Clustering(Kmeans+Hierarchical).ipynb

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      "source": [
        "import pandas as pd\n",
        "import numpy as np\n",
        "from matplotlib import pyplot as plt\n",
        "from sklearn.cluster import AgglomerativeClustering\n",
        "import scipy.cluster.hierarchy as sch"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "df = pd.read_csv('/content/cities_r2.csv')"
      ],
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      "outputs": []
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            "text/plain": [
              "      name_of_city  state_code      state_name  dist_code  population_total  \\\n",
              "0          Abohar            3          PUNJAB          9            145238   \n",
              "1        Achalpur           27     MAHARASHTRA          7            112293   \n",
              "2        Adilabad           28  ANDHRA PRADESH          1            117388   \n",
              "3       Adityapur           20       JHARKHAND         24            173988   \n",
              "4           Adoni           28  ANDHRA PRADESH         21            166537   \n",
              "..             ...         ...             ...        ...               ...   \n",
              "488  Vizianagaram           28  ANDHRA PRADESH         12            227533   \n",
              "489      Warangal           28  ANDHRA PRADESH          9            620116   \n",
              "490        Wardha           27     MAHARASHTRA          8            105543   \n",
              "491   Yamunanagar            6         HARYANA          3            216628   \n",
              "492      Yavatmal           27     MAHARASHTRA         14            116714   \n",
              "\n",
              "     population_male  population_female  0-6_population_total  \\\n",
              "0              76840              68398                 15870   \n",
              "1              58256              54037                 11810   \n",
              "2              59232              58156                 13103   \n",
              "3              91495              82493                 23042   \n",
              "4              82743              83794                 18406   \n",
              "..               ...                ...                   ...   \n",
              "488           111596             115937                 20487   \n",
              "489           310400             309716                 55392   \n",
              "490            53241              52302                  9754   \n",
              "491           115404             101224                 22905   \n",
              "492            58717              57997                 11081   \n",
              "\n",
              "     0-6_population_male  0-6_population_female  ...  literates_female  \\\n",
              "0                   8587                   7283  ...             44972   \n",
              "1                   6186                   5624  ...             43086   \n",
              "2                   6731                   6372  ...             37660   \n",
              "3                  12063                  10979  ...             54515   \n",
              "4                   9355                   9051  ...             45089   \n",
              "..                   ...                    ...  ...               ...   \n",
              "488                10495                   9992  ...             80306   \n",
              "489                28434                  26958  ...            217136   \n",
              "490                 5139                   4615  ...             43339   \n",
              "491                12556                  10349  ...             74255   \n",
              "492                 5894                   5187  ...             46561   \n",
              "\n",
              "     sex_ratio  child_sex_ratio  effective_literacy_rate_total  \\\n",
              "0          890              848                          79.86   \n",
              "1          928              909                          91.99   \n",
              "2          982              947                          80.51   \n",
              "3          902              910                          83.46   \n",
              "4         1013              968                          68.38   \n",
              "..         ...              ...                            ...   \n",
              "488       1039              952                          81.85   \n",
              "489        998              948                          84.16   \n",
              "490        982              898                          94.05   \n",
              "491        877              824                          85.91   \n",
              "492        988              880                          91.81   \n",
              "\n",
              "     effective_literacy_rate_male  effective_literacy_rate_female  \\\n",
