Notebooks/Day43_Heirarchial clustering.ipynb

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    "Kmeans   \n",
    "- we try to select the centroid by calculating the mean of datapoints\n",
    "k-medoids  \n",
    "- selects datapoints from the given dataset\n",
    "\n",
    "Disadvantages  \n",
    "- affect by outliers\n",
    "- choosing the no of clusters\n",
    "- fails to recognize patterns"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c6dab72b",
   "metadata": {},
   "source": [
    "Heirarchial Clustering\n",
    "- 2 methods\n",
    "    - Agglomerative method(bottomup approach)\n",
    "    - divisive(topdown appoach)\n",
    "- Agglomerative method(bottomup approach)\n",
    "    - linkage methods\n",
    "        - single linkage(calculates the distance b/w closest members of the two clusters)\n",
    "        - complete linkage(calculates the distance b/w farthest members of the two clusters)\n",
    "        - average linkage(distance b/w all pairs and calculates the average of all these distances)\n",
    "    - variance methods(ward)\n",
    "    - centroids methods   \n",
    "***Agglomerative method***\n",
    "- each object as a cluster\n",
    "- merge two clusters which are similar untill all objects are merged into a single cluster   \n",
    "***Divisive method***   \n",
    "- all objects stay in one cluster\n",
    "- select a cluster and divide to subclusters   \n",
    "***Dendogram***\n",
    "- a binary tree like structure that shows how clusters are merged/splitted heirachically   \n",
    "***Single Linkage***\n",
    "- sensitive to outliers\n",
    "- can find irregular shaped clusters   \n",
    "***Complete and average linkage***\n",
    "- robust to outliers\n",
    "- break large clusters(spherical clusters)  \n",
    "***choosing optimal value of k from the dendogram***\n",
    "- choose the largest vertical distance without crossing any horizontal line\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "1bfab856",
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>CustomerID</th>\n",
       "      <th>Genre</th>\n",
       "      <th>Age</th>\n",
       "      <th>Annual Income (k$)</th>\n",
       "      <th>Spending Score (1-100)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>Male</td>\n",
       "      <td>19</td>\n",
       "      <td>15</td>\n",
       "      <td>39</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>Male</td>\n",
       "      <td>21</td>\n",
       "      <td>15</td>\n",
       "      <td>81</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>Female</td>\n",
       "      <td>20</td>\n",
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       "      <td>23</td>\n",
       "      <td>16</td>\n",
       "      <td>77</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>Female</td>\n",
       "      <td>31</td>\n",
       "      <td>17</td>\n",
       "      <td>40</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
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       "      <td>...</td>\n",
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       "    <tr>\n",
       "      <th>195</th>\n",
       "      <td>196</td>\n",
       "      <td>Female</td>\n",
       "      <td>35</td>\n",
       "      <td>120</td>\n",
       "      <td>79</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>196</th>\n",
       "      <td>197</td>\n",
       "      <td>Female</td>\n",
       "      <td>45</td>\n",
       "      <td>126</td>\n",
       "      <td>28</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>197</th>\n",
       "      <td>198</td>\n",
       "      <td>Male</td>\n",
       "      <td>32</td>\n",
       "      <td>126</td>\n",
       "      <td>74</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>198</th>\n",
       "      <td>199</td>\n",
       "      <td>Male</td>\n",
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       "      <td>18</td>\n",
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       "      <td>30</td>\n",
       "      <td>137</td>\n",
       "      <td>83</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>200 rows × 5 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "     CustomerID   Genre  Age  Annual Income (k$)  Spending Score (1-100)\n",
