr0aEsVaTP6Dr8krwM+AnxpIx+QZD7J6SSnV1ZWNlqfNHbOnTu3oX6Np43s+X0IeKKqLjTbF5LsA2jai1d7UVUtVNVsVc1OTU1trVppDOzfv39D/RpPGwm/j/HKIS/ACeBw8/gw8MigipLG2bFjx9i5c+er+nbu3MmxY8daqkib0Vf4JdkJ3AN8eU33g8A9Sc4233tw8OVJ42dubo6FhQWmp6dJwvT0NAsLC8zNzbVdmjYgVTWyD5udna3Tp0+P7PMkdUOSx6tqdiOvcYSHpE4y/CR1kuEnqZMMP0mdZPhJ6iTDT1InGX5Sn5zJZXu5se0CpEmwOpPL6oQGqzO5AN7cPKHc85P64Ewu24/hJ/XBmVy2H8NP6oMzuWw/hp/UB2dy2X4MP6kPzuSy/Tiri6SJ56wuktQnw09SJxl+2paGPRrD0R6TzxEe2naGPRrD0R7bgxc8tO3MzMywvLz8mv7p6WmWlpbG/v21cV7wkBj+aIz13n9xEWZmYMeOXusR8Xgy/LTtDHs0xvXef3ER5udheRmqeu38vAE4jgw/bTvDHo1xvfc/ehSumP+AS5fA+Q/Gj+GnbWfYozGu9/7XOrJ2/oPx4wUPaYBmZnqHuleangavhQyPFzyklh07BlccEbNzZ69f46Wv8EvyliQPJ3kuyZkk70+yO8nJJGebdtewi5XG3dwcLCz09vSSXruw0OvXeOl3z+93gK9W1W3A7cAZ4AhwqqoOAKeabanz5uZ6h7iXL/dag288rRt+Sd4E/CLweYCq+vuq+gFwCDjePO04cN9wSpSkwetnz+8dwArwe0meTPK5JDcDe6vqPEDT7hlinZI0UP2E343Ae4Hfrar3AH/HBg5xk8wnOZ3k9MrKyibLlDbGiQe0nn7C7wXghap6rNl+mF4YXkiyD6BpL17txVW1UFWzVTU7NTU1iJql61qdeGB5eZmqenniAQNQa60bflX1t8B3k9zadB0E/hI4ARxu+g4DjwylQmmDXGZS/eh3Sqt/BywmeR3wbeDf0AvOLyZ5ADgHfHQ4JUob4zKT6kdft7pU1VPNoevPV9V9VfV/quqlqjpYVQea9vvDLlbqx7gtM+n5x/HkCA9tO+O0zKTnH8eX4adtZ5yWmfT84/hyYgNpiHbs2MHV/saScPny5RYq2p6c2EAaM+N2/lGvMPykIRqn8496NcNPGqJxOv+oV/Ocn6SJ5zk/SeqT4Sepkwy/CeSIAWnr+h3bqzGxOmJg9cbZ1REDgCfRpQ1wz2/COGJAGgzDb8IMasYSD53VdYbfhBnEiAEH20uG38QZxIgBD50lw2/iDGLEgJN9So7w6KSZmRmWl5df0z89Pc3S0tLoC5K2yBEe6ouD7SXDr5McbC8ZfkM3rreUzM3NsbS0xOXLl1laWjL41DmO8BgiR2NI48s9vyHylhJpfBl+Q+QtJdL4MvyGyPUbpPFl+A2Rt5RI46uv8EuylOTpJE8lOd307U5yMsnZpt013FInj7eUSOOrrxEeSZaA2ar63pq+/wR8v6oeTHIE2FVV//567+MID0nDMOoRHoeA483j48B9W3gvSRqpfsOvgK8leTzJfNO3t6rOAzTtnmEUKEnD0O9NzndX1YtJ9gAnkzzX7wc0YTkPXuWUND762vOrqheb9iLwFeBO4EKSfQBNe/Ear12oqtmqmp2amhpM1ZK0ReuGX5Kbk/zM6mPgl4BngBPA4eZph4FHhlWkJA1aP4e9e4GvJFl9/n+tqq8m+SbwxSQPAOeAjw6vTEkarHX3/Krq21V1e/P1T6vqWNP/UlUdrKoDTfv94ZerbWFxEWZmYMeOXjsmM92oW5zVRaO1uAjz87A64cPycm8bwJu/NUIOb9NoHT36SvCtunSp1y+NkOGn0brWjDbOdKMRM/w0Wte619N7QDVihp9G69gxuGKmG3bu7PVLI2T4abTm5mBhAaanIem1Cwte7NDIGX7akIEsyDQ3B0tLcPlyrzX41AJvdVHfXJBJ24l7fuqbCzJpOzH81DcXZNJ2Yvipby7IpO3E8FPfXJBJ24nhp765IJO2k74WMBoUFzCSNAyjXsBIkiaW4Sepkww/SZ1k+EnqJMNPUicZfpI6yfCT1EmGn6ROMvwkdZLhJ6mTDD9JndR3+CW5IcmTSR5ttncnOZnkbNPuGl6ZkjRYG9nz+yRwZs32EeBUVR0ATjXbkjQR+gq/JLcA/wr43JruQ8Dx5vFx4L6BViZJQ9Tvnt9ngd8ALq/p21tV5wGads9gS5Ok4Vk3/JL8MnCxqh7fzAckmU9yOsnplZWVzbzFyAxkWUZJE6GfpSvvBj6S5MPA64E3JfkD4EKSfVV1Psk+4OLVXlxVC8AC9CYzHVDdA+eyjFK3rLvnV1WfrqpbqmoGuB/4s6r6OHACONw87TDwyNCqHAGXZZS6ZSv3+T0I3JPkLHBPsz2xXJZR6pZ+DntfVlXfAL7RPH4JODj4ktqxf/9+lpeXr9ovaftxhEfDZRmlbjH8Gi7LKHWLS1dKmnguXSlJfTL8JHWS4dciR5RI7dnQrS4aHEeUSO1yz68ljiiR2mX4tcQRJVK7DL+WXGvkiCNKpNEw/FriiBKpXYZfSxxRIrXLER6SJp4jPCSpT4afpE4y/CR1kuEnqZMMP0mdZPhJ6iTDT1InGX6SOsnwk9RJhp+kTjL8JHWS4Sepk9YNvySvT/LnSb6V5Nkkn2n6dyc5meRs0+4afrmSNBj97Pn9GPhAVd0O3AHcm+Qu4AhwqqoOAKeabY0xF0ySXrFu+FXP/2s2b2q+CjgEHG/6jwP3DaNADcbqgknLy8tU1csLJhmA6qq+zvkluSHJU8BF4GRVPQbsrarzAE27Z2hVastcMEl6tb7Cr6r+oaruAG4B7kzyrn4/IMl8ktNJTq+srGyyTG2VCyZJr7ahq71V9QPgG8C9wIUk+wCa9uI1XrNQVbNVNTs1NbW1arVpLpgkvVo/V3unkrylefwG4IPAc8AJ4HDztMPAI0OqUQPggknSq/Wz57cP+HqSvwC+Se+c36PAg8A9Sc4C9zTbGlMumCS9mgsYSZp4LmAkSX0y/CR1kuEnqZMMP0mdZPhJ6iTDT1InGX6SOsnwk9RJhp+kTjL8JHWS4Sepkww/SZ1k+EkamElaJ+bGtguQtD2srhOzulzC6joxwFhOneaen6SBmLR1Ygw/SQMxaevEGH7SAEzSua5hmbR1Ygw/aYtcE7ln0taJMfykLZq0c13DMmnrxLiGh7RFO3bs4Gp/R0m4fPlyCxV1j2t4SC2YtHNd6jH8pC2atHNd6jH8pC2atHNd6vGcn6SJ5zk/SerTuuGX5G1Jvp7kTJJnk3yy6d+d5GSSs027a/jlStJg9LPn91Pg16vq54C7gE8keSdwBDhVVQeAU822JE2EdcOvqs5X1RPN4/8LnAHeChwCjjdPOw7cN6QaJWngNnTOL8kM8B7gMWBvVZ2HXkACewZenSQNSd/hl+SNwB8Cn6qqH23gdfNJTic5vbKyspkaJW2SEy5cW1/hl+QmesG3WFVfbrovJNnXfH8fcPFqr62qhaqararZqampQdQsqQ9OuHB9/VztDfB54ExV/faab50ADjePDwOPDL48SZvlhAvX18809ncD/xp4OslTTd9/AB4EvpjkAeAc8NGhVChpUyZtctFRWzf8qup/ALnGtw8OthxJg7J//36Wl5ev2i9HeEjblhMuXJ/hJ21TTrhwfU5sIGniObGBJPXJ8JPUSYafpE4y/CR1kuEnqZMMP0mdZPhJ6iTDT1InGX6SOsnwk4bMCUXHUz9TWknapNUJRVfn1VudUBRwjG3L3POThsgJRceX4ScNkROKji/DTxqia00c6oSi7TP8pCFyQtHxZfhJQ+SEouPLyUwlTTwnM5WkPhl+kjrJ8OuQxacXmfnsDDs+s4OZz86w+LQjDdRdjvDoiMWnF5n/43ku/aQZafDDZeb/uBlp8G5Pvqt73PPriKOnjr4cfKsu/