Starbucks_Hot_Beverages_Cluster.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Starbucks - Three popular time slots hierarchical clustering"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem: \n",
    "A newly opened Starbucks coffee shop manager wanted to increase loyal customer to his newly opened shop. As part of increasing customer loyalty, he collected data of sale of hot beverages vs popular times of a typical day - in this case Wednesday. The goal of the manager is to offer a sales coupons to customers based on time visit to the store.\n",
    "\n",
    "He consulted you, data scientist, and wanted you to develop clustering (maximum three popular time slots of the day to offer coupon). How do you approach?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Objective\n",
    "This example explains Hierarchical Clustering with Python 3, pandas and scikit-learn on Jupyter Notebook.\n",
    "\n",
    "## Requirements\n",
    "To use this example you need Python 3 and latest versions of pandas and scikit-learn. I used Anaconda distribution to install.\n",
    "\n",
    "### Data Set:\n",
    "array([[8, 1], [7, 2], [7, 3], [8, 7], [7, 9], [6, 9], [5, 7], [5, 4], [4, 5], [4, 8], [3, 3], [3, 6], [3, 8], [3, 9], [2, 6], [2, 9], [1, 5], [1, 7] ])\n",
    "\n",
    "\n",
    "\n",
    "## Hierarchical Clustering\n",
    "Two type of Hierarchical Clustering.\n",
    "1.\tAgglomerative: bottom up approach \n",
    "2.\tDivisive: (opposit) starting at top and dividing down into multiple\n",
    "\n",
    "## Algorithm (Hierarchical - Agglomerative)\n",
    "1.\tMake a individual cluster for each data points. (N cluster)\n",
    "2.\tCluster togather 2 closest clusters. (N-1 Cluster)\n",
    "3.\tRepeat 2 until only one cluster remaining. (N-2....2,1)\n",
    "4.\tOutput: One hudge cluster.\n",
    "5.\tDraw Dendogram as we keep connecting clusters. \n",
    "6.\tExtend all horizontal lines in Dendogram then find longest vertical line. Intersect this line from middle and check how many lines it is ontersecting. That is K cluster value.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Importing the libraries\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[8, 1],\n",
       "       [7, 2],\n",
