{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Activity 3 - Clustering\n",
    "\n",
    "In this example we show a method of k-means clustering. The idea is that we inform the system of how many clusters we want (e.g., 3). The system generates k random points that we use as our group centroids. For each point in our data, we then see which group the point is closest to, and we assign it to that group. Once we have considered all points, we then update the position of the centroid, so that it is at the mean of the selected points. We then repeat this process, of measuring distance to the centroids and updating our centroids. We do this until the centroids are positioned such that they no longer move (i.e., we have found our clusters)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generate some sample data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7fe804439750>"
      ]
     },
     "execution_count": 2,
     "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": [
    "# We will define three clusters where we know the \"ground truth\" of how the data was constructed\n",
    "\n",
    "cluster1 = np.random.normal(0.0,0.5,[100,2])\n",
    "cluster1[:,0] = cluster1[:,0] + 1.0\n",
    "cluster1[:,1] = cluster1[:,1] + 1.0\n",
    "\n",
    "cluster2 = np.random.normal(0.0,0.6,[100,2])\n",
    "cluster2[:,0] = cluster2[:,0] + 1.0\n",
    "cluster2[:,1] = cluster2[:,1] + 4.0\n",
    "\n",
    "cluster3 = np.random.normal(0.0,0.7,[100,2])\n",
    "cluster3[:,0] = cluster3[:,0] + 3.5\n",
    "cluster3[:,1] = cluster3[:,1] + 3.5\n",
    "\n",
    "# We will then stack this data together so that it 'appears' all together\n",
    "\n",
    "all_data = np.vstack([cluster1, cluster2, cluster3])\n",
    "plt.scatter(all_data[:,0], all_data[:,1], color='k')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Defining ***k***\n",
    "\n",
    "***k*** is the number of clusters that we wish to discover. We may either know ***k***, or have some expectation of ***k*** - or, we may have to try different values of ***k*** to see how the results compare.\n",
    "\n",
    "For our example, we will say that ***k*** = 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "k = 3"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Generate ***k*** initial centroid points\n",
    "\n",
    "Here we essentially generate ***k*** randomised centroid points - i.e., a random value of x and a random value of y, for each of our  centroid points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[4.47517996, 4.4403502 ],\n",
       "       [3.79748152, 3.7095377 ],\n",
       "       [2.57755496, 1.4314328 ]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def generate_initial_points(k):\n",
    "    centroids = []\n",
    "    for i in range(k):\n",
    "        c = [1+np.random.random()*4, 1+np.random.random()*4]\n",
    "        centroids.append(c)\n",
    "    centroids = np.array(centroids)\n",
    "    return centroids\n",
    "\n",
    "centroids = generate_initial_points(k)\n",
    "centroids"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting our data\n",
    "\n",
    "We can use a scatter plot to show all of our data, along with the ***k*** centroid points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7fe80454d150>"
      ]
     },
     "execution_count": 5,
     "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(all_data[:,0], all_data[:,1], color='k')\n",
    "plt.scatter(centroids[0,0], centroids[0,1], marker='x', color='r')\n",
    "plt.scatter(centroids[1,0], centroids[1,1], marker='x', color='g')\n",
    "plt.scatter(centroids[2,0], centroids[2,1], marker='x', color='b')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## First pass of the algorithm\n",
    "\n",
    "Here, we will assess each point in the data by measuring the distance between each point and each of the ***k*** centroids. We assign each data point to a class as denoted by the group colour."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7fe804643910>"
      ]
     },
     "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": [
    "group1 = []\n",
    "group2 = []\n",
    "group3 = []\n",
    "    \n",
    "def find_groups(centroids, all_data):\n",
    "    group1 = []\n",
    "    group2 = []\n",
    "    group3 = []\n",
    "    for i in range(all_data.shape[0]):\n",