       "0             1    Male   19                  15                      39\n",
       "1             2    Male   21                  15                      81\n",
       "2             3  Female   20                  16                       6\n",
       "3             4  Female   23                  16                      77\n",
       "4             5  Female   31                  17                      40\n",
       "..          ...     ...  ...                 ...                     ...\n",
       "195         196  Female   35                 120                      79\n",
       "196         197  Female   45                 126                      28\n",
       "197         198    Male   32                 126                      74\n",
       "198         199    Male   32                 137                      18\n",
       "199         200    Male   30                 137                      83\n",
       "\n",
       "[200 rows x 5 columns]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "df=pd.read_csv(\"https://raw.githubusercontent.com/AP-State-Skill-Development-Corporation/Datasets/master/Clustering/Mall_Customers.csv\")\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "4eb437b8",
   "metadata": {
    "collapsed": true
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   "outputs": [
    {
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       "  <thead>\n",
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       "      <th></th>\n",
       "      <th>Age</th>\n",
       "      <th>Annual Income (k$)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
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      "text/plain": [
       "     Age  Annual Income (k$)\n",
       "0     19                  15\n",
       "1     21                  15\n",
       "2     20                  16\n",
       "3     23                  16\n",
       "4     31                  17\n",
       "..   ...                 ...\n",
       "195   35                 120\n",
       "196   45                 126\n",
       "197   32                 126\n",
       "198   32                 137\n",
       "199   30                 137\n",
       "\n",
       "[200 rows x 2 columns]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "x=df.iloc[:,[2,3]]\n",
    "x"
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   "execution_count": 9,
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.scatter(df[\"Age\"],df[\"Annual Income (k$)\"],s=60)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "7ec1dc52",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x504 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import scipy.cluster.hierarchy as dg\n",
    "plt.figure(figsize=(10,7))\n",
    "dendrogram=dg.dendrogram(dg.linkage(x,method=\"ward\"))\n",
    "plt.title(\"Dendrogram\")\n",
    "plt.xlabel(\"input\")\n",
    "plt.ylabel(\"euclidean\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "30860608",
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0,\n",
       "       0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1,\n",
       "       1, 0, 0, 0, 0, 0, 1, 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,\n",
       "       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, 0, 0, 0, 0, 0,\n",
       "       0, 0], dtype=int64)"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.cluster import AgglomerativeClustering\n",
    "model=AgglomerativeClustering(n_clusters=2,affinity='euclidean',linkage=\"ward\")\n",
    "pred=model.fit_predict(x)\n",
    "pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "4d64eaf2",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4104652474372429"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.metrics import silhouette_score\n",
    "silhouette_score(x,pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "id": "ac5405cc",
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\HP\\anaconda3\\lib\\site-packages\\sklearn\\cluster\\_kmeans.py:881: UserWarning: KMeans is known to have a memory leak on Windows with MKL, when there are less chunks than available threads. You can avoid it by setting the environment variable OMP_NUM_THREADS=1.\n",