eQSR0850kDdtG74JflCkotJnlnTtzvJySRnm3bXcMvUVp374TVGGlyjX9ru+tnz+33g3iv6jgCnquoAcKrZ1hjb/+ZrjDS4Rr+03a0bflX134HvX9F9CDjePD4O3DfYsjRoxw4eY+dNV4w0uGknxw460kDdtNlzfnur6jxA0+4ZXEkahrl3z7HwKwtMv3maEKbfPM3Cryx4sUOdNfSrvUnmgXlwMHfb5t49Z9hJjc3u+V1Isg+gaS9e64lVtVBVs1U1OzU1tcmPk6TB2mz4nQAON48PA48MphxJGo1+bnV5CPhfwK1JXkjyAPAgcE+Ss8A9zbYkTYx+rvZ+rKr2VdVNVXVLVX2+ql6qqoNVdaBpr7waLGmIXBRp6xzeJk0YF0UaDIe3SRPGRZEGw/CTJkwbiyJtx8Nsw0+aMKNeFGn1MHt5eZmqevkwe9ID0PCTJsyoF0XarofZhp80YUa9KNJ2XXvYBYwkXdfMzAzLy8uv6Z+enmZpaWn0BV2FCxhJGrjtuvaw4Sfpurbr2sMe9kqaeB72SlKfDD9JnWT4Seokw09SJxl+kjrJ8JPUSYafpE4y/CR1kuEnqZMMP0mdZPhJ6iTDT1InGX6SOsnwk9RJhp+kTtpS+CW5N8nzSf4qyZFBFSVJw7bp8EtyA/CfgQ8B7wQ+luSdgypMkoZpK3t+dwJ/VVXfrqq/B/4bcGgwZUnScG0l/N4KfHfN9gtNnySNvRu38Npcpe81C4IkmQfmm80fJ3lmC585SD8LfK/tIhrW8lrjUgdYy7WMUy23bvQFWwm/F4C3rdm+BXjxyidV1QKwAJDk9EYXGRkWa7m6callXOoAa7mWcatlo6/ZymHvN4EDSd6e5HXA/cCJLbyfJI3Mpvf8quqnSf4t8KfADcAXqurZgVUmSUO0lcNequpPgD/ZwEsWtvJ5A2YtVzcutYxLHWAt1zLRtYx00XJJGhcOb5PUSSMJv7aHwSX5QpKLa2+zSbI7yckkZ5t21wjqeFuSryc5k+TZJJ9ssZbXJ/nzJN9qavlMW7WsqemGJE8mebTNWpIsJXk6yVOrVxFbrOUtSR5O8lzze/P+ln5fbm1+HqtfP0ryqZZq+bXmd/aZJA81v8sbrmPo4Tcmw+B+H7j3ir4jwKmqOgCcaraH7afAr1fVzwF3AZ9ofhZt1PJj4ANVdTtwB3BvkrtaqmXVJ4Eza7bbrOVfVtUda27laKuW3wG+WlW3AbfT+/mMvJaqer75edwBvA+4BHxl1LUkeSvwq8BsVb2L3sXW+zdVR1UN9Qt4P/Cna7Y/DXx62J97lTpmgGfWbD8P7Gse7wOeb6GmR4B72q4F2Ak8Afyztmqhd5/oKeADwKNt/hsBS8DPXtE38lqANwHfoTk332YtV3z+LwH/s41aeGVk2W56F2wfberZcB2jOOwd12Fwe6vqPEDT7hnlhyeZAd4DPNZWLc1h5lPAReBkVbVWC/BZ4DeAy2v62qqlgK8lebwZodRWLe8AVoDfa04HfC7JzS3Vstb9wEPN45HWUlV/A/wWcA44D/ywqr62mTpGEX59DYPrkiRvBP4Q+FRV/aitOqrqH6p3GHMLcGeSd7VRR5JfBi5W1eNtfP5V3F1V76V3quYTSX6xpTpuBN4L/G5VvQf4O0Z76P8azYCGjwBfaunzd9GbQOXtwD8Bbk7y8c281yjCr69hcC24kGQfQNNeHMWHJrmJXvAtVtWX26xlVVX9APgGvfOibdRyN/CRJEv0Zgf6QJI/aKkWqurFpr1I77zWnS3V8gLwQrNHDvAwvTBs8/flQ8ATVXWh2R51LR8EvlNVK1X1E+DLwC9spo5RhN+4DoM7ARxuHh+md/5tqJIE+Dxwpqp+u+VappK8pXn8Bnq/VM+1UUtVfbqqbqmqGXq/H39WVR9vo5YkNyf5mdXH9M4nPdNGLVX1t8B3k6wO2j8I/GUbtazxMV455KWFWs4BdyXZ2fw9HaR3EWjjdYzoBOmHgf8N/DVwdJQnZ5vPf4je+YGf0Pvf9AHgH9M7wX62aXePoI5/Tu+Q/y+Ap5qvD7dUy88DTza1PAP8x6Z/5LVcUde/4JULHm38XN4BfKv5enb197Wtnwu9K/Gnm3+nPwJ2tVjLTuAl4M1r+tr4N/oMvf+onwH+C/CPNlOHIzwkdZIjPCR1kuEnqZMMP0mdZPhJ6iTDT1InGX6SOsnwk9RJhp+kTvr/bnAMkrr5nrwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(5, 5))\n",