    "        distance1 = np.sqrt(np.abs(all_data[i, 0] - centroids[0,0]) ** 2 + np.abs(all_data[i, 1] - centroids[0,1]) ** 2)\n",
    "        distance2 = np.sqrt(np.abs(all_data[i, 0] - centroids[1,0]) ** 2 + np.abs(all_data[i, 1] - centroids[1,1]) ** 2)\n",
    "        distance3 = np.sqrt(np.abs(all_data[i, 0] - centroids[2,0]) ** 2 + np.abs(all_data[i, 1] - centroids[2,1]) ** 2)\n",
    "        distances = [distance1, distance2, distance3]\n",
    "        #print (distances)\n",
    "        if np.argmin(distances) == 0:\n",
    "            group1.append([all_data[i, 0], all_data[i, 1]])\n",
    "        elif np.argmin(distances) == 1:\n",
    "            group2.append([all_data[i, 0], all_data[i, 1]])\n",
    "        elif np.argmin(distances) == 2:\n",
    "            group3.append([all_data[i, 0], all_data[i, 1]])\n",
    "    group1 = np.array(group1)\n",
    "    group2 = np.array(group2)\n",
    "    group3 = np.array(group3)\n",
    "    return group1, group2, group3\n",
    "            \n",
    "group1, group2, group3 = find_groups(centroids, all_data)\n",
    "\n",
    "#print (\"group 1:\", group1)\n",
    "#print (\"group 2:\", group2)\n",
    "#print (\"group 3:\", group3)\n",
    "\n",
    "plt.scatter(group1[:,0], group1[:,1], color='r')\n",
    "plt.scatter(group2[:,0], group2[:,1], color='g')\n",
    "plt.scatter(group3[:,0], group3[:,1], color='b')\n",
    "\n",
    "plt.scatter(centroids[0,0], centroids[0,1], marker='x', color='r')\n",
    "plt.scatter(centroids[1,0], centroids[1,1], marker='x', color='g')\n",
    "plt.scatter(centroids[2,0], centroids[2,1], marker='x', color='b')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Update our centroids\n",
    "\n",
    "Now that the data has been labelled against potential grroup membership, we update each centroid position, based on the mean values denoted by the data in each group."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "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": [
    "centroids = np.array([np.mean(group1, axis=0), np.mean(group2, axis=0), np.mean(group3, axis=0)])\n",
    "\n",
    "plt.scatter(group1[:,0], group1[:,1], color='r')\n",
    "plt.scatter(group2[:,0], group2[:,1], color='g')\n",
    "plt.scatter(group3[:,0], group3[:,1], color='b')\n",
    "\n",
    "plt.scatter(centroids[0,0], centroids[0,1], marker='x', color='r')\n",
    "plt.scatter(centroids[1,0], centroids[1,1], marker='x', color='g')\n",
    "plt.scatter(centroids[2,0], centroids[2,1], marker='x', color='b')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Second pass of the algorithm\n",
    "\n",
    "Here, we repeat ourselves - for each point in the data, find which k marker is closest. If we are not at our optimal solution yet then this should give a different result to the one observed in our first pass."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "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": [
    "all_data = np.vstack([group1, group2, group3])\n",
    "group1, group2, group3 = find_groups(centroids, all_data)\n",
    "\n",
    "plt.scatter(group1[:,0], group1[:,1], color='r')\n",
    "plt.scatter(group2[:,0], group2[:,1], color='g')\n",
    "plt.scatter(group3[:,0], group3[:,1], color='b')\n",
    "\n",
    "plt.scatter(centroids[0,0], centroids[0,1], marker='x', color='r')\n",
    "plt.scatter(centroids[1,0], centroids[1,1], marker='x', color='g')\n",
    "plt.scatter(centroids[2,0], centroids[2,1], marker='x', color='b')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Update our centroids\n",
    "\n",
    "Just as we did earlier, we update our centroids again. By now you should be able to see the updating cycle - for each data point find which k marker is closest, and then update the k marker position based on the group membership."