Similarity_Algo.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "### importing libraries\n",
    "import numpy as np\n",
    "import warnings\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import matplotlib.cm as cm\n",
    "from pandas.tools.plotting import parallel_coordinates\n",
    "from sklearn.decomposition import PCA\n",
    "from sklearn.preprocessing import scale\n",
    "from sklearn.manifold import TSNE\n",
    "from sklearn.cluster import KMeans,SpectralClustering,DBSCAN\n",
    "from scipy.cluster.hierarchy import dendrogram, linkage,fcluster\n",
    "from sklearn.metrics import silhouette_samples,silhouette_score\n",
    "%matplotlib inline\n",
    "warnings.filterwarnings('ignore')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 86,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>entrez</th>\n",
       "      <th>symbol</th>\n",
       "      <th>S1</th>\n",
       "      <th>S2</th>\n",
       "      <th>S3</th>\n",
       "      <th>S4</th>\n",
       "      <th>S5</th>\n",
       "      <th>S6</th>\n",
       "      <th>S7</th>\n",
       "      <th>S8</th>\n",
       "      <th>...</th>\n",
       "      <th>S21</th>\n",
       "      <th>S22</th>\n",
       "      <th>S23</th>\n",
       "      <th>S24</th>\n",
       "      <th>S25</th>\n",
       "      <th>S26</th>\n",
       "      <th>S27</th>\n",
       "      <th>S28</th>\n",
       "      <th>S29</th>\n",
       "      <th>S30</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>14679</td>\n",
       "      <td>Gnai3</td>\n",
       "      <td>7.985282</td>\n",
       "      <td>8.654102</td>\n",
       "      <td>7.851483</td>\n",
       "      <td>9.427284</td>\n",
       "      <td>8.484089</td>\n",
       "      <td>8.430295</td>\n",
       "      <td>8.785142</td>\n",
       "      <td>8.234337</td>\n",
       "      <td>...</td>\n",
       "      <td>8.988352</td>\n",
       "      <td>8.861340</td>\n",
       "      <td>8.698631</td>\n",
       "      <td>8.214616</td>\n",
       "      <td>8.933242</td>\n",
       "      <td>8.523217</td>\n",
       "      <td>8.263034</td>\n",
       "      <td>8.442125</td>\n",
       "      <td>8.683792</td>\n",
       "      <td>8.148272</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>54192</td>\n",
       "      <td>Pbsn</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>...</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>12544</td>\n",
       "      <td>Cdc45</td>\n",
       "      <td>5.342660</td>\n",
       "      <td>5.621617</td>\n",
       "      <td>5.894139</td>\n",
       "      <td>5.530200</td>\n",
       "      <td>5.953490</td>\n",
       "      <td>5.800456</td>\n",
       "      <td>5.750067</td>\n",
       "      <td>5.763297</td>\n",
       "      <td>...</td>\n",
       "      <td>5.066617</td>\n",
       "      <td>5.199745</td>\n",
       "      <td>5.207598</td>\n",
       "      <td>5.158604</td>\n",
       "      <td>4.773268</td>\n",
       "      <td>5.028918</td>\n",
       "      <td>5.392552</td>\n",
       "      <td>5.014560</td>\n",
       "      <td>5.372466</td>\n",
       "      <td>5.033642</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>107815</td>\n",
       "      <td>Scml2</td>\n",
       "      <td>4.720995</td>\n",
       "      <td>5.129361</td>\n",
       "      <td>5.017464</td>\n",
       "      <td>5.126493</td>\n",
       "      <td>5.137191</td>\n",
       "      <td>5.081444</td>\n",
       "      <td>4.804693</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>...</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>11818</td>\n",
       "      <td>Apoh</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>...</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 32 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   entrez symbol        S1        S2        S3        S4        S5        S6  \\\n",
       "0   14679  Gnai3  7.985282  8.654102  7.851483  9.427284  8.484089  8.430295   \n",
       "1   54192   Pbsn  4.402777  4.402777  4.402777  4.402777  4.402777  4.402777   \n",
       "2   12544  Cdc45  5.342660  5.621617  5.894139  5.530200  5.953490  5.800456   \n",
       "3  107815  Scml2  4.720995  5.129361  5.017464  5.126493  5.137191  5.081444   \n",
       "4   11818   Apoh  4.402777  4.402777  4.402777  4.402777  4.402777  4.402777   \n",
       "\n",
       "         S7        S8    ...          S21       S22       S23       S24  \\\n",