              "0                           85.49                           73.59   \n",
              "1                           94.77                           89.00   \n",
              "2                           88.18                           72.73   \n",
              "3                           89.98                           76.23   \n",
              "4                           76.58                           60.33   \n",
              "..                            ...                             ...   \n",
              "488                         88.18                           75.80   \n",
              "489                         91.54                           76.79   \n",
              "490                         97.19                           90.88   \n",
              "491                         89.61                           81.71   \n",
              "492                         95.45                           88.17   \n",
              "\n",
              "                  location  total_graduates male_graduates  female_graduates  \n",
              "0    30.1452928,74.1993043            16287           8612              7675  \n",
              "1     21.257584,77.5086754             8863           5269              3594  \n",
              "2     19.0809075,79.560344            10565           6797              3768  \n",
              "3    22.7834741,86.1576889            19225          12189              7036  \n",
              "4    15.6322227,77.2728368            11902           7871              4031  \n",
              "..                     ...              ...            ...               ...  \n",
              "488  18.1066576,83.3955506            30656          19173             11483  \n",
              "489  17.9689008,79.5940544           109613          69507             40106  \n",
              "490   20.745319,78.6021946            19363          10645              8718  \n",
              "491  30.1290485,77.2673901            29803          14349             15454  \n",
              "492  20.3887937,78.1204073            13511           7397              6114  \n",
              "\n",
              "[493 rows x 22 columns]"
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              "      <th></th>\n",
              "      <th>name_of_city</th>\n",
              "      <th>state_code</th>\n",
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              "      <th>0</th>\n",
              "      <td>Abohar</td>\n",
              "      <td>3</td>\n",
              "      <td>PUNJAB</td>\n",
              "      <td>9</td>\n",
              "      <td>145238</td>\n",
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              "      <td>848</td>\n",
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              "      <td>7675</td>\n",
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              "      <th>1</th>\n",
              "      <td>Achalpur</td>\n",
              "      <td>27</td>\n",
              "      <td>MAHARASHTRA</td>\n",
              "      <td>7</td>\n",
              "      <td>112293</td>\n",
              "      <td>58256</td>\n",
              "      <td>54037</td>\n",
              "      <td>11810</td>\n",
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              "      <th>2</th>\n",
              "      <td>Adilabad</td>\n",
              "      <td>28</td>\n",
              "      <td>ANDHRA PRADESH</td>\n",
              "      <td>1</td>\n",
              "      <td>117388</td>\n",
              "      <td>59232</td>\n",
              "      <td>58156</td>\n",
              "      <td>13103</td>\n",
              "      <td>6731</td>\n",
              "      <td>6372</td>\n",
              "      <td>...</td>\n",
              "      <td>37660</td>\n",
              "      <td>982</td>\n",
              "      <td>947</td>\n",
              "      <td>80.51</td>\n",
              "      <td>88.18</td>\n",
              "      <td>72.73</td>\n",
              "      <td>19.0809075,79.560344</td>\n",
              "      <td>10565</td>\n",
              "      <td>6797</td>\n",
              "      <td>3768</td>\n",
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              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>Adityapur</td>\n",
              "      <td>20</td>\n",
              "      <td>JHARKHAND</td>\n",
              "      <td>24</td>\n",
              "      <td>173988</td>\n",
              "      <td>91495</td>\n",
              "      <td>82493</td>\n",
              "      <td>23042</td>\n",
              "      <td>12063</td>\n",
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              "      <td>902</td>\n",
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              "      <td>89.98</td>\n",
              "      <td>76.23</td>\n",
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              "      <td>19225</td>\n",
              "      <td>12189</td>\n",
              "      <td>7036</td>\n",