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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/9DjOv7EzvRM/vq1oMun845G1av+2+41nwfqx9+1TLwrQ6QT9POJExTlkYWE7ws5Crxe8Nn78mvqyJaKG3YumaWHStiWsSJ/keJvT43cdT7xryOMwyXqevXM9nPneGTD4WjSadPdCRDj60aN9zx396FH88I0fGh3fVjSpO/9w7Gl3YlVOmbd+7IsXsz1PFIhylMcfD6x7WaJhVR+REM8cGzYYGKEG7K3paVqYtPmlcOEoSOpRndVhoiKtUVW0B8oGb4BAmDowpb34hBF1lPueug+37L7F6Pi2LpxJKSiTvt+mKSwXBcfEY0dTCPv2BY+0dELWQlwYUUc5fz67f1n1JYzvs0EMlFDbwtTNY9MSVnZeM4vDRLUYb9p5qs4nKbcdTXssfGgBm7+3iYUPLeDYc8fwc/t/DqNDo33bq45v68JZtIZh8npXVj/dsfHsX2Pi7Axa/3ENEwuM3r9Y316ANklAs9jtommPhQW1mJtGw2lC7JFjwwYDk6O2SZbl52wt61R2XjNrft2k70QUelCfj9QdI6/rI/wbqM5npD2CR+9+1Lt+H2VOee+d62HuyzN4ayhSJ7iimBijm+YdL9hMTQX2PFUBJ+r60M1U1DlGosdptfRNn4aHgd27g/RLRdPB8yBrJlqmCjdP2b0qijZ5SivSDX1uKJM1L4SZQZGiU/xnk/OI0kILX7zni6ULddoFvMwLs3E/EJP1FU2+HMzBvjJFPIr9qrj++mB18ytX9Mf3FCkmWsa0MFnUNRSlrFagIVlu7/OkZXQiDSSnIuKinCTSurFF2cRm6SvJmKQ1iqRpsua2tWmuPfGDG6QTTAo44d8sS9pEl5Nut7e/hMvLQV49KtKq49cQiagd4SLqTmtzWtUq43miP10URyCcuueUtbGbWAnLsMVFMbk7ymsl1L1u9r2z2jayRhG16Yc36wQY0651pvutarV1C0hEXQFF+ryEkTi1GEN7Xwb9u2lMPDQBAEpHQdU9JvaOqic96J4H9JNwDk0esnqBMYlAbdniTCNZE/dJ3oKl7u7mxMoJ7edDebd2FVj8xvXZvaxZXSCmVizT/dZgOngeRKgdkbfPS9SjDSZs/OPNwBMnsfa//5VWfH1aHNYUlRBlmaVpSpqVcLg1bCV9lOVimaWXTJrVL35x0LUKSFoYWXlR+PfLmP6bS9m9rK6aLpnuV7fd1FStV5WR1IcjstRJTF6HPavAfe9SFg+rnOnmw/HTiLo+WtTCJgdj6ox2cOzOY1Yi+CzFXlszJFX7IVCmVrZ8v/3vv7Mm/Kb7VblQlpYq7+WRhrg+KmB+HjhxIvuKQ/rVjTaBB9pK8at69ZKqj+8DSbnw5XuWlU6ZojWFpDy/iVi3qY23f+/tTMfMjAcrp+SOmkpGctQl0usFheeHH+4XXKKgRa8uAAjvylq6v8ieIGeium0u2xHi2/F9ICnPrUqBmKQ10tDluhncl8bQscEbbusYvqycUoN+02mIUGckyXKX1H6AOZgDoNpf9LOs9PAP/xNwx3/Vil+RmXI2pim7XLnbFq77Pyflwl3VC5J6jkQvAkli7WpFHQB2Kuo2csoNKDBK6iMDaZa7tLU+4w6hXi+IsnWLPW9sMto3/gM2fvE/ofuv/1pW5s5JWec5/+Q8Hl5RLAgLN/l60/My6R9u0xJ5jbxWORetLj3oN52G5KgtkZbq0ueX+7cD0idalWH7LCu3XKXHG8h/nlnHneS6cDmD1GSMvXM9HDx9ULsfJ+OzXVEvklP2IVeeggi1JdIChKSIOn4BT4u+y6hzlOHWyDMBwzZ5zjNPFJ61oFg2SRcSJw6dvJFsjSetFEGKiZZIS3WpLJxA0EM9/tlMqmOUtdZnGX2R80zAsE2e88zjTdftrzPaqVykgSCPbrqijhWSei0k5aAbkFO2jQh1BtI896rP5fJysNBFPIDQfeba7fJSZ2W4NZKcCVFcTtDJc555elfrjnPszmOaV5TL9K3TODR5aIdYjw2PYerAlJtiq2rmYZobxMeVyitGhDoDJs2YTGfE6j6LS0vlpc7KcGtkidSKrJaeRJ7zzBOF++Z+UTldjt91HKfuOdU3xl+4+RdKvcNJdYPUYA3DspEcdYVkaePr4nhZ95+nKJhl9pxuFl8Vhci6O2KyOEJmTs8o/x5tamPpk0v2J+sMaA46DclRe0o0+l5cDKJpV3MDis49yNv4SRVlHpo8ZLwUVVXNpsqIjl16u01z7EeePqItgG7wxo73O/PfRJWLlhx0ZiSi9gTXs1yL7t+2lc8kKmvy1HTXEbup08WkDWz0/d73+X1Yv7xzRpfyb6JzfczO+tN7wyPbnkTUNcD1LNei+7e9orrJFGrbx3RJ1ujYdcdD0xy7SQ0hfL9753pKkY5u04cuF33mjB85aF+muBsgQu0Jru8Gi+6/DCufD8fMQ54UjeuLkKnTxWRF+fD9zmxNTIoOTKvuLikyxT2OzSnvCkSoPcG1Iynv/sPP39qnfwB6aA148VPbr3fceKkuzZ5seq51z2eN2NNy7OH+Zk7PYHRoFJ3RDgAorXvh+51mTdx5Mp7nom3dxpYQmYtQe4JrR1Ke/ccXMeDXxkFPfAF48T+UYj3zze6mw6bnWiV4RQq5JisCrV9ex+W3L2P5nuUd1r3o+208oefa1X1te33EayfpkR/a1oXEZmSuIbWYSETXAfgrAO8AMATgfzDz/UmvkWJiM6hJG9/Kcd1LxHZRtch4UwugqgIiURBpdrt+9diw1azJkt2waDHxJwA+wszvBfA+AB8jon9pfHShtjSgjW8p5E3RmPaktp3Pzrs/ozscVXQZirQuF+04v6vF1m1sCSmeVKHmgEtbPw5vPRys32OPqv7uTcP3FKMvuE7R2C6qFtlf6sUl69W9aueFjaJmGVPemTn1AaAN4HkAlwD8vmabOQArAFbGx8e5KpaXmcfGmIO/evAYGwueF4L3odtlJgr+TXpf5L30g+UXl3lscYzxAK49xhbHePnFfH8I2/vro9vt/8CEj243+/ZZPqxVY2GsAFZYp8G6Xyg3Bm4E8AyAdydtd9ttt+U+36Jk/ZwMEnmEt07flTSWX1zm7tEu0wPE3aNdI2HK8xoX5B2H7nXOzivrh4xI/YUNXzdAUUKSUGeemUhE9wP4J2b+A902VRYTpY2AnkEuDuaZCTgo/T7Cba31VMky20/3oWy31UsfNfjDWqiYSET7iejGrf+PAvglAH9nd4j2GNS8qkleXpcmXFtrfi4/j9fZ9exBl/TO9TD7+KzR+E3sf5l83Fnyvrr8rnLxUAxsJdvE9XETgGeI6EUA3wLwNWb+c7fDys8gtrI1rcckXazKrOFUUezN43So0xT2KKHwbrBa7OLjT7sgOW2OpXNedDUL8jY94tJg4vp4kZnfz8zvYeZ3M/PnyhhYXspqZeuTs8TUb69bgSbpNbapqsivczS0qKWNEusyhT2OSnijxMefdkFyfmehisDzRFw+fSkt08iZia7bCFTtKIpj6oiKXsSy7ssWJUziUqLrabHBG9oosS5T2OPo1kUE1ONPuyA5u7NIEtasEZdvX0rLNFKoXVOV2OjIkpcPL2JV3VlWNYkm7nVuU3vHNvEosS5T2OOozi1ENf60C5KTOwsTYc0Scfn2pbSMCHUOfJuxl+cusapcfpXF3uhkjU1WW4DiUaLp7EGf0OWmASjHn3ZBcnJnUVRY49G4yjkCNKb4KEKdA9+cJSZ3ifHPNVBNS2Bfir11zT+b0N2jvl3SPQ9sX5BO3XMKADBzeuZa3t7JnUWRaEcVjcebP4U0pfioM1gXeVQ54aUM6jZjz7fx+jCJxunsvIrJcm7RiS+d3+/w8OeGy3lPisxM0702PnnG5y+lAtiamWj6aLpQM/shNklEx9duy2xNFb7MOnSBybmpBF316B7tOhhggeghaTajz1/KFJKEWtZMbCCq7o0qZLbmYKNrdxonvs6iNfKuV9jQKbayZuKAoarTqGhK+k7YJssMQlN73fiecTcrpuf10fpS6CgREeoGYlKPafjneiDJOoPQpHA6NjyGqQNT7mYm5qGsWW0eIULdQHSRcrs9MJ/rgSTrDEKV7W6kPYLOaKfP3XHme2f863niw+K4JTJU9QAE+ywu2llhSKgXWWcQhva6tK55M6dnMu1XsI8IdQMJxThPnUaoL+N7xpXFwaQUx/St06l+6Dz7FewiqY+GMmB3hgLc9SaxsV8nxcgBQoRaEBqCq94kRffrtE3qgCA+akEQnKLza3f3dLF672r5A/IU8VE3nAa34RUsU0UKoq4LMPiEFBNrTnwWYtgtEpC8tNBPfA3FMAUBqLvq2UKKkcWRiLrmNLwNby3xoXCmGkNVa0DWdQEGnxChrjm+9cb2kTJTQz4UznRj0PX1cJ2CqOsCDD4hxcSa09D+NNZQNahyOfnHh8KZbgxtaisXFZCinh9IMbHBDGB/mkyUnRryoXCmO9YGb0gKoqaIUNccl/1pmuAmKTs15MPKMbpjhSkHSUHUD0l9CErKThm4ouzUUNxZAQRRa5mC6MMYhOxI6kPITFPcJGWnhnwonPkwBsEuElELSlqtYG2jOHVcFSbvQiJ1J7TkJXXGE/xBImohM76ttF6EQWxQVaVN0AcfuTMqKtyIUA8wSZ85cZPUm6omt/jgI3dGWLhZWwtuN8NpwCWIdapQE9EtRPQMEb1ERN8logXnoxKck/aZG8DVjhpFVTbBqi4QpVBh4SY1R01ENwG4iZm/TUS7AJwF8Alm/lvdayRH7T8yUabZVDXxpvVgC4ydmuJsJfMycVy4KZSjZuYfM/O3t/7/JoCXALyz8KiESmny1PMm+L+LUlV/DR985M6osHCTKUdNRBMA3g/gOcXv5ohohYhWLly4YGd0gjOyfubqIn4VphG9oiqLXqMbMFVZuGFmoweAGxCkPe5J2/a2225jwQ3Ly8zdLjNR8O/ycv79jI0xB3IWPMbG1PvLsm3VdLv94wwf3W7VIxscll9c5u7RLtMDxN2jXV5+0cMPSl5sfQEVAFhhnf7qftG3ETAM4CkAnzbZXoQ6nTx/b9uCaTqGOokfkXqsRFWPTBCSSRJqk2IiAVgCcJGZ7zWJ0qWYmEze6dlVFQDrNPlFiqRCXSk64eV2ADMAPkJEz289pqyOcMDI6/KpqgBYp8kv4v8WmoiJ6+NZZiZmfg8zv2/rcaaMwTWVvIJblWDWSfzE/y00EZmZWAF5BbcqwaxbK9X4lHGgHo4VQdCiS14XeQxCMbFI8TdrUTB6rE4neDgoOpdOGW6SOjlWhMEGRV0fWR9NF2obX36V0Ouea6rQ6NwkoaPExjnWybEiDDZJQi1tTnPgwlmgc4KMjgLr63aP5Qs6N0mIjYUK6uRYEQYbaXNqGRfuC50TRCXSeY6VlAuuatZhWk7eRr+bOjlWBEGHCLUBcSHbu1e9XZEvf1bhTTpWfLzz8/pp1UlTrvMKuOnrVMXROEWth3VyrAiCFl1OpMijSTlqVY54ZIR5eNhu3liXS+10shce49vrZut1u/aOm3R8k0JpUq66KA5n/QqCNSDFxPwkCZnNL3+SwJkITZrg6aZV60Q8r3DmLd41uWgqCCaIUBegzN4ReSM/lciZim4ecU+iyPtlev4SIQtNRIS6AHWwd5mIbVxAo9G6KpLtdNxE1EVF1nXkLRcBoSpEqAtQh1vytPTF2Bjz4cPbIhoXIJv+7bQUTtH30uWFsw5/a6G5iFAXxPcoKymi3rWL+dCh7W127WL+5Cez5b3zpGJUr0sSWdNjuUxF1eHuSWguItQ1wWaOenSU+aMfDf4/NNT/u1Zrp2uFKIi6XZIU+ZtGsi7FVHpZC1WSJNTio/aELEtIRX3K+/YBCwvB5JB2O/h9twv80R8BX/0qsGsX8Pbb/a/f3ASuXu1/jhl4+OHAc+0Knfe73VZP9llQrHfv0hctk2MEb9EpeJGHRNTZMY0U0xwe8Ug0rcioih5dpXZ0OeCk8dhMyeQdn2+pLqGZQFIf/hEXmyThjG5vIrahuG9uBjnprGLtMierElnXE16Kjk8QykCE2jOyzB4M25pmjYo3N5kXFlibo057fZFzy7MWpIuxCEKdSBJqyVFXgKoBE3PQ0S3KyAjwxhv6xkw6xo8xbHYAAAugSURBVMeDfd14Y5DnfeyxIG8NBDnru+8GDh/Wv77Vyt6YqdcL8uUHD5rl2aNMTwOdjv5cilJV0ylBsIZOwYs8ikTUg3DrmeR+iJ571khalVPd3Ow/dvTnw4f1Y8mSm03Lm5ukL1zlhyXvLNQF1CX1UeaXqsoLgi4n2273jydrH45OJ99Mv3Y7v8AmnU88fZH2nrv4m4g3WqgLtRHqsr5UVUdZJr05kqZxqwS+yNiTLggm+027oISia/M992GCjCDYpDZCXdaXyocoKyo0uohW1WrUxfuTFBEPD6eLadLrQzG2+Z5nEX0f/taCYEJthLqsL5VvUVbSeJLyyLben7Q0S54WpeGFJhRPm+95ls9J1XdPgmBKklB75fpwOessWvlvac66qhloSTPizpwJ5EXH2BgwNVXM1TA9nXyMtFVWpqeDtQ273cBt0u0Cy8vAq68Gv5+Y0O8/z3ueZSk01diKrsMoCKWjU/AiD99cH6Y54aqirKSoLy3SPXzYTsToYtJJ1lmURccq6QyhzqAuqQ9XmLosqiCavw1z1aYd55J+n/XclpeDJcZU+8rjJkkaW/wcsyLpDKGJFBJqAI8CeAXAd9K2DR++CXWW/GiZtj0TwUnbxsTCZypiy8t6p0keIbRdC4j+bcIZm1VfaAXBFkWF+sMAPlBnoS7S8MhlpJZlXLqLR9b+HzbHFSc+zryrxOj2LVG00GQKpz4ATNRZqE2/5GXnPvNGnPHIMt5bWvcwjT7zjEv1HttcrV3y0kLTSRJqr1wfrjCt/GdxE9ggT//jeN/q9fXgnDqd4N+wJ7UKZrP+G3nGpepfcuUKsHu3HcdF2X8bQfAKnYJHHzCIqAHMAVgBsDI+Pl7mhcgaZUdteW7n09IJJg4XINiPzXG59qZLRC00HQx66sMUG3nQrMXILNsntQMFtl8b3WfS9uGCt6pjZ+3LYTMfrTt3yVELTUaEOgNFXB+uxSStcBhd7TttenoY7eYZq+t8dNJxm95ZURhcCgk1gD8B8GMAVwG8DOC30l5TZ6HOi40udGmYFAxN+4PoHiYrgusuGJ2OCKkg5CVJqIcMctifspcRbyZhgW9jQ/17GwWvXi8oyAXXTj1ZFxmIExYbw8Jg+DOwXQTUnc/Fi9vTxgVBsMdAuD5co3I8RMnbQyTan2R2Nl2ksxBfTSZEtyL4kSPbP+/dq36t6XkmrbjiejUWWe1FqCW6ULvIY9BSH0lFuzx52qQZgmk5at3r4mkJXY+QpHx2ODaVb3tkJH9+O5pbd5njl4Kk4DMY9F4frknqt5FHpLPkmMO8ePivagKMToxUuegkoU861yS7n8l71e26t+CJxU/wGRFqx2SN1GxMCQ+PoYqMge2VxrMW9dKEOmk8JiT5rV17sX3rQy4IUZKEWnLUFlDNfJydDfK68VxofGZhfKZgWuGx3e6f5XfmjDo/vrm53cs7y0xAXTEyfF438zFpRmSUpFmPeWZEZsH1/gXBGToFL/IYtIg6TlKEnbdtqS5Kt736i85i2G4Hv0+LqE0mykiOWhB2Akl9mGNjUkWSGKfdfpssa2VyrLy39WlCnJSjVo09XE4sStJ77HpSi0yaEXxFhNoQWxFXkhibFLSyTitPKj5mjajTxpfk+khyqoggCkIyItSG2HIFJO3Hxe23zq2Rp6BpMr481kFTV4ggDCoi1IbYcgWkiZ2r22/T/RYdn8mqMrrUiSAIakSoDTG57c+SkvAhF6oaR9E7hywWQhFqQTAjSagp+L1dJicneWVlxfp+XRNa56J2t7GxwAYH6H+XpxG+K3q9wBZ4/nww1fvNN4MG/iFjY/rp7kSBrc/kGPH3Iq0PSacjfUAEIQkiOsvMk6rfiY86QtJKMKp+HvEeGFUzPw/MzPSv/hIVaSAYs87zbOonVr1PSSI9PAwcO2a2b0EQdiJCHWN6GlhdDSLL1dX0jnFpE1TKagLU6wEnTiQLZsjGRhBZRwknx5gSf5+6XfV27Tbw2GN+3XUIQt0QoTbExvqGJusV5uXIETORBrbvFGysZRiyuKgW/6UlEWlBKIoItSE6IUqKQstMl5j2vI5OK1fdOeTFdAFhQRCyI0JtSB4hKnPl7KTIPlyhPKkHiQ1si78gCAEi1BnIKkRlNgFSRfxEwOHDgdticzPYZmmpnFSMIAj2EKF2QFhAXFvbuZJK1qKdKaqI/9Qp4Pjx7W3q4FwRBGEn4qO2TJLHuNvN3nbUJq2WuuBo6p8WBMEd4qMuEVXUGop0WrrEtZVP+jELQj0RobZMEb+1aytfHueKIAjVI0JtmbxRaxn5Y7HQCUI9EaG2TN6otSwrn1joBKF+iFBbJm/UKvljQRB0iFA7IE/Uajt/XFaPEUEQ3CNC7Qk288e2C5Mi+oJQLUY+aiL6GIBjANoAvsDM/y1p+0H2UftAONkmTmgRzEJSj27JbwuCPQr5qImoDeAPAdwJ4OcBfIqIft7uEAWb2CxMymxGQagek9THBwF8n5n/npmvAPgSgLvdDksogs3CZJmNpQRBUGMi1O8E8MPIzy9vPdcHEc0R0QoRrVy4cMHW+IQc2CxMihtFEKrHRKhJ8dyOxDYzn2TmSWae3L9/f/GRCbmxWZiU2YyCUD1DBtu8DOCWyM83A/iRm+EItpietlPsC/cRLpg7Pl5tYylBGERMIupvAThARO8iohEAvw7gK26HJRTBtp1OZjMKQrWkRtTM/DYR/S6ApxDY8x5l5u86H5mQi7idLvRQAyKwglBXpB91w7DpoRYEoTykH/UAIXY6QWgeItQNQ+x0gtA8RKgbhtjpBKF5iFA3DFkcQBCah4mPWqgZtjzUgiD4gUTUgiAIniNCLQiC4Dki1IIgCJ4jQi0IguA5ItSCIAieI0ItCILgOSLUgiAInuOkKRMRXQCgaA1UG/YBeLXqQThCzq1+NPW8gOaeW57z6jKzctUVJ0Jdd4hoRdfFqu7IudWPpp4X0Nxzs31ekvoQBEHwHBFqQRAEzxGhVnOy6gE4RM6tfjT1vIDmnpvV85IctSAIgudIRC0IguA5ItSCIAieI0Idg4g+RkT/l4i+T0T/uerx2IKIHiWiV4joO1WPxSZEdAsRPUNELxHRd4looeox2YKIriOibxLRC1vn9mDVY7IJEbWJ6P8Q0Z9XPRabENEqEZ0joueJyMoq35KjjkBEbQD/D8C/BfAygG8B+BQz/22lA7MAEX0YwCUAX2Tmd1c9HlsQ0U0AbmLmbxPRLgBnAXyiIX8zAnA9M18iomEAzwJYYOZvVDw0KxDRpwFMAtjNzB+vejy2IKJVAJPMbG0ij0TU/XwQwPeZ+e+Z+QqALwG4u+IxWYGZ/wrAxarHYRtm/jEzf3vr/28CeAnAO6sdlR044NLWj8Nbj0ZEVkR0M4C7AHyh6rHUARHqft4J4IeRn19GQ770gwARTQB4P4Dnqh2JPbbSA88DeAXA15i5Kef2EIDPAtiseiAOYAD/i4jOEtGcjR2KUPdDiucaEcE0HSK6AcCfAriXmd+oejy2YOYNZn4fgJsBfJCIap+2IqKPA3iFmc9WPRZH3M7MHwBwJ4Df2Uo7FkKEup+XAdwS+flmAD+qaCyCIVv52z8F0GPm01WPxwXM/BqAvwTwsYqHYoPbAfzqVi73SwA+QkTL1Q7JHsz8o61/XwHwOIKUaiFEqPv5FoADRPQuIhoB8OsAvlLxmIQEtgpufwzgJWb+71WPxyZEtJ+Ibtz6/yiAXwLwd9WOqjjM/F+Y+WZmnkDwHfs6Mx+seFhWIKLrt4raIKLrAfwygMJOKxHqCMz8NoDfBfAUgqLUl5n5u9WOyg5E9CcA/gbAzxLRy0T0W1WPyRK3A5hBEJU9v/WYqnpQlrgJwDNE9CKCIOJrzNwoK1sD+WkAzxLRCwC+CeBJZv6LojsVe54gCILnSEQtCILgOSLUgiAIniNCLQiC4Dki1IIgCJ4jQi0IguA5ItSCIAieI0ItCILgOf8fRIVrnDLlOs4AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "centroids = np.array([np.mean(group1, axis=0), np.mean(group2, axis=0), np.mean(group3, axis=0)])\n",
    "\n",
    "plt.scatter(group1[:,0], group1[:,1], color='r')\n",
    "plt.scatter(group2[:,0], group2[:,1], color='g')\n",
    "plt.scatter(group3[:,0], group3[:,1], color='b')\n",
    "\n",
    "plt.scatter(centroids[0,0], centroids[0,1], marker='x', color='r')\n",
    "plt.scatter(centroids[1,0], centroids[1,1], marker='x', color='g')\n",
    "plt.scatter(centroids[2,0], centroids[2,1], marker='x', color='b')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Third pass of the algorithm\n",
    "\n",
    "We run a third pass of the algorithm, however at this point, we would likely have converged to a solution. Nevertheless, the run the algorithm again to validate this (essentially to check that the update distance of each k marker is zero - i.e., they do not move again)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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TlnWevPqi/cZz4brd6b596qEA3W7UzyNNUpxjlpa2Lew89PvRa9PHb2hetljUcOujtA0a+UgJmxjdbnDTnehan0O6zemxTx0zvh+mc3QVXOyf7eP0D0+DwTesUdPfhYhw5L4jA88due8IfvzOj5X7T7/PrixZ3fnHa8/6jNVaMu/aH3vpUr7niSJRTvLcc5GvPI81rOojEhNYxoYLhkaoAXc9mW2/8C6/kLFwJoturr5XrsGN6f0wnWNWMDBGl74I7Ox/ssEbIBAO3HlA+3eJLeokj7zwCO7Yc4dy+/T77OrCacogsfmMWWeg+JhxaMq6SB5v377okXXsvMIfW9RJzp/Pn7+scuGk99kihkqoXWH7hXeZEla1X9N0jum7k+5EF6MjowPbjXfGcfT+o8p9AOrzMaXmJd0eSx9bwuafbmLpY0s4+vJR/NL+Xxq40wDU77OrC2fZuzOr1/sqwtD5Y//mb6K+H8nhs/EAWtOx86TbJd0eS0tqMbe1hrOEOKCMDRcMjY/aJXl8z67GOlXt18zrX198fhEnzpzABm+gQx0s3L1gDJLS43p/pO4YRbM+4r+B6nxclO97ocoZh/1+JNJZWqA7drr8+sCBKD1PVY6dzPrQVSrq/OXJ44yM6Js+jY0Be/ZE7peaysGLIDMTHTMMvSrKNnnKej9GvzCaKzUvhplBiaBT+meb80gyghF86cEvVS7UmRfwKmcc2vbssDm2TapbPD4sz8VItV8Vu3ZF082vXdMfP1AkmOgY21tfl0UNVbUCjclze1/ELaMTacDsikiLskmkdWtLsonNyifJWAWjywT98vq2bf25Nse2Sf+L/2Z53CY6n3Sns+3CWVmJ/OpJkVYdv4GIRe0JH1Z3VpvTuqaMF3HL6O4QCIRTD55ytnabVMJK0uISWN0dFS3C0L1ufl7vjrCxqG2t0rx3ArZd62z3W9e0dQeIRV0DZYJ/sSVOjxNGvzAKepww/cQ0ACgzCuruMbF3Ql30oHse0BfhHJw56PQCYxModJluaHMHZRWMLlqEobNojx/XByZ1HfZ27cpfAJL3TiA5Xsw0Hsx2vw0oBy+CCLUniqaCqdLWABjFN6ThsLaoXCt5qjRtyUolHBsZc+I+ynOxtM4+sRGxtJtDZxmnrcykO0B1UVhZAS5fzhbQNL6aLtnuV7fdgQONniojrg9PFA3+ZfXlUL2+1kq3AI6fRTLrY4RGbnQx7E50cfT+o04s+LyZQE7cYio3h64xvw4P339vTfht96vKQjl5svZeHllI1kcN5CmNTpLlU1WJX93TS+o+fgiY/m4rD64oA82lYwo6C9pWrJNjtXwRwOSUSlMdSyA+6grpn+1j33/YhydXnxz44hII8x+cN3aTm35iOjPwpbptrjojJLTjh4DJz61ygTipktVlazAPujF0bGz4dQGEMjmlAf2msxChLoAuaKQq845hsHakVdovrcM0lKBopZyLFEKfk7td4bv/s8kX7i1eoAuQxZZi7F82ibVuCrkLynTqc1k+34IAo7g+cmLyL+qq32J0va9NfZk71MEGb6B3S08mcxekqvNcfH4RT64qBsLCk7/eNoUvq1hENYXcBUVT5Vz3hw6k33QW4vpwiCnDIiujI317HAuIqULvvT99D/wol2oipaOqbJG65wgWPc+86zYNAfbSGc82hS/eTgezn4KQopas657ZDeg3nYVY1DkxZThM3TKltahVFlyRDA+XVJGtobNm5z84j9M/PF1JgU6R8yxihecNKFaOKX3PR0FIUUu2wUUrZRCL2iGmHFidn1LXN9pkgVcRjKuiL7LOmj2+eryyAp0i51nECtftrzvRrV+kgSjjQldy78Nfa7JkTT7oFviUXSNCnZOsXsTpoNrKgyu4+PmLyi+q7ovdoU4lfuIqsjV0F6O05emzQKfIeRYpWNIdx9TutVJmZ6PBtqop5L4KQlRFO1nZICFOKq8ZEeqcZGU45Em70n2xT372ZCUWWBXZGnms8zKTb0wUOc8iVnhw2S8qq/XYsShwmLRyf/VXzSXmrsnyQbfAp+wcZnb+uPvuu1mwY+W1Fe4d6TE9Rtw70uNDXzs08PPKayvejpV330Vev/LaCk8uTzIew40HPUYDP8eP3pGe8zUXRbXuyeXJyo5fmpUV5slJ5kh6o8fkZPR8ejuiwe3iR6ezc/v4Nb1e9LpeT72NCd3xiIqebSsAsMoaTRWhDgif4lB232Ver7oY2eyrbrH0fZHwuv9eTy2GvZ7ddjpxt70AJLdPi7rt2oYMk1BL1kdA+CzFLrtvHxPVq57iHhLec7vLtgVNkiy11k0dt232H7dcDan3Rghl7pCsj8bgY2q5q327XpuNL9/n++GavDnX3nPYy7YFTRKXWvf7apFObpNE54s+fTocH3QoZe4ZiFAHhM90ubL7riKVL4RjFqFIP3DvF6EybUHTxGJuKjhRCb6px4ZtH2rfuCqu8TExPoEIdUD4TJcruu/YUlx7ew2EwbQu37neTWn25DLnWnsRyisEWZkT8f7m5oCJCaDbjZ5Xpe7F4m5qYqRKnWtCPrSLhk1VWOU653WZhwQTi+MzwJR336aMjaoyMOrK+siDLouFHtNnMeQKlOYN4GVh2p8po0MXBOx2d+4/3jad4VFm3T5wEdh0FBxFmWAiEd0E4K8BvA/AKID/xsyPml4jwcR20OZgnkuKvk/WPald91Muuj+bknDTMINer7ZAnRYXDZsclbyXDSb+DMAnmPmDAD4E4JNE9C+tjy40liYF8+qkqIvGujjKdT/lovuzKURR+XxjkbYdJ1ZlIM9FcU0FLp5Mod6yyi9v/Ti29fAwv8ctdf7t20JTgnl1470i0bUQlNlfVhAw70UghKyLsoHNKkredT6R5ANAB8ArAC4D+PeabRYArAJYnZqayuWbcY1rl16byOPzrbvgRNiiSh91WfL6a03bl62ArBIHa4WrykQAtwJ4CcAHTNvVHUyUwic1RYS3CcE8W4qWwAdx/kWFQPc6XyKY9yKgKyePXzdE1pZJqHNXJhLRowD+HzP/R902dQcTh7SdbSbDHBwsUgnY+Ak4eQJlLqvz8uxLF9jsdKKZjmkCG0jrklLBRCLaT0S3bv1/AsCvAfg7t0t0SxPSN11j45PXBQHX3l6rZfJKlRTJda5qAo4X+v2oVNummMPGT5wn6JPH56vz76pEGmjUQFqX2GR93AbgJSJ6DcB3AXyDmb/md1nlGLZ2trbxGFMQ0Hfz/iR1jOYqksHS2KyX+ANhK3ZZ1Xk+A366rAvdQN42W1sGbLI+XmPmDzPzrzDzB5j5C1UsrAxVtbMNJbPEtgrWNCkbqMZaLFJu7QLdRWqERrQXjMZmvag+EEnSYpeVqeF6hmEalQVexNoK5QvpgdaWkPtuJRBCVlGMbUZUMo1Muy/P1mJd7gTdRWqDN7QXjKaUsO9ANxcRUItdlq/QdR53jElY81pbIX0hPSBtTgviulis6rXUFVisYqCujmQl4AiNKKe/p8/funowJEZH9W6PlRV1INEUdPTxYXdREZgkpC9kQaTNqQd8GRlFKHKXWJe1WKc7IVkJuMnqi0L6jiLPaLVg0Ik0oBbBLOvVR9CnrDslbY3r7iJaEnwUoS5ISJklNneJ6c81Xqtnvl8o7oTG+p9t0AXidM8D277CU6ein+fmtt0RPoI+ZSwdlZujyunqdaBLsC7zqLvgpQqaVP0Y2lpDKCJpddVlnj94svCl22UeG6vmg1KmKk332tA79WUAmZnoh5ArXJNr63SkUlNFCBcMb9h8OFWCXtUHpYz1YKpmDPULaYFJqCWY2EJUcRoVw16pOfSYfLtJfH1QilZDtiBwqEKCiUNGVhptTFvcd0KCPLnEtoG2qSk/OcpFc2iHraINItStxOb71/LP9XCSN5fY5ko9OQkcOBBWjnJVFW0BIa6PFmLqc7O5Wb7njhAoeV0CKh/Z+Diwezdw6dL2B+Xw4Va6GkJDXB9Dhu7O8OTJ+oc+Cx7Jm/Kmskyffhq4eHHwgxJS0cCQIkLdQobwzlAAiiX32/iJQyoaGFJEqFuK714nQoD4CrK52G+LGyZVgQi1ILQFX7dSZffb8oZJVSDBREEQ/NLSvGfXSDCx5chdpWBNHR8WCUaWZrTuBQjlSGdYxXeVgPilhRR1fVimptQWtQQjrRGLuuH4Hr4hFKOOcWODC1BYznV9WIawktA1ItQNR+4qs6n6br+ucWPbC9AE7+rq2Sz5oqWRYGLDkTiNGdeDRGyoa3rO9gKm9aWpqqEC8mEJAgkmthi5qzRTx91+7dPLdRbyxoZ8WBqKCHXD8X1X2fSMkjpcQ7VPj9EF6eIPh7ggGocIdQvwVYXYhjqFOqqfax83ZrrNkpLVRiJCLWhpQ0ZJHa6h2bvqmUe5vQAJ3rUNCSYKWkZGIks6TdMmwxQdJNJ4hvbEm4kEE4VCtKVp2lDe7dfpt2p6YMNETecmQj3EZH3mJKOkwdTlt2pDYENHneemm3obPwDcAeAlAK8D+AGApazXDMsU8iZjOwQ65EnrggHdpG4iv8ft9do78t7zuaHMFHIiug3Abcz8PSLaDeAMgM8w89/qXiM+6vCRQpmWU9cfuC2BDRWez62Uj5qZf8rM39v6/7uILOv3l16VUCttLj1vs4vUmrr8Vm0JbKio8dxy+aiJaBrAhwG8rPjdAhGtEtHqhQsX3KxO8Ebez1xTxK/NLtJc1JWi1+bARp3npvOJpB8Abkbk9ngwa1vxUfvDlc/Y1kedd9u6abOLtDG0ObDh8dxg8FHbivQYgBcAfM5mexFqO/L+zV0Lpu3xmyR+dcXQBKEsJqG2CSYSgJMALjHzwzZWugQTsynS1U3iQ9lIkFRoKmULXu4BMAfgE0T0ytbjgNMVDiFF0lzrCgA2KT7UZhepMLzYZH18i5mJmX+FmT+09ThdxeLaTBHRrUswmyR+0uZCaCNSmVgTRUS3LsH0KX4+sknSJeNAMzJWBEGLznld5jEMwcSywd+8WRfxsbrd6NGGgHoV2SRNylgRhhuUzfrI+2i7ULv68qvEPv3coUPtFRpdNkmcUeLiHJuUsSIMNyahljanBfCVWaDKBCFSZ1y0IYtBl00S42K2YZMyVoThRtqcOsZX9oUqE0QnZHmPZfIF11V1mBUEddHsrUkZK4KgQ4TagrSQ7d2r3q7slz+P+JqOlV7v4qK+rNpUcl1UwG1fpwqOpil78WtSxoogaNH5RMo82uSjVvmjx8eZx8bc+411/tR0tZ3pWKr16qr1ej39MbvdYr7xvP772Cdv8lWXpc0VzUJ7gAQTi2MSMtdffp3IHTqUfawswdNdAHQiXlQ4iwbvJDtDGHZEqEtQde+IItafSuRsRbeIuJso837ZnrtYyEIbEaEuQRPSu2zEVuc+0Vmy3a4fi7rK/POiyIVAqAMR6hI04ZY8y32RdJ/Eoplcvy6f27WP2sV76fvC2YS/t9BORKhLErqFZbKod+9mPnhwe5vdu5k/+1m7cyp63rrXmUTW9li+XVFNuIMS2okIdUMoI4xpK3Bigvm++6L/j44O/m5kxE/WShYmy9/WivUtpNLPWqgLk1BLHnUg5BkhlcxT3rcPWFqKikM6nej3vR7wZ38GfP3rwO7dwHvvDb5+cxO4fn3wuStXgIce8lvwosv97nTULV+XlnZu6zsvWgpkhCDRKXiZh1jU+bG1FLMyPNKWaFaQ0WYfrtD5f01rcemSKbPG0NxdQvuAuD7CIy02OqGKb7nz5EnH4r65Gfmki4i1L5+sSmR9F7y4WKMg+EaEOjDyVA/GbU3ziCxRJNJLS6z1Udvso+i5FckDd70OQWgaJqEWH3UN6JovEQ0+Nz4OvPMOsL6eb/9TU9G+br018vM+80zktwYin/UDDwDdrnkfun4mJhYXgbk5Oz97ktlZ/Xpc+IbrajolCM7QKXiZR1mLuu23nqbsh+R557WkVf7Uzc3BY8c/Z/m6x8byve8rK+aeIjav9+EbFp+z0BTQJNdHlV+sui4IOp9spzO4lrx9OLrd/OLqyj+cx8+ue799/D0kL1poCo0S6qq+WHVaWja9OUxl3CqBL7PuLAvfZt82+3D5fodSICMIrmiUUFf1xarb0koKTaejXouq1XTLWnsAAAqnSURBVKiP9yYrm8RGUE0tWk2We5H3O4/o1/13FgRbGiXUVX2xQrK0TGs5dCjbBVL2vbFxsxRpUxqvP+sc85LnMyI+aqEpmIQ6uKwPX5VnVU1pKYKpGu706UhedExOAgcOlMtqmJ01HwPInrQyOxvNN+z1ooyTXg84dQq4555oTbr9F3m/84xCU62r7BxGQagcnYKXeYSW9aGyqsbGokktIVhaJqsvy/frakp5lvvDlYvCxfst7gyhjaBJrg8fVDmlJS9J/23sq7btOGf6fTqDxGYdOlFNujDykJVRUiaQKO4MoW2UEmoATwN4E8D3s7aNH6EJdR7/aJUpezaCk7WNTQqfrYiZgn5FhNB1HCD5t4krNtuaay8MH2WF+uMAPtJkoS7T8MinpZZnXbqLR97+Hy7XlSa9zqJTYnT7FitaaDOlXR8Appss1LZf8qp9n0UtzrRlme4trXvYWp9F1qV6j11Oaxe/tNB2TEIdXNaHD2wj/3myCVxQpPdxum/1+np0Tt1u9G/ck1oFs13/jSLrUvUvuXYN2LPHTcZF1X8bQQgKnYInH7CwqAEsAFgFsDo1NVXlhcgZVVttRW7ns9ZoU/UIRJa4y3XJiCxBKAeG3fVhiws/aN5gZN7tTeIbvza5T9P28cBb1bHz9uVw6Y9WIT5qoe2IUOegTNZHFWKiKzdPHsumPD22dous1bc/2nTcutMpBcEXpYQawJ8D+CmA6wDeAPD7Wa9pslAXZWVFL4ourUobl4aN60P3SE5d0QliyHnpgtBUTEJN0e/dMjMzw6urq873GypxgC8dTIshigbK+jyGSyYnB48zOTkYBBwZiaQ5jYvzFIRhhYjOMPOM6ndDkfXhG1XGQ5Ki/UOS/Unm592KdHqaTIxuIvjhw9s/l+2TkjVxxedEFpn2IjQSnald5jFsrg9T0K6In3Zlpfh0F93r0m4JXY8Qkz87Xpsqb3t8vLh/O/ke+fTzS0BSCBkMe68P35j6bRQR6Tw+5tgvHv+rKoDRiZHKF20SetO5mtL9bN6rrN4lLvz8kuInhIwItWfyWmouSsLjY6gsY2B70njeoF6WUJvWY0NWvrXPfOyQepALQhqTUIuP2gGqysf5+civm/aFpisL05WCWZV2nc5gld/p02rf9ebmdh/vPJWAuonn8fO6ykdTRWSSrKrHIlWRtvjctyB4RafgZR7DZlGnMVnYRW/9dVa66+kvuhTDTif6fZZFbVMoIz5qQdgJxPVhj4uiCpMYZ91+63zUugnjWa6SvLf1WUJs8lFnjeOKyVv1KEUzwjAgQm2JK4vLJMY2Aa08YpIVfMxrUdv0EtFlfZgyVYoMHhCEYUKE2hJXWQGm/fi4/dZlaxQJaNqsr0jqYDyNXBAENSLUlrjKCrDxw/q4/bbdb9n12UyVcXHBE4RhQoTaEpvb/jwuiRB8oap1lL1zyJNCWOaCJwjDhEmopddHAlU/jbjPBaD/XZFG+L7o96O0wPPno1Lvd9+NGvjHpPt4JLHt1aF6n4giOTbR6wHnzmXvXxCGEen1YYlpEoyqn0e6B0bdLC4Cc3OD01+SIg1Ea9blPNvmE6vepyyRjnO6BUHIjwh1itnZyOrb3Iz+ja3loqOgqmoC1O8Dx49nCyYAbGxEwpkkr5Cm36deT79tmRFcgiCIUFvjYr6hzbzCohw+bCfSwLZwuphlGLO8rBb/lZXBC54gCPkRobZEJ0QmK7RKd4ntkNdkWbnqzqEotgOEBUHIjwi1JUWEqMrJ2SbLPp5QbupB4gLX4i8IQoQIdQ7yClGVTYBUFj8RcOgQcPFitOblZeDkyWpcMYIguEOE2gNxAHFtbeckFV/ZDyqL/9Qp4Nix7W2akLkiCMJOJI/aMaYc414vf9tRl8isQ0EIF8mjrhCV1RqLtI27xGc6n/RjFoRmIkLtmDIBRN/pfEUyVwRBqB8RaseUsVp9+5AlhU4QmokItWPKWK1VpPNJCp0gNA8RaseUsVrFhywIggoRag8UtVpd+pCr6jEiCIJ/RKgDwpUP2XVQUkRfEOrFKo+aiD4J4CiADoAvMvO/M20/zHnUIRAX26Qp0g/a1KNb/NuC4I5SedRE1AHwnwHcD+CXAfwOEf2y2yUKLnEZlJRqRkGoHxvXx0cB/IiZ/56ZrwH4MoAH/C5LKIPLoGSVjaUEQVBjI9TvB/DjxM9vbD03ABEtENEqEa1euHDB1fqEArgMSkomiiDUj41Qk+K5HY5tZj7BzDPMPLN///7yKxMK47KwRaoZBaF+Ri22eQPAHYmfbwfwEz/LEVwxO+sm2BfvIx6YOzVVb2MpQRhGbCzq7wK4k4h+gYjGAfw2gK/4XZZQBtfpdFLNKAj1kmlRM/N7RPRHAF5AlJ73NDP/wPvKhEKk0+niHGpABFYQmor0o24ZLnOoBUGoDulHPURIOp0gtA8R6pYh6XSC0D5EqFuGpNMJQvsQoW4ZMhxAENqHTR610DBc5VALghAGYlELgiAEjgi1IAhC4IhQC4IgBI4ItSAIQuCIUAuCIASOCLUgCELgiFALgiAEjpemTER0AYCiNVCj2AfgYt2L8EBbzwto77m19byA9p5bkfPqMbNy6ooXoW4DRLSq62TVZNp6XkB7z62t5wW099xcn5e4PgRBEAJHhFoQBCFwRKj1nKh7AZ5o63kB7T23tp4X0N5zc3pe4qMWBEEIHLGoBUEQAkeEWhAEIXBEqFMQ0SeJ6P8Q0Y+I6E/qXo8riOhpInqTiL5f91pcQkR3ENFLRPQ6Ef2AiJbqXpMriOgmIvoOEb26dW6P170mlxBRh4j+NxF9re61uISIzhHRWSJ6hYicTPkWH3UCIuoA+L8A/g2ANwB8F8DvMPPf1rowBxDRxwFcBvAlZv5A3etxBRHdBuA2Zv4eEe0GcAbAZ1ryNyMAu5j5MhGNAfgWgCVm/nbNS3MCEX0OwAyAPcz86brX4woiOgdghpmdFfKIRT3IRwH8iJn/npmvAfgygAdqXpMTmPmvAVyqex2uYeafMvP3tv7/LoDXAby/3lW5gSMub/04tvVohWVFRLcD+BSAL9a9liYgQj3I+wH8OPHzG2jJl34YIKJpAB8G8HK9K3HHlnvgFQBvAvgGM7fl3J4A8HkAm3UvxAMM4H8S0RkiWnCxQxHqQUjxXCssmLZDRDcD+AsADzPzO3WvxxXMvMHMHwJwO4CPElHj3VZE9GkAbzLzmbrX4ol7mPkjAO4H8IdbbsdSiFAP8gaAOxI/3w7gJzWtRbBky3/7FwD6zPxs3evxATO/BeCvAHyy5qW44B4Av7nly/0ygE8Q0Uq9S3IHM/9k6983ATyHyKVaChHqQb4L4E4i+gUiGgfw2wC+UvOaBANbAbf/AuB1Zv5Pda/HJUS0n4hu3fr/BIBfA/B39a6qPMz8b5n5dmaeRvQd+yYzP1TzspxARLu2gtogol0Afh1A6UwrEeoEzPwegD8C8AKioNR/ZeYf1LsqNxDRnwP4XwD+BRG9QUS/X/eaHHEPgDlEVtkrW48DdS/KEbcBeImIXkNkRHyDmVuVytZCfh7At4joVQDfAfA8M/9l2Z1Kep4gCELgiEUtCIIQOCLUgiAIgSNCLQiCEDgi1IIgCIEjQi0IghA4ItSCIAiBI0ItCIIQOP8fMQBDED+5QkAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "all_data = np.vstack([group1, group2, group3])\n",
    "group1, group2, group3 = find_groups(centroids, all_data)\n",
    "\n",
    "plt.scatter(group1[:,0], group1[:,1], color='r')\n",
    "plt.scatter(group2[:,0], group2[:,1], color='g')\n",
    "plt.scatter(group3[:,0], group3[:,1], color='b')\n",
    "\n",
    "plt.scatter(centroids[0,0], centroids[0,1], marker='x', color='r')\n",
    "plt.scatter(centroids[1,0], centroids[1,1], marker='x', color='g')\n",
    "plt.scatter(centroids[2,0], centroids[2,1], marker='x', color='b')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "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": [
    "centroids = np.array([np.mean(group1, axis=0), np.mean(group2, axis=0), np.mean(group3, axis=0)])\n",
    "\n",
    "plt.scatter(group1[:,0], group1[:,1], color='r')\n",
    "plt.scatter(group2[:,0], group2[:,1], color='g')\n",
    "plt.scatter(group3[:,0], group3[:,1], color='b')\n",
    "\n",
    "plt.scatter(centroids[0,0], centroids[0,1], marker='x', color='r')\n",
    "plt.scatter(centroids[1,0], centroids[1,1], marker='x', color='g')\n",
    "plt.scatter(centroids[2,0], centroids[2,1], marker='x', color='b')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Result\n",