    "plt.scatter(df['x'], df['y'], color='k')\n",
    "colmap = {1: 'r', 2: 'g', 3: 'b'}\n",
    "for i in centroids.keys():\n",
    "    plt.scatter(*centroids[i], color=colmap[i])\n",
    "plt.xlim(0, 80)\n",
    "plt.ylim(0, 80)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, the blue , red and green circles represent the centroid for these clusters."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Step 3: Assign all the points to the closest cluster centroid\n",
    "Once we have initialized the centroids, we assign each point to the closest cluster centroid:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def assign(df, centroids):\n",
    "    for i in centroids.keys():\n",
    "        df['distance_from_'+ str(i)] = (\n",
    "            np.sqrt((df['x'] - centroids[i][0])** 2 + (df['y'] - centroids[i][1])** 2)\n",
    "        )\n",
    "    centroid_distance = ['distance_from_' + str(i) for i in centroids.keys()]\n",
    "    df['closest'] = df.loc[:, centroid_distance].idxmin(axis=1)\n",
    "    df['closest'] = df['closest'].map(lambda x:int(x.lstrip('distance_from_')))\n",
    "    df['color'] = df['closest'].map(lambda x:colmap[x])\n",
    "    return df\n",
    "# 1069"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Step 4: Recompute the centroids of newly formed clusters\n",
    "Now, once we have assigned all of the points to either cluster, the next step is to compute the centroids of newly formed clusters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def update(k):\n",
    "    for i in centroids.keys():\n",
    "        centroids[i][0] = np.mean(df[df['closest'] == i]['x'])\n",
    "        centroids[i][1] = np.mean(df[df['closest'] == i]['y'])\n",