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              "      <th>4</th>\n",
              "      <td>Adoni</td>\n",
              "      <td>28</td>\n",
              "      <td>ANDHRA PRADESH</td>\n",
              "      <td>21</td>\n",
              "      <td>166537</td>\n",
              "      <td>82743</td>\n",
              "      <td>83794</td>\n",
              "      <td>18406</td>\n",
              "      <td>9355</td>\n",
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              "      <td>1013</td>\n",
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              "      <td>76.58</td>\n",
              "      <td>60.33</td>\n",
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              "      <th>488</th>\n",
              "      <td>Vizianagaram</td>\n",
              "      <td>28</td>\n",
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              "      <td>12</td>\n",
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              "      <td>1039</td>\n",
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              "      <td>81.85</td>\n",
              "      <td>88.18</td>\n",
              "      <td>75.80</td>\n",
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              "      <td>30656</td>\n",
              "      <td>19173</td>\n",
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              "      <th>489</th>\n",
              "      <td>Warangal</td>\n",
              "      <td>28</td>\n",
              "      <td>ANDHRA PRADESH</td>\n",
              "      <td>9</td>\n",
              "      <td>620116</td>\n",
              "      <td>310400</td>\n",
              "      <td>309716</td>\n",
              "      <td>55392</td>\n",
              "      <td>28434</td>\n",
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              "      <td>217136</td>\n",
              "      <td>998</td>\n",
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              "      <td>91.54</td>\n",
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              "      <td>109613</td>\n",
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              "      <th>490</th>\n",
              "      <td>Wardha</td>\n",
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              "      <td>MAHARASHTRA</td>\n",
              "      <td>8</td>\n",
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              "      <td>19363</td>\n",
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              "      <th>491</th>\n",
              "      <td>Yamunanagar</td>\n",
              "      <td>6</td>\n",
              "      <td>HARYANA</td>\n",
              "      <td>3</td>\n",
              "      <td>216628</td>\n",
              "      <td>115404</td>\n",
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              "          document.querySelector('#df-f38f535b-1564-4fca-aec3-8d99faee89dd button.colab-df-convert');\n",
              "        buttonEl.style.display =\n",
              "          google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
              "\n",
              "        async function convertToInteractive(key) {\n",
              "          const element = document.querySelector('#df-f38f535b-1564-4fca-aec3-8d99faee89dd');\n",
              "          const dataTable =\n",
              "            await google.colab.kernel.invokeFunction('convertToInteractive',\n",
              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
              "            + ' to learn more about interactive tables.';\n",
              "          element.innerHTML = '';\n",
              "          dataTable['output_type'] = 'display_data';\n",
              "          await google.colab.output.renderOutput(dataTable, element);\n",
              "          const docLink = document.createElement('div');\n",
              "          docLink.innerHTML = docLinkHtml;\n",
              "          element.appendChild(docLink);\n",
              "        }\n",
              "      </script>\n",
              "    </div>\n",
              "  </div>\n",
              "  "
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "df.dtypes"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "GGCRJHDSudik",
        "outputId": "0f9199ad-2ed2-46a4-b959-f4689fd14a36"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "name_of_city                       object\n",
              "state_code                          int64\n",
              "state_name                         object\n",
              "dist_code                           int64\n",
              "population_total                    int64\n",
              "population_male                     int64\n",
              "population_female                   int64\n",
              "0-6_population_total                int64\n",
              "0-6_population_male                 int64\n",
              "0-6_population_female               int64\n",
              "literates_total                     int64\n",