       "0  8.785142  8.234337    ...     8.988352  8.861340  8.698631  8.214616   \n",
       "1  4.402777  4.402777    ...     4.402777  4.402777  4.402777  4.402777   \n",
       "2  5.750067  5.763297    ...     5.066617  5.199745  5.207598  5.158604   \n",
       "3  4.804693  4.402777    ...     4.402777  4.402777  4.402777  4.402777   \n",
       "4  4.402777  4.402777    ...     4.402777  4.402777  4.402777  4.402777   \n",
       "\n",
       "        S25       S26       S27       S28       S29       S30  \n",
       "0  8.933242  8.523217  8.263034  8.442125  8.683792  8.148272  \n",
       "1  4.402777  4.402777  4.402777  4.402777  4.402777  4.402777  \n",
       "2  4.773268  5.028918  5.392552  5.014560  5.372466  5.033642  \n",
       "3  4.402777  4.402777  4.402777  4.402777  4.402777  4.402777  \n",
       "4  4.402777  4.402777  4.402777  4.402777  4.402777  4.402777  \n",
       "\n",
       "[5 rows x 32 columns]"
      ]
     },
     "execution_count": 86,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### explore data\n",
    "df = pd.read_csv('Species_Data.csv')\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 87,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th>symbol</th>\n",
       "      <th>Gnai3</th>\n",
       "      <th>Pbsn</th>\n",
       "      <th>Cdc45</th>\n",
       "      <th>Scml2</th>\n",
       "      <th>Apoh</th>\n",
       "      <th>Narf</th>\n",
       "      <th>Cav2</th>\n",
       "      <th>Klf6</th>\n",
       "      <th>Scmh1</th>\n",
       "      <th>Cox5a</th>\n",
       "      <th>...</th>\n",
       "      <th>Usp39</th>\n",
       "      <th>Pcdha4</th>\n",
       "      <th>Pcdha7</th>\n",
       "      <th>LOC105243855</th>\n",
       "      <th>Gm34240</th>\n",
       "      <th>Pcdhga3</th>\n",
       "      <th>Gm20750</th>\n",
       "      <th>4932431L22Rik</th>\n",
       "      <th>Rhbg</th>\n",
       "      <th>Mat2a</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>S1</th>\n",
       "      <td>7.985282</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>5.342660</td>\n",
       "      <td>4.720995</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>6.996224</td>\n",
       "      <td>6.746448</td>\n",
       "      <td>11.632144</td>\n",
       "      <td>6.152779</td>\n",
       "      <td>8.335453</td>\n",
       "      <td>...</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.720995</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>S2</th>\n",
       "      <td>8.654102</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>5.621617</td>\n",
       "      <td>5.129361</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>7.205572</td>\n",
       "      <td>6.653430</td>\n",
       "      <td>11.641439</td>\n",
       "      <td>6.020570</td>\n",
       "      <td>8.370482</td>\n",
       "      <td>...</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>S3</th>\n",
       "      <td>7.851483</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>5.894139</td>\n",
       "      <td>5.017464</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>6.938888</td>\n",
       "      <td>6.771460</td>\n",
       "      <td>11.077264</td>\n",
       "      <td>6.142056</td>\n",
       "      <td>8.692579</td>\n",
       "      <td>...</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>S4</th>\n",
       "      <td>9.427284</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>5.530200</td>\n",
       "      <td>5.126493</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>7.057035</td>\n",
       "      <td>7.086915</td>\n",
       "      <td>14.050733</td>\n",
       "      <td>5.961195</td>\n",
       "      <td>8.279990</td>\n",
       "      <td>...</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>S5</th>\n",
       "      <td>8.484089</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>5.953490</td>\n",
       "      <td>5.137191</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>7.621014</td>\n",
       "      <td>6.869015</td>\n",
       "      <td>13.834583</td>\n",
       "      <td>6.011059</td>\n",
       "      <td>8.713771</td>\n",
       "      <td>...</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "      <td>4.402777</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 22411 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "symbol     Gnai3      Pbsn     Cdc45     Scml2      Apoh      Narf      Cav2  \\\n",