    "    return k"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plot(df, centroids):\n",
    "    fig = plt.figure(figsize=(5, 5))\n",
    "    plt.scatter(df['x'],df['y'], color=df['color'], alpha=0.5, edgecolor='k')\n",
    "    for i in centroids.keys():\n",
    "        plt.scatter(*centroids[i], color=colmap[i])\n",
    "    plt.xlim(0, 80)\n",
    "    plt.ylim(0, 80)\n",
    "    plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Step 5: Repeat steps 3 and 4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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gcSJCiYgkmk41EJFQUvmJSCip/EQklFR+IhJKKj8RCSVd0kpi1tLSwh8ef5ytzz2HRyJMW7CAJddeS1ZWVtDRRHpMa34Sk0gkwi//+Z9JeuIJvpSVxVdycshav57VP/oRHR0dQccT6TGVn8Rk+/btUFHB1cXFZA8bxoi0NJYUFzOyspK333476HgiPabyk5js3buXIjOiZ/ocV2zG3rq6gFKJ9J7KT2IyevRodsJHbrtZ485o3ZNEBiGVn8Tk7LPPpmPKFJ6qqqK5vZ2jHR08U11NQ2Eh55xzTtDxRHpMR3slJklJSdxyxx2sX7eOf3r22a6jvZdcwvJly0hNTQ06nkiPxXQPj3jRPTyGhmOfmVP3/4kEpb/v4SFDxZo1UFICSUld0zVr/uzT7TQHPkQGG232ht2aNbBiBTQ3d81XVXXNA9x0U3C5RBJMa35hd9ddHxbfMc3NXeMiQ5jKL+yqq3s2LjJEqPzC7kx31NOd9mSIU/mF3d13Q2bmyWOZmV3jIkOYyi/sbroJVq2C4mIw65quWqWDHTLk6WivdBWdyk5CRmt+IhJKKj8RCSWVn4iEkspPREIp5vIzs2Qz22Rmj0fn88xsvZm9F53mJi6miEh89WTN7w6g4oT5lUCZu08ByqLzIiKDQkzlZ2YTgWuAn50wvBRYHX28GlgW12QiIgkU65rfvcA3gcgJY/nuXgsQnY6Nb7T+19nZSX19PQcPHgw6iogkWLdfcjazTwJ73H2jmX28pwswsxXACoCiAXy+6NYtW3jygQcYduAALUD++efzqeXLdU9akSEqljM85gPXmdnVQDqQbWYPAfVmVuDutWZWAOw53YvdfRWwCrqu5Byn3HFVW1vL/9x7L5/LzmZCURGdkQjPvf46a1tbufVv/kYX7hQZgrrd7HX3b7n7RHcvAW4E/ujuNwPrgOXRpy0HHktYygTb+PLLXODOhOxsAJKTkri0sJCmLVuor68POJ2IJEJfvud3D3C5mb0HXB6dH5Sa9u0jb9iwk8bMjFwzDh8+HFAqEUmkHl3YwN2fBZ6NPm4AFsc/Uv8rOvdcKl5+mXNPGGtqa2N3cjITJkwILJeIJI6u6gKcX1rK62VlPPbBB8zKzaWprY3nmpq48JZbyDz1WnciMiSo/ID09HRu/cY3ePWll/hDeTkZ2dlceumlTJ8+PehoIpIgum+viAx6um+viEiMVH4B6881bxH5kPb5BaSqqoqyX/+amq1bGZGXx9xrrmHBxz9OUpL+PxLpDyq/ANTV1bH27/+eq5KTWV5YyP6WFp544AFampq44rrrgo4nEgpazQjAn8rKmN/ZyYyxY0lOSmLM8OFcX1jIpscf5+jRo0HHEwkFlV8A9u3YQVH0VLpjhqelMbKzk8bGxmBCiYSMyi8AYyZPpurQoZPGjrS1cTAlhZycnGBCiYSMyi8AF112GS+npvJmXR1tnZ3UNTXxq+pqzr/2WtLT04OOJxIKKr8A5Ofnc+O3v80b06fz/dpaHk5K4i9uv50lV18ddDSR0NDR3oAUFhay/I47go4hElpa8xORUFL5iUgoqfxEJJRUfiISSio/EQkllZ+IhJLKT0RCSeUnIqGk8hORUFL5iUgoqfxEJJRUfiISSt1e2MDM0oHngWHR5//G3b9jZnnAr4ASoBK4wd0PJC6q9EVraytvvvkm26u3M270OErnlJKVlRV0LJHAxHJVl1bgMndvMrNU4EUz+x/g00CZu99jZiuBlcDfJjCr9FJTUxM/+JcfUNVRRdqYNNp3tPPbP/yWlV9ayfjx44OOJxKIbjd7vUtTdDY1+suBpcDq6PhqYFkiAkrfPV32NFUpVZQsKGH81PEUzy2mfVI7Dz3yUNDRRAIT0z4/M0s2szeAPcB6d38VyHf3WoDodGzCUkqfvLL5FcZOOfmvZ+yksVRUVdDS0hJQKpFgxVR+7t7p7rOBicA8M5sR6wLMbIWZlZtZ+d69e3sZU/piWNowOto6Thrr7OgkmWSSk5MDSiUSrB4d7XX3RuBZ4Eqg3swKAKLTPWd4zSp3L3X30jFjxvQtrfTKkouWsHfrXiKdEQDcnV1v7eLi2ReTlpYWcDqRYMRytHcM0O7ujWaWASwBvg+sA5YD90SnjyUyqPTegvkLqNpZxTNPP4PlGJGmCOeOO5fPfuqzQUcTCYy5+59/gtl5dB3QSKZrTXGtu/8/MxsFrAWKgGrgenff/+feq7S01MvLy+MSXHpuz5491NXVkZOTQ2FhIWYWdCSRuDCzje5e2pPXdLvm5+6bgY+dZrwBWNyThUmwxo4dy9ixOi4lAjrDQ0RCSuUnIqGk8hORUFL5iUgoqfxEJJRUfiISSio/EQkllZ+IhJLKT0RCSeUnIqGk8hORUIrlMvYiIjFxd+rr64lEIowbN46kpIG7fqXyE5G4qK2t5ZGf/IRIdTXJZrSNGcOyL36RSZMmBR3ttAZuLYvIoNHe3s5//uhHfHzvXr5SVMSXi4q4rqWFX//whzQ1NXX/BgFQ+YlIn23bto1xDQ3MGDv2+HUiJ+flMe3IEd7avDngdKenzV6RPjp8+DDPPP8MG9/eSHZmNksWLOG8884L1cVijxw5Qs5pxnPMOHL4cH/HiYnW/ET6oLm5mXvuu4dHKx6laVITO7J28KO1P+LJ9U8GHa1flZSU8I477Z2dx8ci7rwdiVB81lkBJjszrfmJ9MGrG15lV9IuSkpLAMgii+wx2Tz6h0dZNH8Rw4cPDzZgPxk3bhyTr7ySB3//ey4aMYKUpCQ2HDxI1oIFnH322UHHOy2Vn0gfVHxQwYjxI04aS8tIIzIiQl1dHZMnTw4oWf+77rOfZfP06Wx+6SU629s55+KL+dj55w/YzX+Vn0gf5Ofls7Fm40ljHnEiRyJkZ2cHlCoYZsasWbOYNWtW0FFion1+In0w/8L5JO1KorGuEXens72T6termXP2HHSf6oFN5SfSB+PGjePrf/l1MrZnUPNUDbuf3s2C/AXcetOtQUeTbnR739540n17Zahydw4cOEB6ejqZmZlBxwmdhNy3V0S6Z2bk5eUFHUN6QJu9IhJK3ZafmRWa2TNmVmFmW83sjuh4npmtN7P3otPcxMcVEYmPWNb8OoA73X06cCHwZTM7B1gJlLn7FKAsOi8iMih0W37uXuvur0cfHwYqgAnAUmB19GmrgWUJyigiEnc92udnZiXAx4BXgXx3r4WuggTGxj2diPTJsYuL1tTU0NHREXScASXmo71mNgJ4BPiqux+K9ZQVM1sBrAAoKirqTUYR6YWGhgb+4xf/wXt73sNSjGyyuf2ztzNjxoygow0IMa35mVkqXcW3xt0fjQ7Xm1lB9PcLgD2ne627r3L3Uncv1TfeRfpHJBLhvvvvoyqziqJPFFG0uIjk2cnc+8t72bPntP9UQyeWo70G3A9UuPs/nvBb64Dl0cfLgcfiH09EeqOqqoqqw1UUTC04fmGBrFFZRAoibCjfEHC6gSGWzd75wC3AW2b2RnTs28A9wFozuw2oBq5PSEIR6bHm5mYs/aO7plIzU2k83Nj/gQagbsvP3V8EzrSDb3F844hIPBQVFZF0MIm2ljbSMtKAroMfLbtbOHfuuQGnGxh0epvIEJSVlcUNn7iBNWVrSD8rndRhqRyqPMTsMbOZOXNm0PEGBJWfyBB1+eLLKS4s5sUNL9LU0sTcy+cyt3QuKSn6Zw8qP5Ehy8yYOnUqU6dODTrKgKQLG4gk2Jq31lBybwlJ302i5N4S1ry1JuhIgtb8RBJqzVtrWPG7FTS3NwNQdbCKFb9bAcBNM28KMlroac1PJIHuKrvrePEd09zezF1ldwWUSI5R+YkkUPXB6h6NS/9R+YkkUNHI05/PfqZx6T8qP5EEunvx3WSmnnxPj8zUTO5efHdAieQYlZ9IAt008yZWXbuK4pHFGEbxyGJWXbtKBzsGAN29TUQGvd7cvU1rfiIJ1traSmVlpS4lNcDoe34iCfTKq6/wi//+BUfTjhI5GmFm0Uy+cMsXyM7ODjpa6GnNTyRBKisr+cmjPyHroiyKLi2i+Ipi3u58m5/+8qdBRxNUfiIJ8/yfnidtUhoZ2RkAWJIxccZEttRs0SbwAKDyE0mQxqZG0jLTThqzJMOGGS0tLQGlkmNUfiIJMmvqLA7VHDpprPlgMxntGRQUFASUSo7RAQ+RBLlg3gW8sOEF3n3pXbILs2k90kp7ZTtf/PQXSUtL6/4NJKFUfiIJkp6eztf/6uu8Vv4amyo2kZuby8KrFlJSUhJ0NEHlJ5JQ6enpLFywkIULFgYdRU6hfX4iEkoqPxEJJZWfiISSyk9EQknlJyKh1G35mdnPzWyPmW05YSzPzNab2XvRaW5iY4qIxFcsa34PAleeMrYSKHP3KUBZdF5EZNDotvzc/Xlg/ynDS4HV0cergWXxjSUikli93eeX7+61ANHp2PhFEhFJvIQf8DCzFWZWbmble/fuTfTiRERi0tvyqzezAoDo9IwXJ3P3Ve5e6u6lY8aM6eXiRETiq7fltw5YHn28HHgsPnFERPpHtxc2MLOHgY8Do81sJ/Ad4B5grZndBlQD1ycypIh8aN++fTxZ9iRvvfcWo3NGc+UlVzJz5sygYw06unWlyCCyf/9+vvtP36VpbBOjikbRcqiFg28f5PZrbmfRgkVBxwuMbl0pMsSVPVtG0+gmCmcWkjkyk1GFoyi4qIC1/7OW9vb2oOMNKio/kUGkYkcFI8ePPGksIzuDFmth//5Tv44bH+7O+++/z4svvsiWLVvo6OhIyHL6my5mKjKIjB8znl0HdpE95sP7/na0dWBtRlZWVtyX19rayr/d/2+8uftNyAVrMiamTeTO/3snOTk5cV9ef9Kan8ggsmTREtq2t3Fwz0EA2lraqN5QzeUXXE5mZmbcl/fHZ//IpsZNFC8upmROCcWXFLN7xG4efvThuC+rv6n8RAaRkpIS7rzlToa9M4yq31fR8EwDS2cs5TNLP5OQ5T332nOMnTYWMzs+Nn76eF7b+hptbW0JWWZ/0WavyCAzY8YMvnfu92hqamLYsGEJvROc4ycVH3B8vj+/KZIIWvMTGYTMuvbxJfoWmAvnLKR+W/1JRVf7Ti2l55QybNiwhC470bTmJyJntOTSJVS8X8GWP27B8gyaYJyN48Yv3Rh0tD5T+YnIGaWnp3Pnl+/k3Xffpa6ujpycHM4991xSU1ODjtZnKj8R+bOSkpKYNm0a06ZNCzpKXGmfn4iEkspPREJJ5ScioaTyE5FQUvmJSCip/EQklFR+IhJKKj8RCSWVn4iEkspPREJJ5ScioaTyE5FQUvmJSCip/EQklFR+IhJKfSo/M7vSzN4xs/fNbGW8QomIJFqvy8/MkoF/Ba