Model_Based_Outlier_Detection.ipynb

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      "name": "Model Based Outlier Detection.ipynb",
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      "authorship_tag": "ABX9TyNCHdrZvu6beeZ9a6nbhF1g",
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      "name": "python"
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  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
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      "source": [
        "<a href=\"https://colab.research.google.com/github/nafiul-araf/Anomaly-Detection/blob/main/Model_Based_Outlier_Detection.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "***Reference:*** https://machinelearningmastery.com/model-based-outlier-detection-and-removal-in-python/"
      ],
      "metadata": {
        "id": "51iGj0L5KF9-"
      }
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      "metadata": {
        "id": "qhbjtQt07UiG"
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import pandas as pd\n",
        "from sklearn.model_selection import train_test_split\n",
        "from sklearn.linear_model import LinearRegression\n",
        "from sklearn.metrics import mean_squared_error"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "df=pd.read_csv('https://raw.githubusercontent.com/jbrownlee/Datasets/master/housing.csv', header=None)\n",
        "df.head()"
      ],
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      "execution_count": 104,
      "outputs": [
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              "      <td>17.8</td>\n",
              "      <td>392.83</td>\n",
              "      <td>4.03</td>\n",
              "      <td>34.7</td>\n",
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              "      <td>2.94</td>\n",
              "      <td>33.4</td>\n",
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              "      <td>18.7</td>\n",
              "      <td>396.90</td>\n",
              "      <td>5.33</td>\n",
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              "        0     1     2   3      4      5   ...  8      9     10      11    12    13\n",
              "0  0.00632  18.0  2.31   0  0.538  6.575  ...   1  296.0  15.3  396.90  4.98  24.0\n",
              "1  0.02731   0.0  7.07   0  0.469  6.421  ...   2  242.0  17.8  396.90  9.14  21.6\n",
              "2  0.02729   0.0  7.07   0  0.469  7.185  ...   2  242.0  17.8  392.83  4.03  34.7\n",
              "3  0.03237   0.0  2.18   0  0.458  6.998  ...   3  222.0  18.7  394.63  2.94  33.4\n",
              "4  0.06905   0.0  2.18   0  0.458  7.147  ...   3  222.0  18.7  396.90  5.33  36.2\n",
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        "data"
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        "id": "yN617XoN75oc",
        "outputId": "47073771-c97e-4b93-9ced-643ad4df360d"
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      "outputs": [
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          "data": {
            "text/plain": [
              "array([[6.3200e-03, 1.8000e+01, 2.3100e+00, ..., 3.9690e+02, 4.9800e+00,\n",
              "        2.4000e+01],\n",
              "       [2.7310e-02, 0.0000e+00, 7.0700e+00, ..., 3.9690e+02, 9.1400e+00,\n",
              "        2.1600e+01],\n",
              "       [2.7290e-02, 0.0000e+00, 7.0700e+00, ..., 3.9283e+02, 4.0300e+00,\n",
              "        3.4700e+01],\n",
              "       ...,\n",
              "       [6.0760e-02, 0.0000e+00, 1.1930e+01, ..., 3.9690e+02, 5.6400e+00,\n",
              "        2.3900e+01],\n",
              "       [1.0959e-01, 0.0000e+00, 1.1930e+01, ..., 3.9345e+02, 6.4800e+00,\n",
              "        2.2000e+01],\n",
              "       [4.7410e-02, 0.0000e+00, 1.1930e+01, ..., 3.9690e+02, 7.8800e+00,\n",
              "        1.1900e+01]])"
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          "metadata": {},
          "execution_count": 105
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      "source": [
        "df.shape"
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        },
        "id": "kHbtHxiq9Y0e",
        "outputId": "7fbad9e1-7ca7-4c3e-c6cd-328598fd0753"
      },
      "execution_count": 106,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(506, 14)"
            ]
          },
          "metadata": {},
          "execution_count": 106
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "X, y=data[:, :-1], data[:, -1]"
      ],
      "metadata": {
        "id": "YY2EnWN68Tkh"
      },
      "execution_count": 107,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "X_train, X_test, y_train, y_test=train_test_split(X, y, test_size=0.33, random_state=np.random.seed(10))"
      ],
      "metadata": {
        "id": "1b-peRrZ9GNs"
      },
      "execution_count": 108,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "X_train.shape, X_test.shape, y_train.shape, y_test.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "fWkEZ8Lx9lIb",
        "outputId": "53d99e26-a072-430e-e04e-66a24efde231"
      },
      "execution_count": 109,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "((339, 13), (167, 13), (339,), (167,))"
            ]
          },
          "metadata": {},
          "execution_count": 109
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "###Baseline Model"
      ],
      "metadata": {
        "id": "dP54r3B6-vQu"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "model=LinearRegression()\n",
        "model.fit(X_train, y_train)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2YjbHU899vp6",
        "outputId": "00520ce6-636c-4e48-e1eb-dee5cf9cfe9b"
      },
      "execution_count": 110,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "LinearRegression()"
            ]
          },
          "metadata": {},
          "execution_count": 110
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "y_hat=model.predict(X_test)\n",