      "  warnings.warn(\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1c4b27d4160>]"
      ]
     },
     "execution_count": 32,
     "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": [
    "from sklearn.cluster import KMeans\n",
    "l=[]\n",
    "k=range(1,15)\n",
    "for i in k:\n",
    "    model=KMeans(n_clusters=i,random_state=42)\n",
    "    model.fit(x)\n",
    "    l.append(model.inertia_)\n",
    "plt.plot(k,l)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "id": "d36d1350",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.43295184273333076"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.cluster import KMeans\n",
    "model=KMeans(n_clusters=4,random_state=42)\n",
    "model.fit(x)\n",
    "y_pred=model.predict(x)\n",
    "silhouette_score(x,y_pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "id": "2ae507f7",
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.78488277, 0.61964429],\n",
       "       [0.81373347, 0.58123819],\n",
       "       [0.78086881, 0.62469505],\n",
       "       [0.8209052 , 0.57106449],\n",
       "       [0.87681241, 0.48083261],\n",
       "       [0.791285  , 0.6114475 ],\n",
       "       [0.8892878 , 0.45734801],\n",
       "       [0.787505  , 0.61630826],\n",
       "       [0.95864687, 0.28459829],\n",
       "       [0.84481908, 0.53505208],\n",
       "       [0.96206393, 0.2728241 ],\n",
       "       [0.87885343, 0.47709186],\n",
       "       [0.94537298, 0.32599068],\n",
       "       [0.76822128, 0.6401844 ],\n",
       "       [0.87970651, 0.47551703],\n",
       "       [0.73994007, 0.67267279],\n",
       "       [0.85749293, 0.51449576],\n",
       "       [0.68965517, 0.72413793],\n",
       "       [0.91453534, 0.40450601],\n",
       "       [0.83570548, 0.54917789],\n",
       "       [0.82472885, 0.56552836],\n",
       "       [0.72138732, 0.69253183],\n",
       "       [0.87862451, 0.47751332],\n",
       "       [0.77841304, 0.62775245],\n",
       "       [0.88775453, 0.46031716],\n",
       "       [0.71940146, 0.69459451],\n",
       "       [0.8490566 , 0.52830189],\n",
       "       [0.78086881, 0.62469505],\n",
       "       [0.80961044, 0.58696757],\n",
       "       [0.62139471, 0.78349768],\n",
       "       [0.89442719, 0.4472136 ],\n",
       "       [0.57346234, 0.81923192],\n",
       "       [0.84889691, 0.52855845],\n",
       "       [0.47885213, 0.87789557],\n",
       "       [0.82943693, 0.55860038],\n",
       "       [0.53687549, 0.84366149],\n",
       "       [0.77724487, 0.62919823],\n",
       "       [0.66162164, 0.74983786],\n",
       "       [0.69735496, 0.71672593],\n",
       "       [0.47551703, 0.87970651],\n",
       "       [0.86329679, 0.50469659],\n",
       "       [0.53399299, 0.8454889 ],\n",
       "       [0.776114  , 0.63059263],\n",
       "       [0.62224413, 0.78282325],\n",
       "       [0.78242422, 0.62274581],\n",
       "       [0.52409743, 0.85165832],\n",
       "       [0.78086881, 0.62469505],\n",
       "       [0.55947286, 0.82884867],\n",
       "       [0.58696757, 0.80961044],\n",
       "       [0.61257167, 0.79041505],\n",
       "       [0.7592566 , 0.65079137],\n",
       "       [0.61782155, 0.78631834],\n",
       "       [0.58480158, 0.81117638],\n",
       "       [0.80814336, 0.58898584],\n",
       "       [0.7581852 , 0.65203927],\n",
       "       [0.73780541, 0.67501346],\n",
       "       [0.75715673, 0.65323326],\n",
       "       [0.84315795, 0.53766594],\n",
       "       [0.50620057, 0.86241578],\n",
       "       [0.75521873, 0.65547286],\n",
       "       [0.83570548, 0.54917789],\n",
       "       [0.38176015, 0.92426143],\n",
       "       [0.81865747, 0.57428211],\n",
       "       [0.75430472, 0.65652448],\n",
       "       [0.79543172, 0.60604322],\n",
       "       [0.35112344, 0.93632918],\n",
       "       [0.66724832, 0.74483534],\n",
       "       [0.81696786, 0.5766832 ],\n",
       "       [0.36804845, 0.92980661],\n",
       "       [0.5547002 , 0.83205029],\n",
       "       [0.81923192, 0.57346234],\n",
       "       [0.69222518, 0.72168157],\n",
       "       [0.76822128, 0.6401844 ],\n",
       "       [0.76822128, 0.6401844 ],\n",
       "       [0.73767291, 0.67515826],\n",
