Task_2_GRIP.ipynb

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      "name": "Task 2 GRIP.ipynb",
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        "<a href=\"https://colab.research.google.com/github/Parul25051999/Task-1-GRIP/blob/main/Task_2_GRIP.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "source": [
        "**GRIP : THE SPARKS FOUNDATION**\n",
        "\n",
        "**DATA SCIENCE AND BUSINESS ANALYTICS INTERN**\n",
        "\n",
        "**AUTHOR: PARUL AGARWAL**\n",
        "\n",
        "**TASK 2: Prediction Using Unsupervised ML**\n",
        "\n",
        "AIM: from the given 'IRIS' dataset, predict the optimal number of clusters and represent it visually."
      ],
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        "id": "wvps6wIKdW-E"
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        "Steps:\n",
        "\n",
        "Step 1 - Importing the dataset\n",
        "\n",
        "Step 2 - Visualising the data\n",
        "\n",
        "Step 3 - Finding the optimum number of clusters\n",
        "\n",
        "Step 4 - Applying K means clustering on the data\n",
        "\n",
        "Step 5 - Visualising the clusters"
      ],
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      "source": [
        "# Importing the libraries\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import pandas as pd\n",
        "from sklearn import datasets\n",
        "from sklearn.cluster import KMeans\n",
        "\n",
        "#To ignore the warnings\n",
        "import warnings as wg\n",
        "wg.filterwarnings(\"ignore\")"
      ],
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      "source": [
        "# Load the iris dataset\n",
        "iris = datasets.load_iris()\n",
        "iris_df = pd.DataFrame(iris.data, columns = iris.feature_names)\n",
        "iris_df.head()"
      ],
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              "      <th>sepal length (cm)</th>\n",
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              "      <th>0</th>\n",
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              "   sepal length (cm)  sepal width (cm)  petal length (cm)  petal width (cm)\n",
              "0                5.1               3.5                1.4               0.2\n",
              "1                4.9               3.0                1.4               0.2\n",
              "2                4.7               3.2                1.3               0.2\n",
              "3                4.6               3.1                1.5               0.2\n",
              "4                5.0               3.6                1.4               0.2"
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              "     sepal length (cm)  sepal width (cm)  petal length (cm)  petal width (cm)\n",
              "145                6.7               3.0                5.2               2.3\n",