4CzgE+Z2bnxCuYiEgi9WXNbx7wvrt/4O5twH8BS+MTS0QksfpSfhOAmhPmd0bHREQGvL7cw8NOM/aRG3ma2QpgRXS21cy29GGZ8TQa2Bd0iChl+aiBkgOU5UwGUpapPX1BX8pvJ1B4wvxEYPepT3L3VcAqADMrd/fSPiwzbpTl9AZKloGSA5TlTAZalp6+pi+bva8BU8xskpmlATcC6/rwfiIi/abXa37u3mFmfwU8BSQDP3f3rXFLJiKSQH26b6+7/x74fQ9esqovy4szZTm9gZJloOQAZTmTQZ3F3D9yjEJEZMjT6W0iEkr9Un5BnwZnZj83sz0nfs3GzPLMbL2ZvRed5vZDjkIze8bMKsxsq5ndEWCWdDPbYGZvRrN8N6gsJ2RKNrNNZvZ4kFnMrNLM3jKzN44dRQwwS46Z/cbMtkU/NxcF9HmZGv15HPt1yMy+GlCWr0U/s1vM7OHoZ7nHORJefgPkNLgHgStPGVsJlLn7FKAsOp9oHcCd7j4duBD4cvRnEUSWVuAyd58FzAauNLMLA8pyzB1AxQnzQWa51N1nn/BVjqCy/Bh40t2nAbPo+vn0exZ3fyf685gNzAGagd/2dxYzmwD8NVDq7jPoOth6Y69yuHtCfwEXAU+dMP8t4FuJXu5pcpQAW06YfwcoiD4uAN4JINNjwOVBZwEygdeBC4LKQtf3RMuAy4DHg/w7AiqB0aeM9XsWIBvYQXTffJBZTln+J4CXgsjCh2eW5dF1wPbxaJ4e5+iPzd6BehpcvrvXAkSnY/tz4WZWAnwMeDWoLNHNzDeAPcB6dw8sC3Av8E0gcsJYUFkceNrMNkbPUAoqy1nAXuCB6O6An5nZ8ICynOhG4OHo437N4u67gB8C1UAtcNDdn+5Njv4ov5hOgwsTMxsBPAJ81d0PBZXD3Tu9azNmIjDPzGYEkcPMPgnscfeNQSz/NOa7+/l07ar5spktCihHCnA+8O/u/jHgCP276f8R0RMargN+HdDyc+m6gMokYDww3Mxu7s179Uf5xXQaXADqzawAIDrd0x8LNbNUuopvjbs/GmSWY9y9EXiWrv2iQWSZD1xnZpV0XR3oMjN7KKAsuPvu6HQPXfu15gWUZSewM7pGDvAbusowyM/LVcDr7l4fne/vLEuAHe6+193bgUeBi3uToz/Kb6CeBrcOWB59vJyu/W8JZWYG3A9UuPs/BpxljJnlRB9n0PWh2hZEFnf/lrtPdPcSuj4ff3T3m4PIYmbDzSzr2GO69idtCSKLu9cBNWZ27KT9xcDbQWQ5wef4cJOXALJUAxeaWWb039Niug4C9TxHP+0gvRp4F9gO3NWfO2ejy3+Yrv0D7XT9b3obMIquHezvRad5/ZBjAV2b/JuBN6K/rg4oy3nApmiWLcDfRcf7PcspuT7Ohwc8gvi5nAW8Gf219djnNaifC11H4sujf0//DeQGmCUTaABGnjAWxN/Rd+n6j3oL8EtgWG9y6AwPEQklneEhIqGk8hORUFL5iUgoqfxEJJRUfiISSio/EQkllZ+IhJLKT0RC6f8D9BPPcbZViFIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import copy as cp\n",
    "old_centroids = {}\n",
    "while old_centroids != centroids:\n",
    "    old_centroids = cp.deepcopy(centroids)\n",
    "    df = assign(df, centroids)\n",
    "    centroids = update(centroids)\n",
    "    plot(df, centroids)"
   ]
  }
 ],
 "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": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}