              "literates_male                      int64\n",
              "literates_female                    int64\n",
              "sex_ratio                           int64\n",
              "child_sex_ratio                     int64\n",
              "effective_literacy_rate_total     float64\n",
              "effective_literacy_rate_male      float64\n",
              "effective_literacy_rate_female    float64\n",
              "location                           object\n",
              "total_graduates                     int64\n",
              "male_graduates                      int64\n",
              "female_graduates                    int64\n",
              "dtype: object"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "df['effective_literacy_rate_total']= df['effective_literacy_rate_total'].astype(int)\n",
        "df['effective_literacy_rate_male']= df['effective_literacy_rate_male'].astype(int)\n",
        "df['effective_literacy_rate_female']= df['effective_literacy_rate_female'].astype(int)"
      ],
      "metadata": {
        "id": "o925S551umM4"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "df['name_of_city']= df['name_of_city'].factorize()[0]\n",
        "df['state_name']= df['state_name'].factorize()[0]\n",
        "df['location']= df['location'].factorize()[0]"
      ],
      "metadata": {
        "id": "xUyAYuvxu1Fa"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "df['name_of_city']= df['name_of_city'].astype(int)\n",
        "df['state_name']= df['state_name'].astype(int)\n",
        "df['location']= df['location'].astype(int)"
      ],
      "metadata": {
        "id": "YavEjOk2vMQz"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "df.dtypes"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "TUa3OnNqvSx7",
        "outputId": "3ddf2121-38b5-4612-edab-03c07711a0bc"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "name_of_city                      int64\n",
              "state_code                        int64\n",
              "state_name                        int64\n",
              "dist_code                         int64\n",
              "population_total                  int64\n",
              "population_male                   int64\n",
              "population_female                 int64\n",
              "0-6_population_total              int64\n",
              "0-6_population_male               int64\n",
              "0-6_population_female             int64\n",
              "literates_total                   int64\n",
              "literates_male                    int64\n",
              "literates_female                  int64\n",
              "sex_ratio                         int64\n",
              "child_sex_ratio                   int64\n",
              "effective_literacy_rate_total     int64\n",
              "effective_literacy_rate_male      int64\n",
              "effective_literacy_rate_female    int64\n",
              "location                          int64\n",
              "total_graduates                   int64\n",
              "male_graduates                    int64\n",
              "female_graduates                  int64\n",
              "dtype: object"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "X = df.iloc[:, [15, 16]].values\n",
        "print(X)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "aFuxe1Npt0aA",
        "outputId": "d0f5495d-8b0b-4953-b4c9-c0f41044ef9e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
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          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "dendrogram = sch.dendrogram(sch.linkage(X, method='ward'))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "UdELybzpvp2I",
        "outputId": "d280f95a-0f16-4610-8e7a-86a63e10c65c"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "model = AgglomerativeClustering(n_clusters=4, affinity='euclidean', linkage='ward')\n",
        "model.fit(X)\n",
        "labels = model.labels_"
      ],
      "metadata": {
        "id": "j9PsvxWct0cM"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "labels"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "42TJyU-kt0et",
        "outputId": "5bb0c866-1488-45b2-968a-ada8d4e831c8"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([2, 3, 2, 2, 0, 3, 0, 1, 3, 3, 1, 2, 3, 3, 3, 0, 1, 1, 1, 1, 1, 3,\n",
              "       1, 1, 3, 1, 1, 0, 3, 2, 2, 2, 1, 3, 1, 1, 1, 1, 3, 0, 1, 1, 3, 0,\n",
              "       1, 1, 1, 2, 3, 3, 2, 1, 1, 1, 2, 3, 3, 2, 1, 0, 1, 2, 1, 1, 1, 1,\n",
              "       1, 2, 1, 2, 3, 2, 1, 2, 3, 2, 1, 1, 2, 2, 2, 1, 1, 1, 1, 1, 2, 1,\n",
              "       2, 2, 1, 1, 3, 1, 3, 1, 1, 3, 2, 2, 2, 1, 1, 3, 1, 3, 0, 2, 1, 1,\n",
              "       2, 1, 2, 3, 0, 1, 3, 2, 1, 3, 1, 3, 1, 0, 1, 1, 1, 2, 3, 1, 3, 0,\n",
              "       2, 1, 2, 3, 2, 1, 2, 1, 2, 1, 3, 1, 1, 1, 1, 2, 0, 2, 1, 1, 1, 2,\n",
              "       3, 3, 1, 1, 0, 2, 1, 1, 2, 1, 1, 0, 2, 0, 2, 1, 2, 3, 2, 2, 2, 1,\n",
              "       1, 1, 1, 1, 2, 1, 3, 1, 2, 3, 1, 2, 2, 2, 2, 2, 1, 3, 1, 3, 2, 1,\n",