       "       [0.43381562, 0.90100167],\n",
       "       [0.6401844 , 0.76822128],\n",
       "       [0.59522755, 0.80355719],\n",
       "       [0.39186207, 0.92002398],\n",
       "       [0.67198991, 0.74056031],\n",
       "       [0.72595268, 0.68774465],\n",
       "       [0.57549341, 0.81780642],\n",
       "       [0.77859618, 0.62752528],\n",
       "       [0.64846646, 0.76124323],\n",
       "       [0.36244626, 0.93200467],\n",
       "       [0.66436384, 0.74740932],\n",
       "       [0.69436917, 0.71961896],\n",
       "       [0.36007559, 0.93292313],\n",
       "       [0.5057195 , 0.86269797],\n",
       "       [0.65293962, 0.75740996],\n",
       "       [0.75532247, 0.65535332],\n",
       "       [0.29180664, 0.95647733],\n",
       "       [0.62469505, 0.78086881],\n",
       "       [0.5547002 , 0.83205029],\n",
       "       [0.47058824, 0.88235294],\n",
       "       [0.37139068, 0.92847669],\n",
       "       [0.61666198, 0.78722805],\n",
       "       [0.41036468, 0.91192151],\n",
       "       [0.61839036, 0.78587108],\n",
       "       [0.31155067, 0.95022954],\n",
       "       [0.34780682, 0.93756622],\n",
       "       [0.62005449, 0.78455875],\n",
       "       [0.73396291, 0.67918956],\n",
       "       [0.38672668, 0.92219438],\n",
       "       [0.62005449, 0.78455875],\n",
       "       [0.32080703, 0.94714458],\n",
       "       [0.72335554, 0.69047575],\n",
       "       [0.65079137, 0.7592566 ],\n",
       "       [0.73356146, 0.67962312],\n",
       "       [0.72335554, 0.69047575],\n",
       "       [0.71806768, 0.69597329],\n",
       "       [0.2887418 , 0.95740701],\n",
       "       [0.51053875, 0.85985474],\n",
       "       [0.28459829, 0.95864687],\n",
       "       [0.26687908, 0.96373002],\n",
       "       [0.28056699, 0.95983445],\n",
       "       [0.69597329, 0.71806768],\n",
       "       [0.60196378, 0.79852339],\n",
       "       [0.60568533, 0.79570426],\n",
       "       [0.59808441, 0.80143311],\n",
       "       [0.37377627, 0.92751889],\n",
       "       [0.49334011, 0.8698365 ],\n",
       "       [0.50153044, 0.86514   ],\n",
       "       [0.49205726, 0.87056284],\n",
       "       [0.31215329, 0.95003175],\n",
       "       [0.40492616, 0.91434939],\n",
       "       [0.51803469, 0.85535961],\n",
       "       [0.49084373, 0.87124763],\n",
       "       [0.63911829, 0.76910845],\n",
       "       [0.47187678, 0.88166451],\n",
       "       [0.55198701, 0.83385271],\n",
       "       [0.48144479, 0.87647642],\n",
       "       [0.32801169, 0.94467366],\n",
       "       [0.39545835, 0.91848391],\n",
       "       [0.26423515, 0.96445829],\n",
       "       [0.36919466, 0.92935209],\n",
       "       [0.51622005, 0.85645599],\n",
       "       [0.40147689, 0.91586915],\n",
       "       [0.24869025, 0.96858307],\n",
       "       [0.42756115, 0.90398643],\n",
       "       [0.60508327, 0.79616219],\n",
       "       [0.39243869, 0.91977817],\n",
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       "       [0.388057  , 0.92163538],\n",
       "       [0.30880675, 0.9511248 ],\n",
       "       [0.34174306, 0.93979342],\n",
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       "       [0.38376367, 0.92343134],\n",
       "       [0.39958542, 0.91669596],\n",
       "       [0.39958542, 0.91669596],\n",
       "       [0.48278051, 0.87574139],\n",
       "       [0.4472136 , 0.89442719],\n",
       "       [0.49132119, 0.87097847],\n",
       "       [0.43796942, 0.89898987],\n",
       "       [0.5161097 , 0.85652249],\n",
       "       [0.32711056, 0.94498607],\n",
       "       [0.42858421, 0.90350184],\n",
       "       [0.35897908, 0.93334561],\n",
       "       [0.39958542, 0.91669596],\n",
       "       [0.35897908, 0.93334561],\n",
       "       [0.57830383, 0.81582148],\n",
       "       [0.34460378, 0.93874823],\n",
       "       [0.22836934, 0.97357457],\n",
       "       [0.35743332, 0.93393866],\n",
       "       [0.50702013, 0.86193422],\n",
       "       [0.38999336, 0.92081767],\n",
       "       [0.4388353 , 0.89856752],\n",
       "       [0.3582515 , 0.93362512],\n",
       "       [0.38235179, 0.92401683],\n",
