.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/outlier_detection.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        Click :ref:`here <sphx_glr_download_auto_examples_outlier_detection.py>`
        to download the full example code

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_auto_examples_outlier_detection.py:


==============================
Multivariate Outlier Detection
==============================

Mahalanobis Distance can be used to detect outliers in multivariate space.
This can be combined with Principal Component Analysis (PCA) to reduce dimensionality prior to outlier detection.

.. GENERATED FROM PYTHON SOURCE LINES 10-24

.. code-block:: default

    import logging

    import pandas as pd
    import plotly.io as pio
    import plotly.express as px
    from sklearn.datasets import load_diabetes

    from elphick.sklearn_viz.features import plot_principal_components, plot_scatter_matrix, \
        plot_explained_variance, PrincipalComponents, plot_parallel_coordinates
    from elphick.sklearn_viz.features.outlier_detection import OutlierDetection

    logging.basicConfig(level=logging.DEBUG,
                        format='%(asctime)s %(levelname)s %(module)s - %(funcName)s: %(message)s',
                        datefmt='%Y-%m-%dT%H:%M:%S%z')







.. GENERATED FROM PYTHON SOURCE LINES 25-29

Create a dataset
----------------

From the `sklearn example <https://scikit-learn.org/stable/auto_examples/covariance/plot_mahalanobis_distances.html>`_

.. GENERATED FROM PYTHON SOURCE LINES 29-52

.. code-block:: default


    import numpy as np

    # for consistent results
    np.random.seed(7)

    n_samples = 125
    n_outliers = 25
    n_features = 4

    # generate Gaussian data of shape (125, 4)
    gen_cov = np.eye(n_features)
    gen_cov[0, 0] = 2.0
    X = np.dot(np.random.randn(n_samples, n_features), gen_cov)
    # add some outliers
    outliers_cov = np.eye(n_features)
    outliers_cov[np.arange(1, n_features), np.arange(1, n_features)] = 7.0
    X[-n_outliers:] = np.dot(np.random.randn(n_outliers, n_features), outliers_cov)

    x: pd.DataFrame = pd.DataFrame(X, columns=[f"F{n}" for n in range(1, n_features + 1)])
    test_outlier = pd.Series(x['F1'].index > (n_samples - n_outliers - 1), name='test_outlier').astype('category')
    x






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
    <div>
    <style scoped>
        .dataframe tbody tr th:only-of-type {
            vertical-align: middle;
        }

        .dataframe tbody tr th {
            vertical-align: top;
        }

        .dataframe thead th {
            text-align: right;
        }
    </style>
    <table border="1" class="dataframe">
      <thead>
        <tr style="text-align: right;">
          <th></th>
          <th>F1</th>
          <th>F2</th>
          <th>F3</th>
          <th>F4</th>
        </tr>
      </thead>
      <tbody>
        <tr>
          <th>0</th>
          <td>3.381051</td>
          <td>-0.465937</td>
          <td>0.032820</td>
          <td>0.407516</td>
        </tr>
        <tr>
          <th>1</th>
          <td>-1.577846</td>
          <td>0.002066</td>
          <td>-0.000890</td>
          <td>-1.754724</td>
        </tr>
        <tr>
          <th>2</th>
          <td>2.035316</td>
          <td>0.600499</td>
          <td>-0.625429</td>
          <td>-0.171548</td>
        </tr>
        <tr>
          <th>3</th>
          <td>1.010599</td>
          <td>-0.261356</td>
          <td>-0.242749</td>
          <td>-1.453241</td>
        </tr>
        <tr>
          <th>4</th>
          <td>1.109161</td>
          <td>0.123881</td>
          <td>0.274460</td>
          <td>-1.526525</td>
        </tr>
        <tr>
          <th>...</th>
          <td>...</td>
          <td>...</td>
          <td>...</td>
          <td>...</td>
        </tr>
        <tr>
          <th>120</th>
          <td>-0.118956</td>
          <td>-3.487569</td>
          <td>13.277863</td>
          <td>6.290964</td>
        </tr>
        <tr>
          <th>121</th>
          <td>1.264443</td>
          <td>2.110813</td>
          <td>-3.885861</td>
          <td>8.212846</td>
        </tr>
        <tr>
          <th>122</th>
          <td>1.653950</td>
          <td>4.073715</td>
          <td>-0.169766</td>
          <td>7.566816</td>
        </tr>
        <tr>
          <th>123</th>
          <td>-0.371115</td>
          <td>5.351784</td>
          <td>-4.981090</td>
          <td>-6.792561</td>
        </tr>
        <tr>
          <th>124</th>
          <td>0.566445</td>
          <td>2.365511</td>
          <td>13.330145</td>
          <td>-1.960749</td>
        </tr>
      </tbody>
    </table>
    <p>125 rows × 4 columns</p>
    </div>
    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 53-58