              "       2, 1, 2, 1, 2, 1, 1, 3, 1, 2, 1, 2, 2, 3, 2, 1, 1, 2, 1, 1, 3, 1,\n",
              "       3, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 2, 1, 0, 2, 2, 2, 2, 2, 1, 2,\n",
              "       1, 2, 2, 2, 1, 1, 1, 1, 3, 2, 2, 3, 1, 1, 1, 2, 2, 2, 2, 1, 1, 1,\n",
              "       3, 2, 1, 0, 2, 0, 2, 3, 1, 3, 1, 3, 1, 1, 3, 3, 2, 3, 3, 2, 1, 1,\n",
              "       1, 2, 1, 1, 2, 2, 3, 3, 3, 1, 3, 2, 1, 1, 0, 2, 1, 1, 3, 1, 2, 2,\n",
              "       3, 2, 3, 2, 2, 3, 2, 0, 2, 1, 1, 2, 2, 2, 1, 2, 2, 1, 1, 1, 1, 3,\n",
              "       1, 0, 2, 3, 3, 1, 1, 1, 1, 2, 1, 2, 3, 3, 3, 1, 1, 2, 3, 3, 2, 1,\n",
              "       3, 3, 2, 2, 1, 3, 3, 1, 2, 3, 2, 1, 3, 1, 3, 1, 1, 1, 1, 1, 0, 3,\n",
              "       2, 1, 1, 2, 1, 3, 3, 1, 0, 2, 2, 2, 2, 1, 1, 1, 1, 3, 1, 1, 3, 2,\n",
              "       0, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 3, 0, 3, 3, 2, 2, 1, 1, 0, 1,\n",
              "       2, 2, 3, 1, 2, 1, 1, 3, 1, 0, 2, 2, 3, 3, 1, 2, 2, 3, 1, 2, 2, 2,\n",
              "       1, 1, 1, 3, 1, 0, 2, 2, 1, 1, 1, 1, 2, 0, 3, 2, 3, 1, 3, 3, 3, 3,\n",
              "       3, 3, 1, 1, 2, 1, 2, 0, 1, 3, 1, 3, 1, 1, 2, 2, 3, 3, 3, 2, 3, 1,\n",
              "       2, 1, 2, 2, 2, 1, 3, 1, 3])"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "plt.scatter(X[labels==0, 0], X[labels==0, 1], s=50, marker='o', color='red')\n",
        "plt.scatter(X[labels==1, 0], X[labels==1, 1], s=50, marker='o', color='blue')\n",
        "plt.scatter(X[labels==2, 0], X[labels==2, 1], s=50, marker='o', color='green')\n",
        "plt.scatter(X[labels==3, 0], X[labels==3, 1], s=50, marker='o', color='purple')\n",
        "# plt.scatter(X[labels==4, 0], X[labels==4, 1], s=50, marker='o', color='orange')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "fBIh24f8t0g_",
        "outputId": "44cf7cd6-76e8-4f80-dc1a-7905bbbd921e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Using the elbow method to find the optimal number of clusters\n",
        "from sklearn.cluster import KMeans\n",
        "wcss = []\n",
        "for i in range(1, 11):\n",
        "    kmeans = KMeans(n_clusters = i, init = 'k-means++', random_state = 42)\n",
        "    kmeans.fit(X)\n",
        "    wcss.append(kmeans.inertia_)\n",
        "plt.plot(range(1, 11), wcss)\n",
        "plt.title('The Elbow Method')\n",
        "plt.xlabel('Number of clusters')\n",
        "plt.ylabel('WCSS')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "pvcGOWBAt0jU",
        "outputId": "395fd973-90d5-4c95-9e5e-1b4e7671a211"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Fitting K-Means to the dataset\n",
        "kmeans = KMeans(n_clusters = 4, init = 'k-means++', random_state = 123)\n",
        "y_kmeans = kmeans.fit_predict(X)\n",
        "\n",
        "# Visualising the clusters\n",
        "plt.scatter(X[y_kmeans == 0, 0], X[y_kmeans == 0, 1], s = 50, c = 'red', label = 'Cluster 1')\n",
        "plt.scatter(X[y_kmeans == 1, 0], X[y_kmeans == 1, 1], s = 50, c = 'blue', label = 'Cluster 2')\n",
        "plt.scatter(X[y_kmeans == 2, 0], X[y_kmeans == 2, 1], s = 50, c = 'green', label = 'Cluster 3')\n",
        "plt.scatter(X[y_kmeans == 3, 0], X[y_kmeans == 3, 1], s = 50, c = 'cyan', label = 'Cluster 4')\n",
        "# plt.scatter(X[y_kmeans == 4, 0], X[y_kmeans == 4, 1], s = 50, c = 'magenta', label = 'Cluster 5')\n",
        "plt.scatter(kmeans.cluster_centers_[:, 0], kmeans.cluster_centers_[:, 1], s = 100, c = 'yellow', label = 'Centroids')\n",
        "plt.title('Clusters of customers')\n",
        "plt.xlabel('effective literacy rate')\n",
        "plt.ylabel('Group of Customers)')\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "bIpZNvwLt0l6",
        "outputId": "e555928e-5297-4617-f4d9-0b89d3b4588e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn import metrics\n",
        "score=metrics.silhouette_score(X, labels, metric='euclidean')\n",
        "score"
      ],
      "metadata": {
        "id": "4mRomqvYt0oM",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b0cf622f-9fdb-48aa-eefe-162759b68624"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.4697448984497529"
            ]
          },
          "metadata": {},
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn import metrics\n",
        "score=metrics.silhouette_score(X, y_kmeans, metric='euclidean')\n",
        "score"
      ],
      "metadata": {
        "id": "Ieex7hB5t0qt",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "3e30e673-513d-4ccc-a64a-146b5d6f0df9"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.4818992931281545"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "Z = df.iloc[:, [19, 20]].values\n",
        "print(Z)"
      ],
      "metadata": {
        "id": "af5uwDR0t0tW",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "92c85565-e359-4e85-8b34-ece4a217faed"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[[  16287    8612]\n",
            " [   8863    5269]\n",
            " [  10565    6797]\n",
            " [  19225   12189]\n",