              "146                6.3               2.5                5.0               1.9\n",
              "147                6.5               3.0                5.2               2.0\n",
              "148                6.2               3.4                5.4               2.3\n",
              "149                5.9               3.0                5.1               1.8"
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      "source": [
        "#Determining the shape of the data\n",
        "iris_df.shape"
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      "execution_count": 7,
      "outputs": [
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          "data": {
            "text/plain": [
              "(150, 4)"
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          "metadata": {},
          "execution_count": 7
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    {
      "cell_type": "code",
      "source": [
        "#Determining the different columns\n",
        "iris_df.columns"
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        "id": "2NBkaPk1hzTY",
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      "execution_count": 9,
      "outputs": [
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              "Index(['sepal length (cm)', 'sepal width (cm)', 'petal length (cm)',\n",
              "       'petal width (cm)'],\n",
              "      dtype='object')"
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      "outputs": [
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          "text": [
            "<class 'pandas.core.frame.DataFrame'>\n",
            "RangeIndex: 150 entries, 0 to 149\n",
            "Data columns (total 4 columns):\n",
            " #   Column             Non-Null Count  Dtype  \n",
            "---  ------             --------------  -----  \n",
            " 0   sepal length (cm)  150 non-null    float64\n",
            " 1   sepal width (cm)   150 non-null    float64\n",
            " 2   petal length (cm)  150 non-null    float64\n",
            " 3   petal width (cm)   150 non-null    float64\n",
            "dtypes: float64(4)\n",
            "memory usage: 4.8 KB\n"
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      "source": [
        "# Describing various parameters \n",
        "iris_df.describe()"
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      "execution_count": 12,
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              "      <th>count</th>\n",
              "      <td>150.000000</td>\n",
              "      <td>150.000000</td>\n",
              "      <td>150.000000</td>\n",
              "      <td>150.000000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>mean</th>\n",
              "      <td>5.843333</td>\n",
              "      <td>3.057333</td>\n",
              "      <td>3.758000</td>\n",
