04. Density Based Clustering.ipynb

{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Density Based Clustering\n",
    "## DBSCAN\n",
    "All the previous techniques are distance based & such methods can find only spherical clusters and not suited for clusters of other shapes.  \n",
    "\n",
    "Continue growing the cluster until the density exceeds certain threshold.  \n",
    "\n",
    "Algorithm has two parameters:  \n",
    "ɛ: The radius of our neighborhoods around a data point p.  \n",
    "minPts: The minimum number of data points we want in a neighborhood to define a cluster.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd\n",
    "\n",
    "# Importing the dataset\n",
    "dataset = pd.read_csv(\"Data/Unsupervised/Wholesale customers data.csv\")\n",
    "X = dataset.iloc[:, [2, 3]].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.cluster import DBSCAN"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 -1\n",
      "  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 -1\n",
      "  0  0  0  0  0  0  0  0  0  0  0  0  0 -1  0  0  0 -1  0  0  0  0  0 -1\n",
      "  0  0  0  0  0  0  0  0  0  0  0  0  0 -1 -1  0  0  0  0  0 -1 -1  0  0\n",
      "  0  0  0  0  0  0  0 -1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n",
      "  0  0  0  0  0 -1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n",
      "  0 -1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n",
      "  0  0  0  0  0  0  0  0  0  0  0  0  0 -1  0 -1  0  0  0  0  0  0  0  0\n",
      "  0  0  0  0 -1  0  0  0  0  0  0  0  0  0  0  0  0  0  0 -1  0  0  0  0\n",
      " -1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n",
      "  0  0  0  0  0  0  0  0  0  0  0 -1  0  0  0  0  0  0  0  0  0  0  0  0\n",
      "  0 -1  0  0  0  0  0  0  0  0  0  0  0 -1  0  0  0  0  0  0 -1  0  0  0\n",
      "  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n",
      "  0  0  0  0  0  0  0  0  0  0  0  0  0 -1  0  0  0  0  0  0  0 -1  0  0\n",
      "  0  0 -1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n",
      "  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0\n",
      "  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 -1  0  0  0  0  0  0\n",
      "  0  0  0  0  0 -1  0  0  0  0  0  0  0  0  0  0  0 -1  0 -1  0  0  0 -1\n",
      "  0  0  0 -1  0  0  0  0]\n"
     ]
    }
   ],
   "source": [
    "from sklearn.preprocessing import StandardScaler\n",
    "import numpy as np\n",
    "X = StandardScaler().fit_transform(X)\n",
    "\n",
    "db = DBSCAN(eps=0.5, min_samples=15).fit(X)\n",
    "labels = db.labels_\n",
    "print(labels)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Visualising the clusters\n",
    "y_kmeans = labels\n",
    "size = 25\n",
    "plt.scatter(X[y_kmeans == 0, 0], X[y_kmeans == 0, 1], s = size, c = 'green')\n",
    "plt.scatter(X[y_kmeans == -1, 0], X[y_kmeans == -1, 1], s = size, c = 'red')\n",
    "plt.title('Clusters of customers')\n",
    "plt.xlabel('Milk')\n",
    "plt.ylabel('Grocery')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1. One cluster: DBSCAN able to identify customer clusters which buy milk and grocery close to mean(normal buying)\n",
    "2. Second Cluster: This set of customer's buying pattern differ heavily from other customers\n",
    "\n",
    "Whole saler can target these 2ndset of customer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x2048f59c2b0>"
      ]
     },
     "execution_count": 66,
     "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(X[:,0], X[:,1],s=10,c=labels)"
   ]
  },
  {
   "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": "3.6.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}