       "       [0.34520539, 0.93852716],\n",
       "       [0.41773321, 0.90856974],\n",
       "       [0.30636334, 0.95191465],\n",
       "       [0.38235179, 0.92401683],\n",
       "       [0.38235179, 0.92401683],\n",
       "       [0.50872931, 0.86092653],\n",
       "       [0.32267393, 0.94651019],\n",
       "       [0.55031336, 0.8349582 ],\n",
       "       [0.29332235, 0.9560136 ],\n",
       "       [0.53569996, 0.84440841],\n",
       "       [0.35222606, 0.93591496],\n",
       "       [0.35639585, 0.93433506],\n",
       "       [0.31328916, 0.94965778],\n",
       "       [0.42490714, 0.90523694],\n",
       "       [0.28375517, 0.95889677],\n",
       "       [0.38262654, 0.9239031 ],\n",
       "       [0.2900074 , 0.9570244 ],\n",
       "       [0.47149436, 0.88186908],\n",
       "       [0.26715174, 0.96365448],\n",
       "       [0.36983492, 0.92909748],\n",
       "       [0.32994215, 0.94400115],\n",
       "       [0.31346059, 0.94960121],\n",
       "       [0.29669082, 0.95497359],\n",
       "       [0.28032618, 0.9599048 ],\n",
       "       [0.31874305, 0.94784116],\n",
       "       [0.3646919 , 0.93112825],\n",
       "       [0.28      , 0.96      ],\n",
       "       [0.3363364 , 0.94174191],\n",
       "       [0.24615385, 0.96923077],\n",
       "       [0.22745431, 0.97378875],\n",
       "       [0.21390952, 0.97685348]])"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#scaling the data\n",
    "from sklearn.preprocessing import normalize\n",
    "x_scale=normalize(x)\n",
    "x_scale"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "id": "64ac7849",
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>0</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.784883</td>\n",
       "      <td>0.619644</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.813733</td>\n",
       "      <td>0.581238</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.780869</td>\n",
       "      <td>0.624695</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.820905</td>\n",
       "      <td>0.571064</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.876812</td>\n",
       "      <td>0.480833</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "    <tr>\n",
       "      <th>195</th>\n",
       "      <td>0.280000</td>\n",
       "      <td>0.960000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>196</th>\n",
       "      <td>0.336336</td>\n",
       "      <td>0.941742</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>197</th>\n",
       "      <td>0.246154</td>\n",
       "      <td>0.969231</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>198</th>\n",
       "      <td>0.227454</td>\n",
       "      <td>0.973789</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>199</th>\n",
       "      <td>0.213910</td>\n",
       "      <td>0.976853</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>200 rows × 2 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            0         1\n",
       "0    0.784883  0.619644\n",
       "1    0.813733  0.581238\n",
       "2    0.780869  0.624695\n",
       "3    0.820905  0.571064\n",
       "4    0.876812  0.480833\n",
       "..        ...       ...\n",
       "195  0.280000  0.960000\n",
       "196  0.336336  0.941742\n",
       "197  0.246154  0.969231\n",
       "198  0.227454  0.973789\n",
       "199  0.213910  0.976853\n",
       "\n",
       "[200 rows x 2 columns]"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "scale_data=pd.DataFrame(x_scale)\n",
    "scale_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "id": "3dbe5177",
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1c4b281c1c0>"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.scatter(scale_data[0],scale_data[1],s=60)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "id": "44d6ee32",
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0,\n",
       "       1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0,\n",
       "       0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0,\n",
       "       0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1,\n",
       "       1, 0, 0, 0, 0, 0, 1, 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,\n",