Explore the data and principal components
-----------------------------------------

The parallel coordinate plot is a good place to start.  The test outlier class variable is used to color the plot.
Note, the outliers shown are before outlier detection - this is the synthetically generated outlier class.

.. GENERATED FROM PYTHON SOURCE LINES 58-62

.. code-block:: default


    fig = plot_parallel_coordinates(data=pd.concat([x, test_outlier], axis=1), color='test_outlier')
    fig






.. raw:: html

    <div class="output_subarea output_html rendered_html output_result">
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.. GENERATED FROM PYTHON SOURCE LINES 63-64

Explore the principal components in 2D and then 3D

.. GENERATED FROM PYTHON SOURCE LINES 64-67

.. code-block:: default

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.. GENERATED FROM PYTHON SOURCE LINES 68-72

.. code-block:: default

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    <br />

.. GENERATED FROM PYTHON SOURCE LINES 73-77

.. code-block:: default

    fig = plot_principal_components(plot_3d=True, x=x, color=test_outlier)
    fig.update_layout(height=800)
    fig






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    <br />

.. GENERATED FROM PYTHON SOURCE LINES 78-80

Detect Outliers
---------------

.. GENERATED FROM PYTHON SOURCE LINES 80-84

.. code-block:: default


    od: OutlierDetection = OutlierDetection(x=x, pca_spec=2)
    detected_outliers: pd.Series = od.data['outlier']








.. GENERATED FROM PYTHON SOURCE LINES 85-86

Visualise the detected outliers with the default p_val of 0.001

.. GENERATED FROM PYTHON SOURCE LINES 86-91

.. code-block:: default


    fig = plot_principal_components(plot_3d=False, x=x, color=detected_outliers)
    fig.update_layout(height=800)
    fig






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    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 92-93

We can tighten the threshold to align more closely with our expectation.

.. GENERATED FROM PYTHON SOURCE LINES 93-100

.. code-block:: default


    detected_outliers: pd.Series = OutlierDetection(x=x, pca_spec=2, p_val=0.25).data['outlier']
    fig = plot_principal_components(plot_3d=False, x=x, color=detected_outliers)
    fig.update_layout(height=800)
    # noinspection PyTypeChecker
    pio.show(fig)




.. raw:: html
    :file: images/sphx_glr_outlier_detection_001.html





.. GENERATED FROM PYTHON SOURCE LINES 101-105

.. code-block:: default

    fig = od.plot_outlier_matrix()
    fig.update_layout(height=800)
    fig






.. raw:: html

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    </div>
    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 106-108

The parallel plot allows us to explore the difference between our defined outliers (test_outliers) and what
was detected as an outlier (outlier).

.. GENERATED FROM PYTHON SOURCE LINES 108-112

.. code-block:: default

    fig = plot_parallel_coordinates(data=pd.concat([x, test_outlier, detected_outliers.astype('category')], axis=1),
                                    color='outlier')
    fig






.. raw:: html

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    <br />
    <br />

.. GENERATED FROM PYTHON SOURCE LINES 113-114

We can detect in the original feature space with pca_spec = 0

.. GENERATED FROM PYTHON SOURCE LINES 114-117

.. code-block:: default


    detected_outliers: pd.Series = OutlierDetection(x=x, pca_spec=0, p_val=0.25).data['outlier']
    detected_outliers.sum()




.. rst-class:: sphx-glr-script-out

 .. code-block:: none


    np.int64(30)




.. rst-class:: sphx-glr-timing

   **Total running time of the script:** ( 0 minutes  0.399 seconds)


.. _sphx_glr_download_auto_examples_outlier_detection.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example


    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: outlier_detection.py <outlier_detection.py>`

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: outlier_detection.ipynb <outlier_detection.ipynb>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_