       "       [7, 3],\n",
       "       [8, 7],\n",
       "       [7, 9]])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = np.array([[8, 1], [7, 2], [7, 3], [8, 7], [7, 9], [6, 9], [5, 7], [5, 4], [4, 5], [4, 8], [3, 3], [3, 6], [3, 8], [3, 9], [2, 6], [2, 9], [1, 5], [1, 7] ])\n",
    "X[:5]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([8, 7, 7, 8, 7, 6, 5, 5, 4, 4, 3, 3, 3, 3, 2, 2, 1, 1])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X[:,0]# first column"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Single-link cluster"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "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": [
    "# Using the dendrogram to find the optimal number of clusters\n",
    "import scipy.cluster.hierarchy as sch\n",
    "dendrogram = sch.dendrogram(sch.linkage(X, method = 'single'))\n",
    "plt.title('Dendrogram')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('Euclidean distances')\n",
    "plt.show()\n",
    "#Extend all horizontal lines then find longest vertical line. Intersect this line from middle and check how many lines it is ontersecting. That is K"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Fitting Hierarchical Clustering to the dataset\n",
    "from sklearn.cluster import AgglomerativeClustering\n",
    "hc = AgglomerativeClustering(n_clusters = 3, affinity = 'euclidean', linkage = 'single')#ward\n",
    "y_hc = hc.fit_predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAW4AAAD8CAYAAABXe05zAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDMuMC4wLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvqOYd8AAAGpZJREFUeJzt3XmcXGWd7/HPr7qquro7nb2zkAABZREjsvQNhB0CsoNwLw4o8bIZ76jIoiyiVwYdmdFxHBjgOjcDEWRYBgIRFUH2AQTRTlgCJGwatmwNJKH3rq763T+64JJ0dXd1UqdPPfT3/XrVK51zTtf5vpLqb5966ql6zN0REZFwJOIOICIiQ6PiFhEJjIpbRCQwKm4RkcCouEVEAqPiFhEJjIpbRCQwKm4RkcCouEVEApOM4k4nTpzoM2bMiOKuRUQ+lhYvXvyOuzeUcmwkxT1jxgyampqiuGsRkY8lM3u91GM1VCIiEhgVt4hIYFTcIiKBUXGLiARGxb2Z3J2O1g7y+XzcUUrS3dlNd1c27hgSs+6uLN2d3XHHKEkul6OjtQOtGdBXScVtZueY2fNm9oKZnRt1qErm7vzm337PSVPO4oTxp3PC+NO44e9uI5fLxR2tqNeeXcE397mEY+vnclz9XC458kesffOduGPJMFv52mouOPQyjh11KsfWz+X8A7/PG8vfjjtWUT3ZHv79ohs5YdxpnDD+NE6ePo/f3/Bw3LEqig3228zMZgK3ArOAbuBe4G/d/ZX+vqexsdE/rtMBf3X1PVx78U10