              "      <td>1.199333</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>std</th>\n",
              "      <td>0.828066</td>\n",
              "      <td>0.435866</td>\n",
              "      <td>1.765298</td>\n",
              "      <td>0.762238</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>min</th>\n",
              "      <td>4.300000</td>\n",
              "      <td>2.000000</td>\n",
              "      <td>1.000000</td>\n",
              "      <td>0.100000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>25%</th>\n",
              "      <td>5.100000</td>\n",
              "      <td>2.800000</td>\n",
              "      <td>1.600000</td>\n",
              "      <td>0.300000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>50%</th>\n",
              "      <td>5.800000</td>\n",
              "      <td>3.000000</td>\n",
              "      <td>4.350000</td>\n",
              "      <td>1.300000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>75%</th>\n",
              "      <td>6.400000</td>\n",
              "      <td>3.300000</td>\n",
              "      <td>5.100000</td>\n",
              "      <td>1.800000</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>max</th>\n",
              "      <td>7.900000</td>\n",
              "      <td>4.400000</td>\n",
              "      <td>6.900000</td>\n",
              "      <td>2.500000</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
              "      <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-c3a9c53b-5bc8-454f-9a99-b1f0d9c7fafc')\"\n",
              "              title=\"Convert this dataframe to an interactive table.\"\n",
              "              style=\"display:none;\">\n",
              "        \n",
              "  <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
              "       width=\"24px\">\n",
              "    <path d=\"M0 0h24v24H0V0z\" fill=\"none\"/>\n",
              "    <path d=\"M18.56 5.44l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94zm-11 1L8.5 8.5l.94-2.06 2.06-.94-2.06-.94L8.5 2.5l-.94 2.06-2.06.94zm10 10l.94 2.06.94-2.06 2.06-.94-2.06-.94-.94-2.06-.94 2.06-2.06.94z\"/><path d=\"M17.41 7.96l-1.37-1.37c-.4-.4-.92-.59-1.43-.59-.52 0-1.04.2-1.43.59L10.3 9.45l-7.72 7.72c-.78.78-.78 2.05 0 2.83L4 21.41c.39.39.9.59 1.41.59.51 0 1.02-.2 1.41-.59l7.78-7.78 2.81-2.81c.8-.78.8-2.07 0-2.86zM5.41 20L4 18.59l7.72-7.72 1.47 1.35L5.41 20z\"/>\n",
              "  </svg>\n",
              "      </button>\n",
              "      \n",
              "  <style>\n",
              "    .colab-df-container {\n",
              "      display:flex;\n",
              "      flex-wrap:wrap;\n",
              "      gap: 12px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert {\n",
              "      background-color: #E8F0FE;\n",
              "      border: none;\n",
              "      border-radius: 50%;\n",
              "      cursor: pointer;\n",
              "      display: none;\n",