       "S1      7.985282  4.402777  5.342660  4.720995  4.402777  6.996224  6.746448   \n",
       "S2      8.654102  4.402777  5.621617  5.129361  4.402777  7.205572  6.653430   \n",
       "S3      7.851483  4.402777  5.894139  5.017464  4.402777  6.938888  6.771460   \n",
       "S4      9.427284  4.402777  5.530200  5.126493  4.402777  7.057035  7.086915   \n",
       "S5      8.484089  4.402777  5.953490  5.137191  4.402777  7.621014  6.869015   \n",
       "\n",
       "symbol       Klf6     Scmh1     Cox5a    ...        Usp39    Pcdha4    Pcdha7  \\\n",
       "S1      11.632144  6.152779  8.335453    ...     4.402777  4.402777  4.402777   \n",
       "S2      11.641439  6.020570  8.370482    ...     4.402777  4.402777  4.402777   \n",
       "S3      11.077264  6.142056  8.692579    ...     4.402777  4.402777  4.402777   \n",
       "S4      14.050733  5.961195  8.279990    ...     4.402777  4.402777  4.402777   \n",
       "S5      13.834583  6.011059  8.713771    ...     4.402777  4.402777  4.402777   \n",
       "\n",
       "symbol  LOC105243855   Gm34240   Pcdhga3   Gm20750  4932431L22Rik      Rhbg  \\\n",
       "S1          4.402777  4.402777  4.720995  4.402777       4.402777  4.402777   \n",
       "S2          4.402777  4.402777  4.402777  4.402777       4.402777  4.402777   \n",
       "S3          4.402777  4.402777  4.402777  4.402777       4.402777  4.402777   \n",
       "S4          4.402777  4.402777  4.402777  4.402777       4.402777  4.402777   \n",
       "S5          4.402777  4.402777  4.402777  4.402777       4.402777  4.402777   \n",
       "\n",
       "symbol     Mat2a  \n",
       "S1      4.402777  \n",
       "S2      4.402777  \n",
       "S3      4.402777  \n",
       "S4      4.402777  \n",
       "S5      4.402777  \n",
       "\n",
       "[5 rows x 22411 columns]"
      ]
     },
     "execution_count": 87,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# clustering operations cannot be performed directly on this data directly,it needs to be processed\n",
    "df_species = df.drop(['entrez'],axis=1).set_index('symbol').transpose()\n",
    "df_species.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# KMeans"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 88,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# creating clusters with kmeans\n",
    "def kmeans(x,clusters):\n",
    "    km = KMeans(n_clusters=clusters,algorithm='elkan').fit(x)\n",
    "    return km.labels_,km.cluster_centers_\n",
    "\n",
    "# visualising clusters after PCA and scaling on data\n",
    "def plot_clusters_withPCA(clusters,x,labels,cls_center=None):\n",
    "    pca = PCA(n_components=2)\n",
    "    x = pca.fit_transform(x)\n",
    "    colors = ['b','g','r','y','c','k','m',(0.5,0.1,0.3),'0.44']#cm.rainbow(np.linspace(0, 1,clusters))\n",
    "    for i in range(clusters):\n",
    "        ds = x[np.where(labels==i)]\n",
    "        plt.scatter(ds[:,0],ds[:,1],color=colors[i])\n",
    "    plt.title(\"{}clusters after PCA\".format(clusters))\n",
    "    plt.show()\n",
    "    return\n",
    "\n",
    "# printing similar species\n",
    "def SimilarSpecies(labels,df):\n",
    "    symbol = list(df.index)\n",
    "    for label in set(labels):\n",
    "        print \"group of similar species-{}\".format(label)\n",
    "        for ind in range(30):\n",
    "            if labels[ind]==label:\n",
    "                print symbol[ind],\n",
    "        print \n",
    "    return   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Elbow Method\n",
    "Elbow method tries to find clustering step or value of k where the cost function decreases abruptly. This produces an \"elbow effect\" in the graph"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 89,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# calculates cost function\n",
    "def CostFunction(clus_centres,x,labels):\n",
    "    cost = 0.0\n",
    "    for label,value in zip(labels,x):\n",
    "        cost = cost + pow(sum(clus_centres[label]-value)**2,0.5)\n",
    "    return cost/len(x)\n",
    "\n",
    "# plot graph for testing elbow method\n",
    "def Cluster_Analysis(x,iterations=15):\n",
    "    costJ = np.array([0]*(iterations))\n",
    "    for i in range(1,iterations+1):\n",
    "        print \"wait\",i\n",
    "        labels,clus_centres = kmeans(x,i)\n",
    "        costJ[i-1] = CostFunction(clus_centres,x,labels)\n",
    "    plt.figure(figsize=(25,10))\n",
    "    plt.title(\"Elbow Method\")\n",
