K-Mean Clustering/K-Mean simple explanation (from scratch).ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### First we create some random data for 2D space"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.DataFrame({\n",
    "    'x':[12,55,58,60,72,25,28,29,20,28,18,29,33,24,45,45,52,51,52,55,53,55,61,64,69,72],\n",
    "    'y':[39,15,25,24,28,42,40,38,36,30,52,54,46,55,59,63,70,66,63,58,23,14,8,19,7,24]\n",
    "})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# make a copy to check with library implementation\n",
    "df1 = df.copy(deep=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "k = 3  # we create 3 clusters ?? How we know about that!! hmmm..... plot and check $$\n",
    "# but there is no algorithm which find the exact value for 'K' you have to check on different value and calculate their\n",
    "# variences and take with lowest variences 'k' value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(5,5))\n",
    "plt.scatter(df.x,df.y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{0: [21, 68], 1: [48, 22], 2: [12, 56]}\n"
     ]
    }
   ],
   "source": [
    "np.random.seed(10) # make this 10 to clear explanation because I explain according to this random data\n",
    "centroids = {}\n",
    "for i in range(k):\n",
    "    x = np.random.randint(df.x.min(),df.x.max())\n",
    "    y = np.random.randint(df.y.min(), df.y.max())\n",
    "    centroids[i] = [x,y]\n",
    "print(centroids) \n",
    "# these are the 3 random center points of those clusters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(5,5))\n",
    "plt.scatter(df.x,df.y,c='k')\n",
    "colmap = {0:'r',1:'g',2:'b'} # try to make color them! yehh..\n",
    "for i in centroids.keys():\n",
    "    plt.scatter(*centroids[i],color=colmap[i])\n",
    "plt.show() \n",
    "# colored points are random new data points while black points are original data points"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Assignment() : \n",
    "#### This function calculate euclidian distance between cluster_centroid _points with  all data_points and assign new label to the nearest point respective to cluster_centroid_point "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Assignment stage\n",
    "def assignment(df,centroids):\n",
    "    \n",
    "    for i in centroids.keys(): # calculating euclidian distance\n",
    "        df[f'distance_from_{i}'] = np.sqrt(np.square(df.x - centroids[i][0]) + np.square(df.y - centroids[i][1]))\n",
    "\n",
    "    centroids_distance_cols = [f'distance_from_{i}' for i in centroids.keys()]\n",
    "    \n",
    "    df['closest'] = df[centroids_distance_cols].idxmin(axis=1)\n",
    "    df['closest'] = df['closest'].map(lambda x: int(x[-1]))\n",
    "    df['color']   = df['closest'].map(lambda x: colmap[x])\n",
    "    \n",
    "    return df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "      <th>distance_from_0</th>\n",
       "      <th>distance_from_1</th>\n",
       "      <th>distance_from_2</th>\n",
       "      <th>closest</th>\n",
       "      <th>color</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>12</td>\n",
       "      <td>39</td>\n",
       "      <td>30.364453</td>\n",
       "      <td>39.812058</td>\n",
       "      <td>17.000000</td>\n",
       "      <td>2</td>\n",
       "      <td>b</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>55</td>\n",
       "      <td>15</td>\n",
       "      <td>62.968246</td>\n",
       "      <td>9.899495</td>\n",
       "      <td>59.413803</td>\n",
       "      <td>1</td>\n",
       "      <td>g</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>58</td>\n",
       "      <td>25</td>\n",
       "      <td>56.727418</td>\n",
       "      <td>10.440307</td>\n",
       "      <td>55.470713</td>\n",
       "      <td>1</td>\n",
       "      <td>g</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>60</td>\n",
       "      <td>24</td>\n",
       "      <td>58.796258</td>\n",
       "      <td>12.165525</td>\n",
       "      <td>57.688820</td>\n",
       "      <td>1</td>\n",
       "      <td>g</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>72</td>\n",
       "      <td>28</td>\n",
       "      <td>64.815122</td>\n",
       "      <td>24.738634</td>\n",
       "      <td>66.211781</td>\n",
       "      <td>1</td>\n",
       "      <td>g</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    x   y  distance_from_0  distance_from_1  distance_from_2  closest color\n",
       "0  12  39        30.364453        39.812058        17.000000        2     b\n",
       "1  55  15        62.968246         9.899495        59.413803        1     g\n",
       "2  58  25        56.727418        10.440307        55.470713        1     g\n",
       "3  60  24        58.796258        12.165525        57.688820        1     g\n",