              "      fill: #1967D2;\n",
              "      height: 32px;\n",
              "      padding: 0 0 0 0;\n",
              "      width: 32px;\n",
              "    }\n",
              "\n",
              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
              "      fill: #174EA6;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
              "      fill: #D2E3FC;\n",
              "    }\n",
              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
              "      background-color: #434B5C;\n",
              "      box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
              "      filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
              "      fill: #FFFFFF;\n",
              "    }\n",
              "  </style>\n",
              "\n",
              "      <script>\n",
              "        const buttonEl =\n",
              "          document.querySelector('#df-c3a9c53b-5bc8-454f-9a99-b1f0d9c7fafc 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-c3a9c53b-5bc8-454f-9a99-b1f0d9c7fafc');\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",
              "  "
            ],
            "text/plain": [
              "       sepal length (cm)  sepal width (cm)  petal length (cm)  petal width (cm)\n",
              "count         150.000000        150.000000         150.000000        150.000000\n",
              "mean            5.843333          3.057333           3.758000          1.199333\n",
              "std             0.828066          0.435866           1.765298          0.762238\n",
              "min             4.300000          2.000000           1.000000          0.100000\n",
              "25%             5.100000          2.800000           1.600000          0.300000\n",
              "50%             5.800000          3.000000           4.350000          1.300000\n",
              "75%             6.400000          3.300000           5.100000          1.800000\n",
              "max             7.900000          4.400000           6.900000          2.500000"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Finding the optimum number of clusters for k-means classification\n",
        "\n",
        "x = iris_df.iloc[:, [0, 1, 2, 3]].values\n",
        "\n",
        "from sklearn.cluster import KMeans\n",
        "wcss = []\n",
        "\n",
        "for i in range(1, 15):\n",
        "    kmeans = KMeans(n_clusters = i, init = 'k-means++', \n",
        "                    max_iter = 300, n_init = 10, random_state = 0)\n",
        "    kmeans.fit(x)\n",
        "    wcss.append(kmeans.inertia_)\n",
        "    \n",
        "# Plotting the results onto a line graph, \n",
        "# `allowing us to observe 'The elbow'\n",
        "plt.plot(range(1, 15), wcss)\n",
        "plt.title('The elbow method')\n",
        "plt.xlabel('Number of clusters')\n",