    "    plt.xlabel(\"number of clusters\")\n",
    "    plt.ylabel(\"J(Cost Function)\")\n",
    "    plt.plot(range(1,1+iterations),costJ)\n",
    "    plt.show()\n",
    "    return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "wait 1\n",
      "wait 2\n",
      "wait 3\n",
      "wait 4\n",
      "wait 5\n",
      "wait 6\n",
      "wait 7\n",
      "wait 8\n",
      "wait 9\n",
      "wait 10\n",
      "wait 11\n",
      "wait 12\n",
      "wait 13\n",
      "wait 14\n",
      "wait 15\n"
     ]
    },
    {
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FyfXXJ1OnJj/9aQnXhw1LPvCB5KKL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\nEq6fckqZRv6cc5IlS6quEAAAAID1JVwHAADoAvvsk9xwQ/L446WL/ey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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff0e94ecb90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = df_species.values\n",
    "pca = PCA(n_components=2)\n",
    "x = pca.fit_transform(scale(x))\n",
    "Cluster_Analysis(x,15)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the above plot of Elbow method it is clear that number of clusters must be 2.But we know that elbow method is \n",
    "a heuristic approach of finding clusters,and one cannot depend on it solely and we have to take possible numbers of clusters and performs some other tests to confirm our heuristic."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Silhouette Test"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now to determine which of these 2,3,4,5,6 would be best to cluster our data into groups naturally.\n",
    "For that purpose we are going to use Silhouette test."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 91,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.326451114456\n",
      "0.286529039486\n",
      "0.217330864677\n",
      "0.258458407208\n",
      "0.260694070562\n"
     ]
    }
   ],
   "source": [
    "x = df_species.values\n",
    "for i in [2,3,4,5,6]:\n",
    "    labels,clus_centres = kmeans(x,i)\n",
    "    print silhouette_score(x,labels)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For running multiple times we found tha silhoutte score for 2 is always positive and largest among all,\n",
    "this gives us a proof that among 2,3,4,5,6 only 2 is providing a natural cluster for our dataset."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ABgyAgw6KuwpJ0sZwpEGSJEViaJAkSZE4PSFJKlqr163moYUPsb55PUfudCTV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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff0e92f0e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# ploting clusters after PCA \n",
    "x = df_species.values\n",
    "labels,clus_centres = kmeans(x,2)\n",
    "plot_clusters_withPCA(2,x,labels)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# TSNE(t-distributed stochastic neighbor embedding)\n",
    "The technique has become widespread in the field of machine learning,as it can from data with hundreds or even thousands of dimensions it can convert into two-dimensonal."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# visualising clusters after using TSNE and scaling on data\n",
    "def plot_clusters_withTSNE(clusters,x,labels,cls_center=None):\n",
    "    x = TSNE(learning_rate=100).fit_transform(x)\n",
    "    colors = ['b','g','r','y','c','k','m',(0.5,0.1,0.3),'0.44']#cm.rainbow(np.linspace(0, 1,clusters))\n",
    "    for i in range(clusters):\n",
    "        ds = x[np.where(labels==i)]\n",
    "        plt.scatter(ds[:,0],ds[:,1],color=colors[i])\n",
    "    plt.title(\"{}clusters after TSNE\".format(clusters))\n",
    "    plt.show()\n",
    "    return "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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8dPJLHLnpkWz+3c05YMQBPHX8U5y+7elRh5a1I44ILQnxpucbSkrg9NOhS5do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\nJEmSJEmSJEmSJEmSlOb/A8PBiUj1j0qAAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff0e95e0210>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_clusters_withTSNE(2,x,labels,)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Similarity by KMeans clustering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "group of similar species-0\n",
      "S13 S14 S15 S16 S17 S18 S19 S20 S21 S22 S23 S24 S25 S26 S27 S28 S29 S30\n",
      "group of similar species-1\n",
      "S1 S2 S3 S4 S5 S6 S7 S8 S9 S10 S11 S12\n"
     ]
    }
   ],
   "source": [