    "\n",
    "Above we have found our solution, and have identified the three original clusters of the data. Try editing this notebook to see how the algorithm performs when different data distributions are provided, or when different values of k are used."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "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": [
    "all_data = np.vstack([group1, group2, group3])\n",
    "group1, group2, group3 = find_groups(centroids, all_data)\n",
    "\n",
    "plt.scatter(group1[:,0], group1[:,1], color='r')\n",
    "plt.scatter(group2[:,0], group2[:,1], color='g')\n",
    "plt.scatter(group3[:,0], group3[:,1], color='b')\n",
    "\n",
    "plt.scatter(centroids[0,0], centroids[0,1], marker='x', color='r')\n",
    "plt.scatter(centroids[1,0], centroids[1,1], marker='x', color='g')\n",
    "plt.scatter(centroids[2,0], centroids[2,1], marker='x', color='b')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "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": [
    "centroids = np.array([np.mean(group1, axis=0), np.mean(group2, axis=0), np.mean(group3, axis=0)])\n",
    "\n",
    "plt.scatter(group1[:,0], group1[:,1], color='r')\n",
    "plt.scatter(group2[:,0], group2[:,1], color='g')\n",
    "plt.scatter(group3[:,0], group3[:,1], color='b')\n",
    "\n",
    "plt.scatter(centroids[0,0], centroids[0,1], marker='x', color='r')\n",
    "plt.scatter(centroids[1,0], centroids[1,1], marker='x', color='g')\n",
    "plt.scatter(centroids[2,0], centroids[2,1], marker='x', color='b')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "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": [
    "all_data = np.vstack([group1, group2, group3])\n",
    "group1, group2, group3 = find_groups(centroids, all_data)\n",
    "\n",
    "plt.scatter(group1[:,0], group1[:,1], color='r')\n",
    "plt.scatter(group2[:,0], group2[:,1], color='g')\n",
    "plt.scatter(group3[:,0], group3[:,1], color='b')\n",
    "\n",
    "plt.scatter(centroids[0,0], centroids[0,1], marker='x', color='r')\n",
    "plt.scatter(centroids[1,0], centroids[1,1], marker='x', color='g')\n",
    "plt.scatter(centroids[2,0], centroids[2,1], marker='x', color='b')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "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": [
    "centroids = np.array([np.mean(group1, axis=0), np.mean(group2, axis=0), np.mean(group3, axis=0)])\n",
    "\n",
    "plt.scatter(group1[:,0], group1[:,1], color='r')\n",
    "plt.scatter(group2[:,0], group2[:,1], color='g')\n",
    "plt.scatter(group3[:,0], group3[:,1], color='b')\n",
    "\n",
    "plt.scatter(centroids[0,0], centroids[0,1], marker='x', color='r')\n",
    "plt.scatter(centroids[1,0], centroids[1,1], marker='x', color='g')\n",
    "plt.scatter(centroids[2,0], centroids[2,1], marker='x', color='b')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "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": [
    "all_data = np.vstack([group1, group2, group3])\n",
    "group1, group2, group3 = find_groups(centroids, all_data)\n",
    "\n",
    "plt.scatter(group1[:,0], group1[:,1], color='r')\n",
    "plt.scatter(group2[:,0], group2[:,1], color='g')\n",
    "plt.scatter(group3[:,0], group3[:,1], color='b')\n",
    "\n",
    "plt.scatter(centroids[0,0], centroids[0,1], marker='x', color='r')\n",
    "plt.scatter(centroids[1,0], centroids[1,1], marker='x', color='g')\n",
    "plt.scatter(centroids[2,0], centroids[2,1], marker='x', color='b')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "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": [
    "centroids = np.array([np.mean(group1, axis=0), np.mean(group2, axis=0), np.mean(group3, axis=0)])\n",
    "\n",
    "plt.scatter(group1[:,0], group1[:,1], color='r')\n",
    "plt.scatter(group2[:,0], group2[:,1], color='g')\n",
    "plt.scatter(group3[:,0], group3[:,1], color='b')\n",
    "\n",
    "plt.scatter(centroids[0,0], centroids[0,1], marker='x', color='r')\n",
    "plt.scatter(centroids[1,0], centroids[1,1], marker='x', color='g')\n",
    "plt.scatter(centroids[2,0], centroids[2,1], marker='x', color='b')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "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": "3.9.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}