       "       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, 0, 0, 0, 0, 0,\n",
       "       0, 0], dtype=int64)"
      ]
     },
     "execution_count": 42,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from sklearn.cluster import AgglomerativeClustering\n",
    "model=AgglomerativeClustering(n_clusters=2,affinity='euclidean',linkage=\"ward\")\n",
    "pred=model.fit_predict(x_scale)\n",
    "pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "id": "4f92e0d7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.6332340091836156"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "silhouette_score(x_scale,pred)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "id": "2d594795",
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,\n",
       "       1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0,\n",
       "       1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 0,\n",
       "       0, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0,\n",
       "       0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1,\n",
       "       1, 0, 0, 0, 0, 0, 1, 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,\n",
       "       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, 0, 0, 0, 0, 0,\n",
       "       0, 0], dtype=int64)"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pred"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "id": "301ec663",
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 19,  15],\n",
       "       [ 21,  15],\n",
       "       [ 20,  16],\n",
       "       [ 23,  16],\n",
       "       [ 31,  17],\n",
       "       [ 22,  17],\n",
       "       [ 35,  18],\n",
       "       [ 23,  18],\n",
       "       [ 64,  19],\n",
       "       [ 30,  19],\n",
       "       [ 67,  19],\n",
       "       [ 35,  19],\n",
       "       [ 58,  20],\n",
       "       [ 24,  20],\n",
       "       [ 37,  20],\n",
       "       [ 22,  20],\n",
       "       [ 35,  21],\n",
       "       [ 20,  21],\n",
       "       [ 52,  23],\n",
       "       [ 35,  23],\n",
       "       [ 35,  24],\n",
       "       [ 25,  24],\n",
       "       [ 46,  25],\n",
       "       [ 31,  25],\n",
       "       [ 54,  28],\n",
       "       [ 29,  28],\n",
       "       [ 45,  28],\n",
       "       [ 35,  28],\n",
       "       [ 40,  29],\n",
       "       [ 23,  29],\n",
       "       [ 60,  30],\n",
       "       [ 21,  30],\n",
       "       [ 53,  33],\n",
       "       [ 18,  33],\n",
       "       [ 49,  33],\n",
       "       [ 21,  33],\n",
       "       [ 42,  34],\n",
       "       [ 30,  34],\n",
       "       [ 36,  37],\n",
       "       [ 20,  37],\n",
       "       [ 65,  38],\n",
       "       [ 24,  38],\n",
       "       [ 48,  39],\n",
       "       [ 31,  39],\n",
       "       [ 49,  39],\n",
       "       [ 24,  39],\n",
       "       [ 50,  40],\n",
       "       [ 27,  40],\n",
       "       [ 29,  40],\n",
       "       [ 31,  40],\n",
       "       [ 49,  42],\n",
       "       [ 33,  42],\n",
       "       [ 31,  43],\n",
       "       [ 59,  43],\n",
       "       [ 50,  43],\n",
       "       [ 47,  43],\n",
       "       [ 51,  44],\n",
       "       [ 69,  44],\n",
       "       [ 27,  46],\n",
       "       [ 53,  46],\n",
       "       [ 70,  46],\n",
       "       [ 19,  46],\n",
       "       [ 67,  47],\n",
       "       [ 54,  47],\n",
       "       [ 63,  48],\n",
       "       [ 18,  48],\n",
       "       [ 43,  48],\n",
       "       [ 68,  48],\n",
       "       [ 19,  48],\n",
       "       [ 32,  48],\n",
       "       [ 70,  49],\n",
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       "       [ 60,  50],\n",
       "       [ 60,  50],\n",
       "       [ 59,  54],\n",
       "       [ 26,  54],\n",
       "       [ 45,  54],\n",
       "       [ 40,  54],\n",
       "       [ 23,  54],\n",
       "       [ 49,  54],\n",
       "       [ 57,  54],\n",
       "       [ 38,  54],\n",
       "       [ 67,  54],\n",
       "       [ 46,  54],\n",
       "       [ 21,  54],\n",
       "       [ 48,  54],\n",
       "       [ 55,  57],\n",
       "       [ 22,  57],\n",
       "       [ 34,  58],\n",
       "       [ 50,  58],\n",