       "4  72  28        64.815122        24.738634        66.211781        1     g"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = assignment(df,centroids)\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, \n",
    "1. x,y are data points\n",
    "2. distance_from_0 , distance_from_1 and distance_from_2 is a distance from 3 clusters to the x,y data point\n",
    "3. Now, we find among three distances which cluster is close to the data point for instance 3rd cluster is closest to the first data point and we label first point as color 'b'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize = (5,5))\n",
    "plt.scatter(df.x,df.y,c=df.color,edgecolors='k',s=80,alpha=.7)\n",
    "for i in centroids.keys():\n",
    "    plt.scatter(*centroids[i],c=colmap[i])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we calculate mean of each cluster and set the new centroid points to the mean values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# update stage\n",
    "import copy\n",
    "old_centroids = copy.deepcopy(centroids) # make a copy of old centeroid to campare with updated centeroid points\n",
    "\n",
    "def update(centroids):\n",
    "    \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",
    "        \n",
    "    return centroids"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Old_centroids:  {0: [21, 68], 1: [48, 22], 2: [12, 56]}\n",
      "New_centroids:  {0: [47.0, 61.857142857142854], 1: [58.81818181818182, 19.727272727272727], 2: [23.625, 43.5]}\n"
     ]
    }
   ],
   "source": [
    "centroids = update(centroids)\n",
    "print('Old_centroids: ',old_centroids)\n",
    "print('New_centroids: ',centroids)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now, we plot both old and new center points to check is it working"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(5,5))\n",
    "ax = plt.axes()\n",
    "plt.scatter(df.x,df.y,c=df.color,edgecolors='k',s=80,alpha=.7)\n",
    "for i in centroids.keys():\n",
    "    plt.scatter(*centroids[i],c=colmap[i])\n",
    "    \n",
    "for i in old_centroids.keys():\n",
    "    oldx = old_centroids[i][0]\n",
    "    oldy = old_centroids[i][1]\n",
    "    dx = (centroids[i][0] - old_centroids[i][0]) * .75\n",
    "    dy = (centroids[i][1] - old_centroids[i][1]) * .75\n",
    "    ax.arrow(oldx,oldy,dx,dy,head_width=2,head_length=3\n",
    "            ,fc=colmap[i],ec=colmap[i])\n",
    "    \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The tail part of arrow is old location of center point and the head part of arrow is new location of center points\n",
    "\n",
    "and we done!!!!\n",
    "\n",
    "now, we repeat assignment and update again and again until our center point doesn't stop changing. How we know if we get correct center point?? we are labelling each data point so after next iteration we compare previous label and new label if both are same which means we are done.\n",
    "\n",
    "Since, KMean algorithm doesn't tell us that the labels are correct or not it's just seperate all data points into sub small parts or 'k' parts"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# continue until all assigned categories don't change any more\n",
    "while True:\n",
    "    closest_centroids = df.closest.copy(deep=True)\n",
    "    centroids = update(centroids)\n",
    "    df = assignment(df,centroids)\n",
    "    if closest_centroids.equals(df.closest):\n",
    "        break\n",
    "    \n",
    "fig = plt.figure(figsize = (5,5))\n",
    "plt.scatter(df.x,df.y,c=df.color,edgecolors='k',s=80,alpha=.7)\n",
    "for i in centroids.keys():\n",
    "    plt.scatter(*centroids[i],c=colmap[i])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{0: [50.0, 63.166666666666664], 1: [61.9, 18.7], 2: [24.6, 43.2]}"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "centroids"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Now, I will show this answer using sklearn"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[50.        , 63.16666667],\n",
       "       [61.9       , 18.7       ],\n",
       "       [24.6       , 43.2       ]])"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.cluster import KMeans\n",
    "\n",
    "kmean = KMeans(n_clusters=3)\n",
    "kmean.fit(df1)\n",
    "\n",
    "labels = kmean.predict(df1)\n",
    "centroids = kmean.cluster_centers_\n",
    "centroids"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# BAAM!!!!!!"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize = (5,5))\n",
    "colors = map(lambda x : colmap[x],labels)\n",
    "color1 = list(colors)\n",
    "plt.scatter(df.x,df.y,c=color1,edgecolors='k',s=80,alpha=.7)\n",
    "for i,cent in enumerate(centroids):\n",
    "    plt.scatter(*cent,c=colmap[i])\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## very sensitive towards scalling so for best practice first normalize your data"
   ]
  }
 ],
 "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": "3.6.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}