            " [  11902    7871]\n",
            " [  52711   30215]\n",
            " [ 185813  106082]\n",
            " [ 769858  435267]\n",
            " [  51661   29832]\n",
            " [  26832   14900]\n",
            " [  77989   42454]\n",
            " [   9745    5811]\n",
            " [  49715   28812]\n",
            " [  45971   25463]\n",
            " [  22263    9900]\n",
            " [  99341   55965]\n",
            " [ 233129  138248]\n",
            " [  58764   35297]\n",
            " [  34943   17809]\n",
            " [  20618   10689]\n",
            " [  26596   14444]\n",
            " [  97186   52224]\n",
            " [  20857   12369]\n",
            " [   7813    5076]\n",
            " [  91996   51456]\n",
            " [  11305    6579]\n",
            " [ 140359   69241]\n",
            " [  13879    7635]\n",
            " [  29803   17331]\n",
            " [  43700   27392]\n",
            " [  12666    7291]\n",
            " [  35354   25045]\n",
            " [  65625   40231]\n",
            " [  11992    7093]\n",
            " [  13141    9371]\n",
            " [ 159308   96576]\n",
            " [  51647   27742]\n",
            " [  19911   11691]\n",
            " [  25115   13878]\n",
            " [   3744    2756]\n",
            " [  14090    9038]\n",
            " [  22521   13025]\n",
            " [  32154   19679]\n",
            " [  20490   11537]\n",
            " [  17224   10311]\n",
            " [  23170   14071]\n",
            " [  16114   10252]\n",
            " [  36100   22170]\n",
            " [  12354    7562]\n",
            " [  23732   14538]\n",
            " [  24015   15215]\n",
            " [  19082   12321]\n",
            " [   8566    5264]\n",
            " [  13852    7837]\n",
            " [  11553    7362]\n",
            " [  49711   28274]\n",
            " [  45516   27143]\n",
            " [  12672    7191]\n",
            " [  52387   32325]\n",
            " [ 110691   61065]\n",
            " [  17589   10953]\n",
            " [  12665    6213]\n",
            " [  29910   17514]\n",
            " [  13351    8564]\n",
            " [  20037   12083]\n",
            " [  20183   12071]\n",
            " [  16436    8120]\n",
            " [  43428   22471]\n",
            " [  13767    8257]\n",
            " [  24616   16492]\n",
            " [  64200   37682]\n",
            " [  36855   23011]\n",
            " [1591163  908363]\n",
            " [  13438    9372]\n",
            " [  17125    9918]\n",
            " [  13311    8191]\n",
            " [  12406    7066]\n",
            " [   9225    5743]\n",
            " [  49656   33692]\n",
            " [   8348    5164]\n",
            " [  33411   20734]\n",
            " [  14059    8210]\n",
            " [  29055   18147]\n",
            " [  51875   30315]\n",
            " [  81620   43751]\n",
            " [  41788   24856]\n",
            " [  18298   11541]\n",
            " [  20470   13748]\n",
            " [  10135    6331]\n",
            " [  24688   14404]\n",
            " [  28123   17068]\n",
            " [ 282813  155418]\n",
            " [ 200788  121563]\n",
            " [  16457    9536]\n",
            " [  19815   11257]\n",
            " [  19030   12252]\n",
            " [  25910   16824]\n",
            " [  65863   35756]\n",
            " [  28092   20487]\n",
            " [  37265   24355]\n",
            " [  73369   44965]\n",
            " [  67396   38607]\n",
            " [  61034   39496]\n",
            " [  10286    6684]\n",
            " [   4578    2997]\n",
            " [  50782   32587]\n",
            " [  19204   10705]\n",
            " [  32546   18503]\n",
            " [  13148    8081]\n",
            " [  17914   11136]\n",
            " [  15203    9325]\n",
            " [  12464    8920]\n",
            " [   7167    4654]\n",
            " [  30933   17942]\n",
            " [  15436    8436]\n",
            " [ 189312  101491]\n",
            " [  37686   21317]\n",
            " [  22852   15710]\n",
            " [  15277   10431]\n",
            " [ 879695  487428]\n",
            " [  20807   12484]\n",
            " [  28233   16058]\n",
            " [  13204    7441]\n",
            " [   9526    6302]\n",
            " [  16857   10213]\n",
            " [  16833    9875]\n",
            " [  21345   12973]\n",
            " [   8756    5873]\n",
            " [ 168145   87123]\n",
            " [  21572   12022]\n",
            " [ 110147   66347]\n",
            " [   2532    1703]\n",
            " [  17134    9918]\n",
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            " [  13511    7397]]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Using the elbow method to find the optimal number of clusters\n",
        "from sklearn.cluster import KMeans\n",
        "wcss = []\n",
        "for i in range(1, 11):\n",
        "    kmeans = KMeans(n_clusters = i, init = 'k-means++', random_state = 42)\n",
        "    kmeans.fit(Z)\n",