    "SimilarSpecies(labels,df_species)## printing clusters members/ similar species according kmeans"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Hiearchical Clustering Dendrogram\n",
    "In Hiearchical Clustering Dendogram,we starts from each data points as singleton clusters,in each iteration we calculate the distance between two clusters (aka data points initially) and combine clusters in each successive layer having distance within cutoff decided by metric and method used."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Linkage Matrix\n",
    "Scipy's linkage function return Linkage matrix.Linkage matrix contains steps of each clusters formed by Hiearchical\n",
    "Clustering Dendrogram."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "#### generates linkage matrix \"Z\"\n",
    "x = scale(df_species.values)\n",
    "# pca = PCA(n_components=2)\n",
    "# x = pca.fit_transform(scale(x))\n",
    "Z = linkage(x, 'ward')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Dendrogram\n",
    "A dendrogram is a visualization in form of a tree showing the order and distances of merges during the hierarchical clustering.A dendrogram is made up of many U-shaped lines connecting data in a hiearchical tree, where height of each U represents the distance where two clusters are merged."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "def plot_dendrogram(Z,max_d=None):\n",
    "#     plt.figure(figsize=(25,10))\n",
    "    plt.title('Hiearchical Clustering Dendrogram')\n",
    "    plt.xlabel('species')\n",
    "    plt.ylabel('distances')\n",
    "    dendrogram(\n",
    "        Z,\n",
    "        leaf_rotation = 90,\n",
    "        leaf_font_size = 12,\n",
    "    )\n",
    "    if max_d!=None:\n",
    "        plt.axhline(y=max_d, c='k')\n",
    "    plt.show()\n",
    "    return"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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8RaLzrHOJjrZuJHIr1qSmnwc8DVyQTHslcDjW05DUYtqmTqV92rRmJ0Mado0E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\nO0227jO8OgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff0e9320810>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot dendrogram\n",
    "plot_dendrogram(Z)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "By looking at the dendrogram,we can say that a total of 7 clusters are there.And\n",
    "180 seems to be good fit for maximum distance above which no merging of clusters takes place."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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gSJKk0hlgSJKk0hlgSJKk0hlgSJKk0hlgSJKk0hlgSJKk0hlgSJKk0hlgSJKk0hlgSJKk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\nkiRJkiRJkiRJ0sTz/wAkmMyNGAuqRwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff0e4fb5c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot dendrogram with max_d=180\n",
    "plot_dendrogram(Z,175)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### FCluster\n",
    "Scipy's fcluster function creates flat clusters from the hierarchical clustering with help of linkage matrix 'Z' defined earlier.It accepts maximun distance for cluster merging and create clusters therefore."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# finding labels for each data points\n",
    "max_d = 175\n",
    "labels = fcluster(Z,max_d,criterion='distance')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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M+8owhl0yjFg8VujyJElFzKChVs390lyW3LQEUh0Z9avqefvSt6lbVcdeP96r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\nB0K9rxJ2CplBo9TakukrhE8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      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff1243fd610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plotting clusters after processing it with PCA to 2-D\n",
    "# plt.figure(figsize=(25,10))\n",
    "plot_clusters_withPCA(8,x,labels)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### similarity by Hiearchical Clustering"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "group of similar species-1\n",
      "S1 S2 S3\n",
      "group of similar species-2\n",
      "S4 S5 S6 S7 S8 S9\n",
      "group of similar species-3\n",
      "S10 S11 S12\n",
      "group of similar species-4\n",
      "S13 S14 S15\n",
      "group of similar species-5\n",
      "S28 S29 S30\n",
      "group of similar species-6\n",
      "S20 S23 S24 S25 S26 S27\n",
      "group of similar species-7\n",
      "S16 S17 S18 S19 S21\n",