        "plt.ylabel('WCSS') # Within cluster sum of squares\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 294
        },
        "id": "GO-QqyyLi4B7",
        "outputId": "19eb3017-c4fb-4ce1-8b24-d3ca84e8e5e2"
      },
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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SEY9M5HYj4uaIWBYRy7q6uiZy08fUnM9x+rwO7ymY2YzXVMNtvxp4k6QrgTZgNvBJYI6kprQ3sBjYkNbfAJwGrJfUBJwEbKthfeNSKhZY7RvYzGyGq9meQkR8MCIWR0Q38DbguxHxDuBe4M1ptWuBO9L0nWmetPy7ERG1qm+8uosF1mzrZXh4ypRkZjbhRgwFSRdKOqVq/hpJd0j6lKR5x/mefwL8oaRVZOcMbknttwDzU/sfAjce5/ZrolQs0D8wzKbd/fUuxcysZkY7fPQ54HIASZcANwHvA84HbubgL/4RRcT3gO+l6dXAK46yTj/wlrGVPfmqh+ZcOKe9ztWYmdXGaIeP8hGxPU3/OnBzRHwjIv4MOKu2pU0tpS73lmpmM9+ooZBO+gJcBny3alktT1JPOQtmtdHenHcomNmMNtoX+5eB+yRtBfYB3weQdBbZfQQNI5cT3e4DycxmuBFDISL+StI9wKnAXVVXA+XIzi00lCXFAk9t3F3vMszMambEUJDUATwSEQNp/hzgSuCFiPjmJNQ3pZSKBb7z5CYGhoZpzruDWTObeUb7ZvsO0A2VQ0YPAEuA6yV9uLalTT2lYoGh4WDd9r56l2JmVhOjhcLciFiZpq8FvhwR7wOuAN5Y08qmoG6P12xmM9xooVB9++6lwN0AEXGAg53cNYwlDgUzm+FGu/roMUkfI+uX6CzgLgBJc2pd2FQ0t9DCnI5mj6tgZjPWaHsK7wG2kp1X+KWIKB9MPxf4WA3rmrJKxQJrHApmNkONtqfQCfyfiHjysPZdZCehG06pWOCB56ZM561mZhNqtD2Fv+coA90A88i6wW44S4oFNu7qp+/A4Ogrm5lNM6OFwlkRcf/hjRHxfeBltSlpaisPzblmqy9LNbOZZ7RQmDXCsuaJLGS6KPkKJDObwUYLhVVp5LRDSLoCWF2bkqa27mIHgMdrNrMZabQTzTcA/yrprUB5rOVlwMU04M1rAB0tTZwyu82XpZrZjDRaKPwK8E7gPOCc1HYf8DtpUJyGVHJvqWY2Q412+Ggx8Angb4ALgQPAFqCjxnVNaaUuh4KZzUwjhkJEfCAiXgUsAD4IbAfeDTwh6alJqG9KWlIssLNvgB29B+pdipnZhBpr/8/twGzgpPR4EXioVkVNdZUrkLZ5b8HMZpbRxlO4GXgpsIcsBH4I/F1E7JiE2qasSij09HLB6XPrXI2Z2cQZbU/hdKAV2ETWKd56YOdYNiypTdKPJP1U0pOSPpTaS5IekrRK0lcltaT21jS/Ki3vPt4PVWunzesgn5PPK5jZjDPaOYU3kJ1gLnd+90fAw5LuKn/Jj2A/cGlEnAecD7xB0kXAR4CPR8RZwA7gurT+dcCO1P7xtN6U1JzPcfq8DoeCmc04o55TiMwTwLeBfwN+AJwJvH8Mryvf4dWcHkE2LsPXU/ttwNVp+qo0T1p+mSSN/aNMrlKx4HsVzGzGGTEUJP2+pK9IWkt2f8IbgWeA/0rWKd6IJOUlPUp2GevdwHPAzogo9ya3HliUphcB6wDS8l0cpTM+ScslrZC0oqenZwwfsTa652ddaA8Px+grm5lNE6PdvNYN/DPwBxGxcbwbj4gh4Pw0KM+3gJeMu8Ijt3kzcDPAsmXL6vaNXOoqsG9giM17+jn1pPZ6lWFmNqFGDIWI+MOJeJOI2CnpXrLuMeZIakp7A4vJTmCTnk8D1ktqIrv0dcoOXLCk6gokh4KZzRRjvU9h3CR1lYftlNQOvB54GrgXeHNa7VrgjjR9Z5onLf9uREzZYzO+V8HMZqLRDh+diFOB2yTlycLnaxHxL+lO6K9I+kvgJ8Ataf1bgP8taRXZndNvq2FtJ+yU2W20Ned4vsehYGYzR81CISIeA15+lPbVwCuO0t4PvKVW9Uy0XE50z3cfSGY2s9Ts8FEjWOKO8cxshnEonIBSscDa7X0MDA3XuxQzswnhUDgBpWIng8PB+h376l2KmdmEcCicgJKH5jSzGcahcAJKxU4AVvsKJDObIRwKJ2BuRzMntTf7ZLOZzRgOhRMgiVKxwBrfwGZmM4RD4QQtKRZ8A5uZzRgOhRNUKhZ4cVc/+w4M1bsUM7MT5lA4QaWurA8kH0Iys5nAoXCCKh3j+WSzmc0ADoUT1D3foWBmM4dD4QQVWptYMLvV9yqY2YzgUJgApWLBdzWb2YzgUJgApWKnDx+Z2YzgUJgAS4oFdvQNsLPvQL1LMTM7IQ6FCeArkMxspnAoTIDyvQoOBTOb7hwKE+C0uR3kc3IomNm051CYAC1NOU6b285qh4KZTXMOhQlScsd4ZjYD1CwUJJ0m6V5JT0l6UtL7U/s8SXdLWpme56Z2SfqUpFWSHpN0Qa1qq4XuYoHnt/YSEfUuxczsuNVyT2EQ+KOIOBe4CLhe0rnAjcA9EbEUuCfNA1wBLE2P5cBnaljbhFtSLLBvYIjNu/fXuxQzs+NWs1CIiI0R8eM0vQd4GlgEXAXclla7Dbg6TV8F3B6ZB4E5kk6tVX0TrTI0p+9sNrNpbFLOKUjqBl4OPAQsiIiNadEmYEGaXgSsq3rZ+tR2+LaWS1ohaUVPT0/Nah6vShfaW/vqXImZ2fGreShI6gS+AdwQEburl0V2AH5cB+Ej4uaIWBYRy7q6uiaw0hNz6uw2Wpty7gPJzKa1moaCpGayQPhSRHwzNW8uHxZKz1tS+wbgtKqXL05t00Iup9Qxnq9AMrPpq5ZXHwm4BXg6Iv6uatGdwLVp+lrgjqr2a9JVSBcBu6oOM00LpWLB9yqY2bRWyz2FVwO/CVwq6dH0uBK4CXi9pJXA5Wke4NvAamAV8Hng92pYW02UigXWbutjcGi43qWYmR2XplptOCL+A9AxFl92lPUDuL5W9UyGUrHA4HCwfsc+ulMneWZm04nvaJ5A7i3VzKY7h8IEKoeCzyuY2XTlUJhA8wotzG5r8mWpZjZtORQmkCRKXZ2+gc3Mpi2HwgRb4nsVzGwacyhMsFKxwIad++gfGKp3KWZm4+ZQmGDlk81rtnlvwcymH4fCBKtcluoBd8xsGnIoTLBSsUBrU47/9b3n2N57oN7lmJmNi0NhghVam/j0b1zAzzbv4dc/9wCbdvXXuyQzszFzKNTA5ecu4NZ3X8iLO/fxls/9kLXbfImqmU0PDoUaedWZRb70novY0z/Imz/7Q57dvKfeJZmZjcqhUEPnnzaHry6/GIC3fu4BfrpuZ50rMjMbmUOhxs45ZRb//N6L6Wxt4jc+/yAPPLet3iWZmR2TQ2ESnDG/wNff+ypOndPOu774I777zOZ6l2RmdlQOhUlyykltfO13LubsBbNYfvsj3PHotBlp1MwaiENhEs0rtPBP73klF5wxlxu++ij/9NDaepdkZnYIh8Ikm9XWzO2/9Qped3YXf/qtx/ncfc/VuyQzswqHQh20Nef53G8u440vO5UP/9szfPT/PkM2GqmZWX3VbIxmG1lLU45Pvu3lzGpr4tP3Psee/kH+4ldfSi53rGGtzcxqz6FQR/mc+Ov/8p+Z1dbMzfevZk//IB9988toynsHzszqo2bfPpL+QdIWSU9Utc2TdLeklel5bmqXpE9JWiXpMUkX1KquqUYSH7ziJXzgl87mWz/ZwO9+6ccei8HM6qaWP0lvBd5wWNuNwD0RsRS4J80DXAEsTY/lwGdqWNeUI4n/dulSPvSml3L3U5u57raH6d0/WO+yzKwB1SwUIuJ+YPthzVcBt6Xp24Crq9pvj8yDwBxJp9aqtqnq2ld187dvOY8HV2/nnbc8xM4+d71tZpNrsg9eL4iIjWl6E7AgTS8C1lWttz61HUHSckkrJK3o6empXaV18ms/v5j/9Y4LeHLDbt5284Ns2eOut81s8tTtjGZk12CO+zrMiLg5IpZFxLKurq4aVFZ/v/zSU/iHd13IC9v6eOtnH2D9Dne9bWaTY7JDYXP5sFB63pLaNwCnVa23OLU1rNcsLfKPv/1Ktvce4C2ffYBVW/bWuyQzawCTHQp3Atem6WuBO6rar0lXIV0E7Ko6zNSwfv6MuXxl+cUMDA3z6597gCc27Kp3SWY2w9XyktQvAw8A50haL+k64Cbg9ZJWApeneYBvA6uBVcDngd+rVV3TzbkLZ/PP730Vbc153v75B1mx5vBz92ZmE0fTuXuFZcuWxYoVK+pdxqR4cec+3vmFh3hx1z4+9pbzeP25C2htyte7LDObhiQ9EhHLjrrMoTB9bN27n2tu+RFPbdxNR0uei5bM55KlRV57dhdLigUkd5FhZqMbKRTczcU0Uuxs5Zu/9yr+Y+VW7l/Zw/3P9vDdZ7Jz9YvmtHPJ2V1csrTIq84qclJ7c52rNbPpyHsK09zabX2VgPjhc9vYu3+QfE6cf9ocXru0yCVnd3He4jnk3dGemSU+fNQgBoaGeXTdTu5/tof7V27lsfU7iYCT2pt5zVnFSkgsnNNe71LNrI4cCg1qR+8B/mPVVr6/sof7n93Kpt3Z3dFndhWyQ01nd3FRaT7tLT5hbdZIHApGRLByy97KXsRDq7exf3CYlnyOC0tzuWRpFhIvOWWWT1ibzXAOBTtC/8AQD6/ZnoXEs1v52eY9QHYye+nJnZwxv4PT53dwxrxCZXp2m09em80EDgUb1ebd/dz/bA8PrN7G81t7Wbutj229h/bSOq/QwunzOjhjfgdnzOvgjPkHA6Ors9V7GGbThEPBjsue/gHWbu9j7bY+XtjexwvbenlhWx8vbOtj4659DFf90+loyXP6vA5On9dBd7FQFR4FFs5p82hyZlOI71Ow4zKrrZmXLjyJly486YhlBwaHWb+jL4VELy+k8Fi9tZfvPdvDgcHhyrpNObFobjunz+tg8dx2ujpb6ZrVStesNrpmtXLyrGy+rdknvM3qzaFgx6WlKceSrk6WdHUesWx4ONi0u58XtvWxdnvau0ih8fTGPWzr3c/RdlBntTVlYdHZysmz2yrhUQ6N8mNeRws533dhVhMOBZtwuZxYOKedhXPaufjM+UcsHxwaZnvvAbbs2U/P3v307E7Pe7LHlj39PL5+Jz179tN74MjxqvM5UexsSYFxMDyKnS3Mbm9mdlszs9qamN1+8LmzpclBYjYGDgWbdE35HCfPbuPk2W2jrtu7fzALixQaW3b3HxIgm3f388SGXWzdu/+QcxyHk6CztelgYLQ1M7u9iVltzcxuS8+V+cNCJc378JY1AoeCTWmF1iYKrU10Fwsjrjc0HOzsO8Ce/kF29w9kz/sGKvO7D5vf0z/Aizv72bN/D7v3DbKnf2DEUAFoyefobGuis7Xq0XbweVZqK1TPp+Wz2probG2m0Jqn4L0Wm8IcCjYj5HNifmcr8ztbj+v1EUHvgSH29A9UQqI6XHb3D7J3/yB70/Oe/kH27h9gy55+VvcMsnf/EHv3D9A/MDz6m8ERodLRkqc5n6M5n6OlSTTnczTlDk5XluXTsnyO5rxoacpVLdch0y35HM1NB+dbm/K0NuVoacrRkk/PTTmacvLlxFbhUDADJFW+qE898mKrMRsYGqa3EhqHBkl5ek+lbaASMPsODNF7YIiBwWEGhsqP4ECaHkzT1Vd1TRQp