tXd9uK26tpojzjiYb/zrmTEm62vtG82c9Zlv0dHS8eG2RFWCsQ2juf6Vq6ipy8SYToZLy7pWTtvxbFrWteH53p93M6gbU8eC5VcybtKYmBNu7MenXc1jtz9JV8f/f2ZQXVvNOT//CofNPTDGZNEys8Xu3ljKsaVccX8K+KO7t7t7D/BfwAlbEjBUuVyOX/7dbRuVNkBXexf3XPsgLetaY0pW3J1X3k22c+PhkXwuT3tLBw/f/HhMqWS43bvgIbrauz8sbQD33uGz3/7bfTEm6+vdVet49LYnNipt6P0ZW3DJzRo2KSiluJ8HDjCzCWZWCxwFbB1trMrU8l4rnW1dRfclq1O89fKqYU40sBeeeJmebE+f7Z1tXSx7qt8nTPIx8+KTL/cpQoDuziwvPPFSDIn69/oLb5KqThXd996qdWT1Og1QQnG7+zLgx8D99A6TPAv0aQMzm2dmTWbW1NzcXPaglaBuTC2JKiu6L9uVpWH6+GFONLBpO0wlkeibN51JMW2HqTEkkjhM33EqyXRVn+1VySqm71hZj4NJ20ykp7vvxQZAZlSm31IfaUp6cdLdr3P3Pdz9AOA9oM/lmrvPd/dGd29saCjp7fbBSaVTHHnmHKpr0htvr06y28EzmThtQkzJivsf5x1DKtP3gZ6oquLw0w4a/kASi6PnHUZVsu+nWyTTSY7/+hExJOrf9B234pO7b0cytfEvmuraNCd88yjMil84jTSlziqZVPhzG+BE4JYoQ1Wyef80l/1O3It0JkXdmFrSmRSf2X8XvnvzOXFH6+OTu2/HBQu+Tt2YWmpH11BTn2Hc5LH8wz2XMG7y2LjjyTCZMmMSly26gNET6qmtr6F2dA314+r43q3nsfVO0+KO18dlv7qQnffagXRNmroxtaQyKeZ86QDmXnpS3NEqxqCzSgDM7DFgApAFznf3Bwc6/uM8q+QD761ex5vLVzJ5RgNTZkyKO86Ast1ZXvrza6TSSXbYc3sSCU3fH4lyPTleanoN3Nmx8RMkU5F8xlzZrHxtNc1vvsu2n57O2IbKmvkShaHMKimpuIdqJBS3iEg5lXs6oIiIVBAVt4hIYFTcIiKBUXGLiARGxS0iEhgVt4hIYFTcIiKBUXGLiARGxS0iEhgVt4hIYFTcIiKBUXGLiARGxS0iEhgVt4hIYFTcIiKBqexPUpeyWPN6M3+652mSqSpmH9dY0R9K39XRxR9/s5h1azawyz47suOen4g7kkjFKam4zew84CzAgaXA6e7eGWUwKY9f/O9bWPjPv8HMsIRx9dnXcfY1Z3HE6YfEHa2P5X96hYsP/3vy+Ty5bA5LJJi538784K6LSGuRWJEPDTpUYmbTgG8Cje4+E6gCTo46mGy5xfc/y51X3E13Z5aujm4627ro7sxy1Teu4+1XV8UdbyM92R6+e/TltG1op6OlszdzexdLH1vGzT+6I+54IhWl1DHuJFBjZkmgFlgZXSQpl7uuuZfOtq4+2/M9OX5//SPDH2gATz+4lJ5srs/27o5u7v6/98eQSKRyDVrc7v428FPgDWAVsMHd79v0ODObZ2ZNZtbU3Nxc/qQyZBua3y+6vSeb63dfXFrWtdHf+qcdrRqVE/moUoZKxgHHA9sBWwF1Znbqpse5+3x3b3T3xoaGhvInlSHb65g9SWfSfbbXjMrQePhuMSTq38z9diZX5Iob4NP77jzMaUQqWylDJYcCf3X3ZnfPAncC+0QbS8rhuL89nNETRpFMVX24LZVJMX3HqexzXEmLSQ+bSVtP5PAzDiFTW/3hNjMjU1fNV37S5zpBZEQrpbjfAPY2s1ozM2AOsCzaWFIOo8bW8X8W/4Sjv3oY46eMZdLWE/nCBcfzz//1A6qSVYPfwTA7+6oz+dqVp7PNp6YzpmE0s49r5F+fvJxP7rZd3NFEKor1N6640UFmlwF/A/QATwNnuXvfV70KGhsbvampqWwhRUQ+7sxssbuX9FS4pHnc7n4pcOkWpRIRkbLQW95FRAKj4hYRCYyKW0QkMCpuEZHAqLhFRAKj4hYRCYyKW0QkMCpuEZHAqLhFRAKj4hYRCYyKW0QkMCpuEZHAqLhFRAKj4hYRCYyKW0QkMIN+HreZ7QT850c2bQ98392vKFcI9zx03oW33Qj+PqQPxEbNw6oml+sUImX35ktvc9OP7uTFJ15i4rTxfOGC49n7mD3jjiXDbO0bzdx8+SKWPPAcYxpGc+I5R3PQ3+xD74Jh0ShpBZwPDzarAt4G9nL31/s7bqgr4OQ3XASd94J3FLYkweqxiXdhVVNKvh+R4fLq03/lvAO/T3dHN/lcHoBMXTVf+t5/5+SLTog5nQyXla+t5mv/7SI6W7vI9fQudp2pq+aIMw7h61eeMaT7GsoKOEMdKpkDvDZQaQ+VZ1+Bjns+UtoAPeAteOs15TqNSFldc84COls7PyxtgM62Lm687HZa17fFmEyG04Lv3kLH+x0fljb0Pg7u/vcHWL1ibWTnHWpxnwzcUtYE3U8A+SI7eqDrkbKeSqQc3J0Xnnip6L5kOskLf1g+zIkkLovvf5Z8vu+oRVVVgqcfXBrZeUsubjNLA8cBt/ezf56ZNZlZU3Nzc+kJrBasnxXHrab0+xEZJmZGujpVfKdDZlRmeANJbKprqotut4RRWx9dfw3livtIYIm7rym2093nu3ujuzc2NDSUfq+Zw6DoOHsGak8ZQjyR4XPIl/Ynle772n4qk2LmfjvHkEjicNRX5pCuSffZ7nln1tF7RHbeoRT3KZR7mASwxFgY81MgU7glgBpIz8JqTy336UTK4qv/NJetd55GzagMZkamLkPt6Bp++OuLqarq5xmkfOycfNHn2XnWJ8nUVWMJo7o2TXVtNd9f+G1q6qJ75lXSrBIzqwXeBLZ39w2DHT/UWSUAnnsXOn8H3gLp2ZDaLdLpNCJbKp/Ps/i+Z3npz68xcdp4DjhpdqRPj6UyuTvPPfoizz+2nNET6znwC7MZPb5+yPczlFklQ5oOWKrNKW4RkZEsyumAIiISMxW3iEhgVNwiIoFRcYuIBEbFLSISGBW3iEhgVNwiIoFRcYuIBEbFLSISGBW3iEhgVNwiIoFRcYuIBEbFLSISGBW3iEhgVNwiIoFRcW8mz7fg2Rfx/HtxRxmUex7PvoL3/JUoPn9dRIZX30XzijCzscC1wEzAgTPc/ckog1Uq9xzecjm03waWAu/Gq+dgY/8Rq8DFjb3rUXzDxeDt4Hmomgxjr8BSn447mohsplKvuK8E7nX3nYHPAsuii1TZvOUK6FgIdIG3At3Q9RC+/sK4o/Xh2Vfwdd+A/Du9xU0n5F7H35uL59fFHU9ENtOgxW1mo4EDgOsA3L3b3ddHHawSuWeh40bwjk32dEHXI3iuOZZc/fH2BUC2yI4evH3RsOcRkfIo5Yp7e6AZ+IWZPW1m15pZ3aYHmdk8M2sys6bm5soqsLLxFvBc8X2WgtzK4c0zmJ5XgWJ5OyH36nCnEZEyKaW4k8AewM/dfXegDbh404Pcfb67N7p7Y0NDQ5ljVggbDZYuvs+zkNx6ePMMJjmToi9jWA0kdxn2OCJSHqUU91vAW+7+VOHvC+kt8hHHLAl183qLbyMZqDkGS4yPJVd/rO703mcCG28FqrGaz8cRSUTKYNDidvfVwJtmtlNh0xzgxUhTVTCrmwd1XwWrAzK9t9qTsNGXxR2tD0tug427Hqq2B9JAClK7YhP+E0uMijmdiGyukqYDAmcDN5lZGvgLcHp0kSqbmWGjvobXfQXy70JiHGbVccfql6V3xxruxXPvgCWxxNi4I4nIFiqpuN39GaAx4ixBMUtB1ZS4Y5TMqibGHUFEykTvnBQRCYyKW0QkMCpuEZHAqLhFRAKj4hYRCYyKW0QkMCpuEZHAqLhFRAKj4hYRCYyKW0QkMCpuEZHAqLhFRAKj4hYRCYyKW0QkMCpuEZHAlPR53Ga2Amihd+XZHncv+2dze88KvGMR5Ndj1ftD9cGYVZX7NFLhPLcSb78T8mux9CzIfA7rb51PkRGq1BVwAA5293eiCJFvvw3e/3ugB+jBO++C5A4w/kbMMlGcUiqQdz6Arz8fyAPdeMevofUqmHA7lhgddzyRihH7UInn3oH3fwh00lvcgLdD9iW87RdxRpNh5N6Bb/g2vY+D7sLWdsi9hbf8S4zJRCpPqcXtwH1mttjM5pU1QdcD/cTohI6FZT2VVLCux+ldgX5TWej89XCnEalopQ6V7OvuK81sEnC/mS1390c/ekCh0OcBbLPNNqUn8G56nxoX25ct/X4kbAP+X/cMWwyREJR0xe3uKwt/rgUWAbOKHDPf3RvdvbGhoaH0BNUH9bMjBZkjSr8fCVv1bPBiBZ2A9MHDHkekkg1a3GZWZ2b1H3wNfA54vlwBLLkN1H4JrOYjW6shMQEb9b/KdRqpcJYYB/XnAh99HKTBRmP1344rlkhFKmWoZDKwyMw+OP5md7+3nCGs/iKo3htvuwny6