      "group of similar species-8\n",
      "S22\n"
     ]
    }
   ],
   "source": [
    "# printing similar species\n",
    "def SimilarSpecies(labels,df):\n",
    "    symbol = list(df.index)\n",
    "    for label in set(labels):\n",
    "        print \"group of similar species-{}\".format(label)\n",
    "        for ind in range(30):\n",
    "            if labels[ind]==label:\n",
    "                print symbol[ind],\n",
    "        print \n",
    "    return\n",
    "SimilarSpecies(labels,df_species)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Summary\n",
    "Reasons why i preferred Hiearchical Clustering over Kmeans Clustering for our dataset are described below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##### About KMeans Clustering"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**A major problem with KMeans clustering while dealing with high dimensional data is using euclidean distance**\n",
    "Since multiple dimension as in our case are hard to think in,impossible to visualise due to the exponential growth of the number with each dimesion.Thus the concept of distance become less precise or invaluable as the number of dimension increases.Because when number of dimensions reachs infinity distance between any two points converges meaning the maximum and minimum distance between any two points in the dataset remains the same.This condition is known as ** Curse Of Dimensionality **.***If we still want to use KMeans we can change the distance metric with cosine matrics,instead we can also use hiearchical clustering***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "** KMeans is extremely sensitive to cluster centre initialisation **.Since bad cluster initialisation can lead to poor convergence,bad overall clustering,could struck into local optima."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "** KMeans can struck in local optima.**In our when we use Elbow method to find numbers of clusters for KMeans clustering, we can clearly see from the plot that at number 2 the decrement in cost function was maximum.And this was supported by silhouette test ****(here both elbow method and silhoutte used euclidean distance metric)****."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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SGWBIkqTSGWBIkqTSGWBIkqTSGWBIkqTSGWBIkqTSGWBIkqTSGWBIkqTSGWBIkqTSGWBI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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff0e95e0a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_dendrogram(Z,310)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our KMeans find this value of max_id>300 and struck into local optima instead of finding global optima, thus predicting number of clusters to be 2."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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GDS1Tjx4tO+6882Du3GhrkSSVH4OGlmn77WHgQKisXPZxixfDpEnFqUmSVD4M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\nSZIkSZIkRev/AeNDbuKrU5IpAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff0e92f0e10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "labels,clus_centres = kmeans(x,2)\n",
    "plot_clusters_withPCA(2,x,labels)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "***Here we can clearly see that our kmeans only creates clusters with distance greater than 300 and got struck into local optima,with creating only two  big clusters one on each side of the plot.***Though it sheerly ignores other small clusters(identified later) within those two big clusters.SO it is clear we can't really depend on kmeans or elbow method blindly when we donot know much about our dataset i.e. in datatset having dimension of several thousands."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### About Hiearchical Clustering"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I preferred Hiearchical Clustering as *** it doesnot need the number of clusters as input, partitions can be visualised using a tree structure called dendrogram***"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**It is slow but doesnot struck into local optima and always reach global optima as we can view partitions as different level of merging and can visually select the value of clusters that was naturally present in the dataset**"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
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 },
 "nbformat": 4,
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