        "print('Mean Squared Error Baseline for Model: %.3f'%mean_squared_error(y_test, y_hat))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "57n2XmG19_FC",
        "outputId": "548bceda-6c0e-4956-c057-1c607c21e166"
      },
      "execution_count": 111,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mean Squared Error Baseline for Model: 27.101\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "###Outlier Detection with IForest"
      ],
      "metadata": {
        "id": "aAXSEQyh-3SO"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.ensemble import IsolationForest"
      ],
      "metadata": {
        "id": "jbYehigx-cOL"
      },
      "execution_count": 112,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "#identify outliers in the training dataset\n",
        "iso=IsolationForest(contamination=0.1)\n",
        "y_hat=iso.fit_predict(X_train)"
      ],
      "metadata": {
        "id": "wM9Dlzlu_fKE"
      },
      "execution_count": 113,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "print(y_hat)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7PjQMono__Yu",
        "outputId": "09e9e7b7-39bc-4386-cb79-edc86770fc80"
      },
      "execution_count": 114,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[ 1  1  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  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  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  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  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  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  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  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  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  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  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 -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  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  1  1\n",
            "  1  1  1]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "#select all rows that are not outliers\n",
        "mask=y_hat != -1\n",
        "X_train_iso, y_train_iso=X_train[mask, :], y_train[mask]\n",
        "X_train_iso.shape, y_train_iso.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "yccQq6GlAE7P",
        "outputId": "27d32741-9401-42a8-aef9-4155a604a525"
      },
      "execution_count": 115,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "((305, 13), (305,))"
            ]
          },
          "metadata": {},
          "execution_count": 115
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "***Removed 34 outliers***"
      ],
      "metadata": {
        "id": "Ofk0JOykC4pq"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "model=LinearRegression()\n",
        "model.fit(X_train_iso, y_train_iso)\n",
        "\n",
        "y_hat=model.predict(X_test)\n",
        "print('Mean Squared Error with Isoforest Outlier Detector: %.3f'%mean_squared_error(y_test, y_hat))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "2VtuXTktAY2B",
        "outputId": "91ba3cb4-61eb-484a-8419-f84916cd1f69"
      },
      "execution_count": 116,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mean Squared Error with Isoforest Outlier Detector: 28.586\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "***Not performing well***"
      ],
      "metadata": {
        "id": "GMP_KKj9BZmc"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "###Minimum Coviance Determinant"
      ],
      "metadata": {
        "id": "62WMEHHEC8kz"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.covariance import EllipticEnvelope"
      ],
      "metadata": {
        "id": "nRNsOxQcA5zH"
      },
      "execution_count": 117,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "ee=EllipticEnvelope(contamination=0.1)\n",
        "y_hat=ee.fit_predict(X_train)\n",
        "print(y_hat)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "RcSIlQ5GDbF7",
        "outputId": "ff673932-f322-4725-84c4-4997809e707a"
      },
      "execution_count": 118,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[ 1  1  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  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  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  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  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  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  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  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  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  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  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  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  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  1  1\n",
            "  1  1  1]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "mask=y_hat != -1\n",
        "X_train_ee, y_train_ee=X_train[mask, :], y_train[mask]\n",
        "X_train_ee.shape, y_train_ee.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "JP3kvVGXD0EL",
        "outputId": "7856b488-cf22-4cec-9837-bff8b5c7a7f4"
      },
      "execution_count": 119,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "((305, 13), (305,))"
            ]
          },
          "metadata": {},
          "execution_count": 119
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "***Removed 34 outliers***"
      ],
      "metadata": {
        "id": "9GChH_8qFBeF"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "model=LinearRegression()\n",
        "model.fit(X_train_ee, y_train_ee)\n",
        "\n",
        "y_hat=model.predict(X_test)\n",
        "print('Mean Squared Error with Minimum Variance Determinant Outlier Detection Method: %.3f'%mean_squared_error(y_test, y_hat))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "8osxvzxZEB5m",
        "outputId": "2aa47000-3bf9-4fb4-b9e2-ce2a51d6ac34"
      },
      "execution_count": 120,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mean Squared Error with Minimum Variance Determinant Outlier Detection Method: 24.945\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "***Far Better than Isoforest Method and Performs well***"