yEzB6v9omYSjDCJujPx1Gfwthsgtwaq98Fqv4xVTYw7mkhFGbS43f0vwGejDGFmUH0Q1u+wiYwUlp7VO39bRPoV+3RAEREZGhW3iEhgVNwiIoFRcYuIBEbFLSISGBW3iEhgVNwiIoFRcYuIBEbFLSISGBW3iEhgVNwiIoFRcYuIBEbFLSISGBW3iEhgVNwiIoFRcYuIBKbk4jazKjN72sx+G2UgkVB41x/Jv3Mi+dUzya/dj3zrAtz7WfhapIyGcsV9DrAsqiAiIfGuP+Dr5kHP80A35NdC65X4+5fGHU1GgJKK28ymA0cD10YbRyQM3vIPQOcmWzugYxGeWxNHJBlBSr3ivgK4ENDzQBnx3B16Xim+09KQfWF4A8mIM2hxm9kxwFp3XzzIcfPMrMnMmpqbm8sWUKTSmBnYqH725iExYVjzyMhTyhX3vsBxZrYCuBU4xMz+Y9OD3H2+uze6e2NDQ0OZY4pUmNovAplNNhokJkJq1zgSyQgyaHG7+3fcfbq7zwBOBh5y91MjTyZSwWzU2VB9AFANVtd7S2yFjVvQe0UuEqFk3AFEQmSWxsZdjfesgOzzUDUZUntiprdGSPSGVNzu/gjwSCRJRAJkyRmQnBF3DBlhdHkgIhIYFbeISGBU3CIigVFxi4gERsUtIhIYFbeISGBU3CIigVFxi4gERsUtIhIYFbeISGBU3CIigVFxi4gERsUtIhIYFbeISGBU3CIigdFCCiOA51ug+ymwJKRnY1YddySRAbk7z65ZzcqW99mlYRIzxo6LO1JFGbS4zSwDPApUF45f6O6XRh1MyiPfdhO0/CNYqrDFYczPsMzBseYS6c+qlha+/KuFrGptIWFGNpdn/2235aojjqE6qWtNKG2opAs4xN0/C+wGHGFme0cbS8rBu5dAy4+BLvDWwq0NX38OnlsVdzyRos76zSJWrF9HezZLa3c3XbkeHn/jdX7yxGNxR6sYpSwW7O7eWvhrqnDzSFNJWXjbDfT+3t1UHm+/Y7jjiAzq5XffYcX6deR844rp7Onh1ueXkndVD5T44qSZVZnZM8Ba4H53f6rIMfPMrMnMmpqbm8udUzZHfiXFf8d2Q15X3FJ5mtvbSCaK11JXrodsLjfMiSpTScXt7jl33w2YDswys5lFjpnv7o3u3tjQ0FDunLI50nsD6b7brRZLzxr2OCKD+dTEBrr6Kefp9aM1xl0wpOmA7r6e3lXej4gkjZSV1f5PsBo2/m9OQmICZPRfKJVnfE0tX5y5KzWbFHQmmeSS/Q+MKVXlGbS4zazBzMYWvq4BDgWWRx1MtpxVTcQm3AHVhwDp3hKvORabcLumBErF+t4BB/Ot2fsxqbaOZCLBDuMncPWRx/K5T+wQd7SKYT7IYL+Z7QrcAFTRW/S3ufsPBvqexsZGb2pqKltIEZGPOzNb7O6NpRw76ICRuz8H7L7FqUREpCz0lncRkcCouEVEAqPiFhEJjIpbRCQwKm4RkcCouEVEAqPiFhEJjIpbRCQwKm4RkcCouEVEAqPiFhEJjIpbRCQwKm4RkcCouEVEAqPiFhEJzKCfx21mWwO/BKYAeWC+u18ZdTARGbleWLuGBc8s4fUN62mcuhWn7bYHU0bVxx2rYpSy8mYP8C13X2Jm9cBiM7vf3V+MOJuIjEC/fXk5Fz7we7pzOfLuLF2zhpuff46FJ53CjhMmxh2vIgw6VOLuq9x9SeHrFmAZMC3qYCIy8nT19PCdB++js6eHfGFZxWw+R1t3N99/+MGY01WOIY1xm9kMepcxeyqKMCIysj27ZjVm1me7A02r3iabyw1/qApUcnGb2SjgDuBcd3+/yP55ZtZkZk3Nzc3lzCgiI0RVwuhv/fIEVrTUR6KSitvMUvSW9k3ufmexY9x9vrs3untjQ0NDOTOKyAix2+SppKuq+mxPmHHAtjNIJjQRDkoobuv9FXcdsMzdfxZ9JBEZqaoSCa456lhqkimqCwVem0wxsaaWHx58aMzpKkcps0r2BeYCS83smcK2S9z9d9HFEpGRau/pW/PQl8/g9heX8vqGDewxZSrH77wLtalU3NEqxqDF7e6PAxpYEpFhM3nUKL4xa3bcMSqWBoxERAKj4hYRCYyKW0QkMCpuEZHAqLhFRAKj4hYRCYyKW0QkMCpuEZHAqLhFRAKj4hYRCYyKW0QkMCpuEZHAqLhFRAKj4hYRCYyKW0QkMCpuEZEt5O68095ORzY7LOcbdCEFM1sAHAOsdfeZ0UcSEQnHva+8zGWPPsy6zg4ADt3uE1w+5zBGV2ciO2cpV9zXA0dElkBEJFCPvbGC8++/hzVtrXTncnTnctz/l1eZu2gh3t9y9WUwaHG7+6PAe5ElEBEJ1L88+Qc6e3o22pbN53lt3Xs8vXpVZOfVGLeIyGZ6dV3xa1p35+V334nsvGUrbjObZ2ZNZtbU3NxcrrsVEalYW9XXF92eMGPrMWMiO2/Zitvd57t7o7s3NjQ0lOtuRUQq1jdnzaYmufEcjyozJtTWMnv6NpGdV0MlIiKb6agdduK8vfelJpliVDpNdVWSTzdM4uYTv0DCLLLzljId8BbgIGCimb0FXOru10WWSEQkIGft0cipu36Wl999l3GZmkiHSD4waHG7+ymRpxARCVgmmWLXyVOG7XwaKhERCYyKW0QkMCpuEZHAqLhFRAKj4hYRCYxF8UEoZtYMvL6Z3z4RiO69ouUXUl5ljU5IeZU1OluSd1t3L+ndi5EU95YwsyZ3b4w7R6lCyqus0Qkpr7JGZ7jyaqhERCQwKm4RkcBUYnHPjzvAEIWUV1mjE1JeZY3OsOStuDFuEREZWCVecYuIyAAqprjNbIGZrTWz5+POMhgz29rMHjazZWb2gpmdE3emgZhZxsz+ZGbPFvJeFnemwZhZlZk9bWa/jTvLQMxshZktNbNnzKwp7jyDMbOxZrbQzJYXHr+z485UjJntVPg3/eD2vpmdG3eu/pjZeYWfrefN7BYzi26lYCpoqMTMDgBagV9W+mryZjYVmOruS8ysHlgMfN7dX4w5WlFmZkCdu7eaWQp4HDjH3f8Yc7R+mdn5QCMw2t2PiTtPf8xsBdDo7kHMNTazG4DH3P1aM0sDte6+Pu5cAzGzKuBtYC9339z3h0TGzKbR+zO1i7t3mNltwO/c/fqozlkxV9whLUrs7qvcfUnh6xZgGTAt3lT9816thb+mCrfK+I1dhJlNB44Gro07y8eJmY0GDgCuA3D37kov7YI5wGuVWNofkQRqzCwJ1AIrozxZxRR3qMxsBrA78FS8SQZWGHp4BlgL3O/ulZz3CuBCIB93kBI4cJ+ZLTazeXGHGcT2QDPwi8Iw1LVmVhd3qBKcDNwSd4j+uPvbwE+BN4BVwAZ3vy/Kc6q4t4CZjQLuAM519/fjzjMQd8+5+27AdGCWmVXkcJSZHQOsdffFcWcp0b7uvgdwJPD1wpBfpUoCewA/d/fdgTbg4ngjDawwnHMccHvcWfpjZuOA44HtgK2AOjM7Ncpzqrg3U2Gs+A7gJne/M+48pSo8NX4EOCLmKP3ZFziuMHZ8K3CImf1HvJH65+4rC3+uBRYBs+JNNKC3gLc+8mxrIb1FXsmOBJa4+5q4gwzgUOCv7t7s7lngTmCfKE+o4t4MhRf7rgOWufvP4s4zGDNrMLOxha9r6H2gLY83VXHu/h13n+7uM+h9ivyQu0d69bK5zKyu8OI0hSGHzwEVOyvK3VcDb5rZToVNc4CKfEH9I06hgodJCt4A9jaz2kI3zKH3da/IVExxFxYlfhLYyczeMrMz4840gH2BufReDX4wXemouEMNYCrwsJk9B/yZ3jHuip5mF4jJwONm9izwJ+Bud7835kyDORu4qfBY2A24POY8/TKzWuAweq9gK1bhGcxCYAmwlN5ejfQdlBUzHVBEREpTMVfcIiJSGhW3iEhgVNwiIoFRcYuIBEbFLSISGBW3iEhgVNwiIoFRcYuIBOb/AYQxAQH+CHKGAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Scatter chart of the clusters\n",
    "plt.scatter(X[:, 0], X[:, 1], c=y_hc, s=40, cmap='viridis');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Complete-link Clusters"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# complete"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "scrolled": true
   },
   "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": [
    "# Using the dendrogram to find the optimal number of clusters\n",