       "       [ 68,  59],\n",
       "       [ 18,  59],\n",
       "       [ 48,  60],\n",
       "       [ 40,  60],\n",
       "       [ 32,  60],\n",
       "       [ 24,  60],\n",
       "       [ 47,  60],\n",
       "       [ 27,  60],\n",
       "       [ 48,  61],\n",
       "       [ 20,  61],\n",
       "       [ 23,  62],\n",
       "       [ 49,  62],\n",
       "       [ 67,  62],\n",
       "       [ 26,  62],\n",
       "       [ 49,  62],\n",
       "       [ 21,  62],\n",
       "       [ 66,  63],\n",
       "       [ 54,  63],\n",
       "       [ 68,  63],\n",
       "       [ 66,  63],\n",
       "       [ 65,  63],\n",
       "       [ 19,  63],\n",
       "       [ 38,  64],\n",
       "       [ 19,  64],\n",
       "       [ 18,  65],\n",
       "       [ 19,  65],\n",
       "       [ 63,  65],\n",
       "       [ 49,  65],\n",
       "       [ 51,  67],\n",
       "       [ 50,  67],\n",
       "       [ 27,  67],\n",
       "       [ 38,  67],\n",
       "       [ 40,  69],\n",
       "       [ 39,  69],\n",
       "       [ 23,  70],\n",
       "       [ 31,  70],\n",
       "       [ 43,  71],\n",
       "       [ 40,  71],\n",
       "       [ 59,  71],\n",
       "       [ 38,  71],\n",
       "       [ 47,  71],\n",
       "       [ 39,  71],\n",
       "       [ 25,  72],\n",
       "       [ 31,  72],\n",
       "       [ 20,  73],\n",
       "       [ 29,  73],\n",
       "       [ 44,  73],\n",
       "       [ 32,  73],\n",
       "       [ 19,  74],\n",
       "       [ 35,  74],\n",
       "       [ 57,  75],\n",
       "       [ 32,  75],\n",
       "       [ 28,  76],\n",
       "       [ 32,  76],\n",
       "       [ 25,  77],\n",
       "       [ 28,  77],\n",
       "       [ 48,  77],\n",
       "       [ 32,  77],\n",
       "       [ 34,  78],\n",
       "       [ 34,  78],\n",
       "       [ 43,  78],\n",
       "       [ 39,  78],\n",
       "       [ 44,  78],\n",
       "       [ 38,  78],\n",
       "       [ 47,  78],\n",
       "       [ 27,  78],\n",
       "       [ 37,  78],\n",
       "       [ 30,  78],\n",
       "       [ 34,  78],\n",
       "       [ 30,  78],\n",
       "       [ 56,  79],\n",
       "       [ 29,  79],\n",
       "       [ 19,  81],\n",
       "       [ 31,  81],\n",
       "       [ 50,  85],\n",
       "       [ 36,  85],\n",
       "       [ 42,  86],\n",
       "       [ 33,  86],\n",
       "       [ 36,  87],\n",
       "       [ 32,  87],\n",
       "       [ 40,  87],\n",
       "       [ 28,  87],\n",
       "       [ 36,  87],\n",
       "       [ 36,  87],\n",
       "       [ 52,  88],\n",
       "       [ 30,  88],\n",
       "       [ 58,  88],\n",
       "       [ 27,  88],\n",
       "       [ 59,  93],\n",
       "       [ 35,  93],\n",
       "       [ 37,  97],\n",
       "       [ 32,  97],\n",
       "       [ 46,  98],\n",
       "       [ 29,  98],\n",
       "       [ 41,  99],\n",
       "       [ 30,  99],\n",
       "       [ 54, 101],\n",
       "       [ 28, 101],\n",
       "       [ 41, 103],\n",
       "       [ 36, 103],\n",
       "       [ 34, 103],\n",
       "       [ 32, 103],\n",
       "       [ 33, 113],\n",
       "       [ 38, 113],\n",
       "       [ 47, 120],\n",
       "       [ 35, 120],\n",
       "       [ 45, 126],\n",
       "       [ 32, 126],\n",
       "       [ 32, 137],\n",
       "       [ 30, 137]], dtype=int64)"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x=df.iloc[:,[2,3]]\n",
    "x=x.values\n",
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "id": "e328d876",
   "metadata": {},
   "outputs": [],
   "source": [
    "x1=x[pred==0,0]\n",
    "y1=x[pred==0,1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "id": "e5776dd6",
   "metadata": {},
   "outputs": [],
   "source": [
    "x2=x[pred==1,0]\n",
    "y2=x[pred==1,1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "id": "10b5d1b7",
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(x1,y1,s=60,label=\"cluster 0\")\n",
    "plt.scatter(x2,y2,s=60,label=\"cluster 1\")\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "45d4275b",
   "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": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}