      ],
      "metadata": {
        "id": "3rt7pZyIFDaa"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "###Local Outlier Factor"
      ],
      "metadata": {
        "id": "ZqE_DbvDGUZP"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.neighbors import LocalOutlierFactor"
      ],
      "metadata": {
        "id": "wbjjEib5E2cr"
      },
      "execution_count": 121,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "lof=LocalOutlierFactor(contamination=0.1)\n",
        "y_hat=lof.fit_predict(X_train)\n",
        "print(y_hat)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "rPWPSNogGnv1",
        "outputId": "eaeecdc9-e342-467f-a4bd-ae63b86417a5"
      },
      "execution_count": 122,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[ 1  1  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  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  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  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  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  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  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  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  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  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  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 -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  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  1  1\n",
            " -1  1  1]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "mask=y_hat != -1\n",
        "X_train_lof, y_train_lof=X_train[mask, :], y_train[mask]\n",
        "X_train_lof.shape, y_train_lof.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "QZHi8a2oG2VF",
        "outputId": "46647b43-c0ba-451b-89ae-4374aa7713d3"
      },
      "execution_count": 123,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "((305, 13), (305,))"
            ]
          },
          "metadata": {},
          "execution_count": 123
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "***Removed 34 Outliers***"
      ],
      "metadata": {
        "id": "fE6y1e3cHwMJ"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "model=LinearRegression()\n",
        "model.fit(X_train_lof, y_train_lof)\n",
        "\n",
        "y_hat=model.predict(X_test)\n",
        "print('Mean Squared Error with Local Outlier Factor Method: %.3f'%mean_squared_error(y_test, y_hat))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7kY_od-xHHlT",
        "outputId": "3e6c7e23-e20f-4ffe-e9aa-02446185c78c"
      },
      "execution_count": 124,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mean Squared Error with Local Outlier Factor Method: 27.592\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "***Better than Isoforest Method***"
      ],
      "metadata": {
        "id": "Qker5cH7H0K_"
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "###One-Class SVM"
      ],
      "metadata": {
        "id": "Ifzdh0VNIiWr"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "from sklearn.svm import OneClassSVM"
      ],
      "metadata": {
        "id": "gSB0OgbLHo9Y"
      },
      "execution_count": 125,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "ocs=OneClassSVM(nu=0.1)\n",
        "y_hat=ocs.fit_predict(X_train)\n",
        "print(y_hat)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Ua5ZZUc1IrBn",
        "outputId": "8e21d3f5-859c-4311-94e6-bab112243916"
      },
      "execution_count": 126,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "[ 1  1  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  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  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  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  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  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  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  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  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  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  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 -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  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  1  1\n",
            "  1 -1  1]\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "mask=y_hat!=-1\n",
        "X_train_ocs, y_train_ocs=X_train[mask, :], y_train[mask]\n",
        "X_train_ocs.shape, y_train_ocs.shape"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "3akBw2dQI6oO",
        "outputId": "e5d4903c-4b97-4ebc-a65e-3c3b35df0266"
      },
      "execution_count": 127,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "((305, 13), (305,))"
            ]
          },
          "metadata": {},
          "execution_count": 127
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "***Removed 34 Outliers***"
      ],
      "metadata": {
        "id": "k4L7EBWcJX_D"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "model=LinearRegression()\n",
        "model.fit(X_train_ocs, y_train_ocs)\n",
        "\n",
        "y_hat=model.predict(X_test)\n",
        "print('Mean Squared Error with One Class SVM Outlier Detection Method: %.3f'%mean_squared_error(y_test, y_hat))"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "AdZWq2MoJMT0",
        "outputId": "91cd8574-14c9-46fc-97b0-8b100bfbddd0"
      },
      "execution_count": 128,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Mean Squared Error with One Class SVM Outlier Detection Method: 27.709\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "***Better than Isoforest but not Overall***"
      ],
      "metadata": {
        "id": "a1uVaL9nJew0"
      }
    },
    {
      "cell_type": "code",
      "source": [
        ""
      ],
      "metadata": {
        "id": "c-GBm1IHJTW4"
      },
      "execution_count": 128,
      "outputs": []
    }
  ]
}