    "import scipy.cluster.hierarchy as sch\n",
    "dendrogram = sch.dendrogram(sch.linkage(X, method = 'complete'))\n",
    "plt.title('Dendrogram')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('Euclidean distances')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Fitting Hierarchical Clustering to the dataset\n",
    "from sklearn.cluster import AgglomerativeClustering\n",
    "hc = AgglomerativeClustering(n_clusters = 3, affinity = 'euclidean', linkage = 'complete')#ward\n",
    "y_hc = hc.fit_predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "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": [
    "# Scatter chart of the clusters\n",
    "plt.scatter(X[:, 0], X[:, 1], c=y_hc, s=40, cmap='viridis');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Average-ling Clusters"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "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": [
    "# Using the dendrogram to find the optimal number of clusters\n",
    "import scipy.cluster.hierarchy as sch\n",
    "dendrogram = sch.dendrogram(sch.linkage(X, method = 'average'))\n",
    "plt.title('Dendrogram')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('Euclidean distances')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Fitting Hierarchical Clustering to the dataset\n",
    "from sklearn.cluster import AgglomerativeClustering\n",
    "hc = AgglomerativeClustering(n_clusters = 3, affinity = 'euclidean', linkage = 'average')#ward\n",
    "y_hc = hc.fit_predict(X)"
   ]
  },
  {
   "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": [
    "# Scatter chart of the clusters\n",
    "plt.scatter(X[:, 0], X[:, 1], c=y_hc, s=40, cmap='viridis');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "## Manual Steps\n",
    "[Manual steps excel](https://github.com/manojknit/PySpark_Python-ML-Models/blob/master/ManualSteps/StarbucksHOTBeveragesAndPopularTimes.xlsx)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Manual cluster draw"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<img src=\"images/Starbucks_Hot_Beverages_Cluster.png\">\n",
    "<img src=\"images/Starbucks_Hot_Beverages_Cluster_Dendrogram.png\">"
   ]
  }
 ],
 "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
}