2wvKAuPowXHMthRCTfksXJryoikn8rksiPI5VZblc0ptOZpz5WWiKVd+bS5rq24vh1t630oQ5nLe26oRh4LZBGrO55jT0cKcjpaabD8iGBqOIwJjYGi4Mj8wmC0brATLEAcGh9k/mIVKOVwOVM2Xlx26zqGv27t/sPKa/eXXDQwxOBzZY2h41ENwE6kpd+ieUmvTwb2lcntLJbgOrttStbwpL/IS+XKYKQutfA7yKaxyOVVCrfw4ZF4HAy6nLMzyh4TewYArT+fzqgrG3CFBmBN13XNzKJhNI1L68shDO1PvxPdwCoih4WBwOAuswarpSvtwVJYNDWfhlYXdcFqnvDwLoYFy8A0eDL8Dg8NVbXFI20AKuoGhYfYNDLFr3/BRX1+udahS89S4mbe8l9WcAqS8N3Vwb0vccPnZ/Op5Cyf8vR0KZjZhcjnRUjmsM/VCayyqg20ogqGh7HlwePiIADlk3XJbHAy0oarwO3T+0GAcHDoYUOXpwcPWHRoKBqq2MaejNn2RORTMzKocGmyNxx3SmBuvotQAAAfRSURBVJlZxZQKBUlvkPQzSask3VjveszMGs2UCQVJeeDTwBXAucDbJZ1b36rMzBrLlAkF4BXAqohYHREHgK8AV9W5JjOzhjKVQmERsK5qfn1qO4Sk5ZJWSFrR09MzacWZmTWCqRQKYxIRN0fEsohY1tXVVe9yzMxmlKkUChuA06rmF6c2MzObJFMpFB4GlkoqSWoB3gbcWeeazMwaypQao1nSlcAnyG6F/IeI+KtR1u8BXpiM2o5DEdha7yKO03StfbrWDa69Xhq19jMi4qjH36dUKMwkklYca2DsqW661j5d6wbXXi+u/UhT6fCRmZnVmUPBzMwqHAq1c3O9CzgB07X26Vo3uPZ6ce2H8TkFMzOr8J6CmZlVOBTMzKzCoTCBJJ0m6V5JT0l6UtL7613TeEnKS/qJpH+pdy3jIWmOpK9LekbS05IurndNYyXpD9K/lyckfVlSW71rOhZJ/yBpi6QnqtrmSbpb0sr0PLeeNR7LMWr/aPo385ikb0maU88aj+ZodVct+yNJIak4Ue/nUJhYg8AfRcS5wEXA9dOw++/3A0/Xu4jj8EngOxHxEuA8pslnkLQI+H1gWUT8HNmNm2+rb1UjuhV4w2FtNwL3RMRS4J40PxXdypG13w38XES8DHgW+OBkFzUGt3Jk3Ug6DfglYO1EvplDYQJFxMaI+HGa3kP2xXRET69TlaTFwK8AX6h3LeMh6STgEuAWgIg4EBE761vVuDQB7ZKagA7gxTrXc0wRcT+w/bDmq4Db0vRtwNWTWtQYHa32iLgrIgbT7INkfa5NKcf4mwN8HPhjYEKvFnIo1IikbuDlwEP1rWRcPkH2j2y43oWMUwnoAb6YDn19QVKh3kWNRURsAD5G9mtvI7ArIu6qb1XjtiAiNqbpTcCCehZzAn4L+Ld6FzEWkq4CNkTETyd62w6FGpDUCXwDuCEidte7nrGQ9EZgS0Q8Uu9ajkMTcAHwmYh4OdDL1D2EcYh0/P0qsmBbCBQkvbO+VR2/yK5xn3bXuUv672SHf79U71pGI6kD+FPgz2uxfYfCBJPUTBYIX4qIb9a7nnF4NfAmSWvIRr27VNI/1rekMVsPrI+I8l7Z18lCYjq4HHg+InoiYgD4JvCqOtc0XpslnQqQnrfUuZ5xkfQu4I3AO2J63Lh1JtmPiJ+m/18XAz+WdMpEbNyhMIEkiey49tMR8Xf1rmc8IuKDEbE4IrrJTnR+NyKmxS/WiNgErJN0Tmq6DHiqjiWNx1rgIkkd6d/PZUyTk+RV7gSuTdPXAnfUsZZxkfQGskOmb4qIvnrXMxYR8XhEnBwR3en/1/XABen/gxPmUJhYrwZ+k+xX9qPpcWW9i2oQ7wO+JOkx4Hzgr+tcz5ikvZuvAz8GHif7f3LKdr0g6cvAA8A5ktZLug64CXi9pJVkez431bPGYzlG7f8TmAXcnf5//WxdizyKY9Rdu/ebHntLZmY2GbynYGZmFQ4FMzOrcCiYmVmFQ8HMzCocCmZmVuFQsCkt9QD5t1XzH5D0FxO07VslvXkitjXK+7wl9dx6by3rktQt6TfGX6HZQQ4Fm+r2A/91IrsGngip87qxug54T0T8Yq3qSbqBcYXCOD+HNQCHgk11g2Q3c/3B4QsO/0UtaW96fp2k+yTdIWm1pJskvUPSjyQ9LunMqs1cLmmFpGdT/0/lMSU+Kunh1M/+71Rt9/uS7uQod0xLenva/hOSPpLa/hx4DXCLpI8e5TV/kl7zU0lH3PQlaU05ECUtk/S9NP0LVTdI/kTSLLKbxl6b2v5grJ9DUkHSv6YanpD062P5D2Mzk38l2HTwaeAxSX8zjtecB/wnsi6HVwNfiIhXKBv46H3ADWm9buAVZP3J3CvpLOAast5KL5TUCvxAUrnn0gvI+t9/vvrNJC0EPgL8PLADuEvS1RHx/0q6FPhARKw47DVXkHWG98qI6JM0bxyf7wPA9RHxg9QBYz9ZJ4AfiIhyuC0fy+eQ9GvAixHxK+l1J42jDpthvKdgU17qafZ2ssFoxurhNL7FfuA5oPxl+DhZEJR9LSKGI2IlWXi8hGzgkmskPUrW9fl8YGla/0eHB0JyIfC91LFdubfNS0ap8XLgi+U+dyLiaH3mH8sPgL+T9PvAnKoxAaqN9XM8TtZNxUckvTYido2jDpthHAo2XXyC7Nh89TgJg6R/w5JyQEvVsv1V08NV88Mcuod8eD8vAQh4X0Scnx6lqjEOek/oU4xf5TMClWE6I+Im4LeBdrI9gJcc5bVj+hwR8SzZnsPjwF+mQ17WoBwKNi2kX9FfIwuGsjVkh2sA3gQ0H8em3yIpl84zLAF+Bvxf4HeVdYOOpLM1+qA9PwJ+QVJRUh54O3DfKK+5G3i3sv7xOcbhozUc/Iy/Vm6UdGbqLfMjwMNkezh7yDp3KxvT50iHvvoi4h+BjzJ9uh23GvA5BZtO/hb4b1XznwfukPRT4Dsc36/4tWRf6LOB90ZEv6QvkB1i+rEkkY3qNuIQkxGxUdKNwL1kv9D/NSJG7EI6Ir4j6XxghaQDwLfJBk+p9iGyk9T/H/C9qvYbJP0i2Z7Pk2Qjhg0DQ+nvcSvZuNVj+Rz/GfiopGFgAPjdkeq2mc29pJqZWYUPH5mZWYVDwczMKhwKZmZW4VAwM7MKh4KZmVU4FMzMrMKhYGZmFf8/g8z1o1j9ZiUAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "You can clearly see why it is called 'The elbow method' from the above graph, the optimum clusters is where the elbow occurs. This is when the within cluster sum of squares (WCSS) doesn't decrease significantly with every iteration.\n",
        "\n",
        "From this we choose the number of clusters as **'3'**."
      ],
      "metadata": {
        "id": "i56VXfK3jpHg"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "# Applying kmeans to the dataset / Creating the kmeans classifier\n",
        "kmeans = KMeans(n_clusters = 3, init = 'k-means++',\n",
        "                max_iter = 300, n_init = 10, random_state = 0)\n",
        "y_kmeans = kmeans.fit_predict(x)\n",
        "y_kmeans"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "5_gPRWcxjvug",
        "outputId": "756d7c8d-2719-4156-884e-d6062a2a9d4b"
      },
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "execute_result",
          "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, 0, 0, 2, 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, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,\n",
              "       0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 2, 2, 2, 2, 0, 2, 2, 2,\n",
              "       2, 2, 2, 0, 0, 2, 2, 2, 2, 0, 2, 0, 2, 0, 2, 2, 0, 0, 2, 2, 2, 2,\n",
              "       2, 0, 2, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 0], dtype=int32)"
            ]
          },
          "metadata": {},
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Visualising the clusters - On the first two columns\n",
        "plt.scatter(x[y_kmeans == 0, 0], x[y_kmeans == 0, 1], \n",
        "            s = 100, c = 'red', label = 'Iris-setosa')\n",
        "plt.scatter(x[y_kmeans == 1, 0], x[y_kmeans == 1, 1], \n",
        "            s = 100, c = 'blue', label = 'Iris-versicolour')\n",
        "plt.scatter(x[y_kmeans == 2, 0], x[y_kmeans == 2, 1],\n",
        "            s = 100, c = 'green', label = 'Iris-virginica')\n",
        "\n",
        "# Plotting the centroids of the clusters\n",
        "plt.scatter(kmeans.cluster_centers_[:, 0], kmeans.cluster_centers_[:,1], \n",
        "            s = 100, c = 'yellow', label = 'Centroids')\n",
        "\n",
        "plt.legend()\n",
        "plt.grid()\n",
        "plt.show()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 267
        },
        "id": "lvYkskrXkcf2",
        "outputId": "1719f53a-e6c2-4c67-ae3e-202328cf752d"
      },
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**END OF TASK 2**"
      ],
      "metadata": {
        "id": "W_ktKAySkqhh"
      }
    }
  ]
}