        "    wcss.append(kmeans.inertia_)\n",
        "plt.plot(range(1, 11), wcss)\n",
        "plt.title('The Elbow Method')\n",
        "plt.xlabel('Number of clusters')\n",
        "plt.ylabel('WCSS')\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "NdvIZ1lWKhkQ",
        "outputId": "f3a19b59-fb11-41ac-ae2c-c1336eadaf6d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Fitting K-Means to the dataset\n",
        "kmeans = KMeans(n_clusters = 4, init = 'k-means++', random_state = 43)\n",
        "y_kmeans = kmeans.fit_predict(Z)\n",
        "\n",
        "# Visualising the clusters\n",
        "plt.scatter(Z[y_kmeans == 0, 0], Z[y_kmeans == 0, 1], s = 50, c = 'red', label = 'Cluster 1')\n",
        "plt.scatter(Z[y_kmeans == 1, 0], Z[y_kmeans == 1, 1], s = 50, c = 'blue', label = 'Cluster 2')\n",
        "plt.scatter(Z[y_kmeans == 2, 0], Z[y_kmeans == 2, 1], s = 50, c = 'green', label = 'Cluster 3')\n",
        "plt.scatter(Z[y_kmeans == 3, 0], Z[y_kmeans == 3, 1], s = 50, c = 'cyan', label = 'Cluster 4')\n",
        "# plt.scatter(X[y_kmeans == 4, 0], X[y_kmeans == 4, 1], s = 50, c = 'magenta', label = 'Cluster 5')\n",
        "plt.scatter(kmeans.cluster_centers_[:, 0], kmeans.cluster_centers_[:, 1], s = 100, c = 'yellow', label = 'Centroids')\n",
        "plt.title('Clusters of customers')\n",
        "plt.xlabel('total graduate')\n",
        "plt.ylabel('Group of Customers)')\n",
        "plt.legend()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "id": "hblg1UtXKhnX",
        "outputId": "70a3f681-4a73-4066-b7a1-2ec309c321e3"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [],
      "metadata": {
        "id": "NsdYwbA6LFPh"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn import metrics\n",
        "score=metrics.silhouette_score(Z, y_kmeans, metric='euclidean')\n",
        "score"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "HbyvTr5tKhqP",
        "outputId": "988653bf-63af-49c8-9161-12bd4d4f3192"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.8079708170511092"
            ]
          },
          "metadata": {},
          "execution_count": 24
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "labels = kmeans.labels_"
      ],
      "metadata": {
        "id": "2ciXHXK6KhtL"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "labels"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "n8MxbDIQKhwE",
        "outputId": "6474700d-1359-4366-fba2-029b65598133"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0, 0, 0, 0, 0, 0, 3, 2, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0,\n",
              "       0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0,\n",
              "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0,\n",
              "       0, 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, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
              "       0, 0, 0, 0, 0, 3, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 3, 0,\n",
              "       0, 0, 0, 0, 0, 0, 0, 3, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0,\n",
              "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
              "       0, 0, 0, 0, 0, 0, 0, 3, 2, 1, 0, 0, 0, 0, 0, 0, 3, 3, 3, 0, 0, 0,\n",
              "       0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0,\n",
              "       0, 3, 3, 0, 0, 2, 3, 0, 0, 0, 0, 3, 0, 3, 0, 0, 0, 0, 0, 0, 0, 3,\n",
              "       0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
              "       0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 2, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0,\n",
              "       0, 0, 2, 3, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
              "       0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0,\n",
              "       0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 3, 3, 0, 0, 0, 0, 0, 0, 0, 3,\n",
              "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 3,\n",
              "       0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 3, 0, 0, 0,\n",
              "       0, 3, 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, 3, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 3, 0, 0, 3, 0, 0,\n",
              "       3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 3, 3, 0,\n",
              "       0, 0, 3, 3, 0, 3, 0, 0, 0], dtype=int32)"
            ]
          },
          "metadata": {},
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn import metrics\n",
        "score=metrics.silhouette_score(Z, labels, metric='euclidean')\n",
        "score"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "wQ46ckOkKhyy",
        "outputId": "cb58bc79-1709-4484-82b9-a1c0c1e7c4cb"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.8079708170511092"
            ]
          },
          "metadata": {},
          "execution_count": 29
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "b4tFMushKh1n"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "js61lj56Kh46"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}