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.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "auto_examples/miscellaneous/plot_anomaly_comparison.py"
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.. only:: html

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

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

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

.. _sphx_glr_auto_examples_miscellaneous_plot_anomaly_comparison.py:


============================================================================
Comparing anomaly detection algorithms for outlier detection on toy datasets
============================================================================

This example shows characteristics of different anomaly detection algorithms
on 2D datasets. Datasets contain one or two modes (regions of high density)
to illustrate the ability of algorithms to cope with multimodal data.

For each dataset, 15% of samples are generated as random uniform noise. This
proportion is the value given to the nu parameter of the OneClassSVM and the
contamination parameter of the other outlier detection algorithms.
Decision boundaries between inliers and outliers are displayed in black
except for Local Outlier Factor (LOF) as it has no predict method to be applied
on new data when it is used for outlier detection.

The :class:`sklearn.svm.OneClassSVM` is known to be sensitive to outliers and
thus does not perform very well for outlier detection. This estimator is best
suited for novelty detection when the training set is not contaminated by
outliers. That said, outlier detection in high-dimension, or without any
assumptions on the distribution of the inlying data is very challenging, and a
One-class SVM might give useful results in these situations depending on the
value of its hyperparameters.

:class:`sklearn.covariance.EllipticEnvelope` assumes the data is Gaussian and
learns an ellipse. It thus degrades when the data is not unimodal. Notice
however that this estimator is robust to outliers.

:class:`sklearn.ensemble.IsolationForest` and
:class:`sklearn.neighbors.LocalOutlierFactor` seem to perform reasonably well
for multi-modal data sets. The advantage of
:class:`sklearn.neighbors.LocalOutlierFactor` over the other estimators is
shown for the third data set, where the two modes have different densities.
This advantage is explained by the local aspect of LOF, meaning that it only
compares the score of abnormality of one sample with the scores of its
neighbors.

Finally, for the last data set, it is hard to say that one sample is more
abnormal than another sample as they are uniformly distributed in a
hypercube. Except for the :class:`sklearn.svm.OneClassSVM` which overfits a
little, all estimators present decent solutions for this situation. In such a
case, it would be wise to look more closely at the scores of abnormality of
the samples as a good estimator should assign similar scores to all the
samples.

While these examples give some intuition about the algorithms, this
intuition might not apply to very high dimensional data.

Finally, note that parameters of the models have been here handpicked but
that in practice they need to be adjusted. In the absence of labelled data,
the problem is completely unsupervised so model selection can be a challenge.

.. GENERATED FROM PYTHON SOURCE LINES 53-152



.. image-sg:: /auto_examples/miscellaneous/images/sphx_glr_plot_anomaly_comparison_001.png
   :alt: Robust covariance, One-Class SVM, Isolation Forest, Local Outlier Factor
   :srcset: /auto_examples/miscellaneous/images/sphx_glr_plot_anomaly_comparison_001.png
   :class: sphx-glr-single-img





.. code-block:: default


    # Author: Alexandre Gramfort <alexandre.gramfort@inria.fr>
    #         Albert Thomas <albert.thomas@telecom-paristech.fr>
    # License: BSD 3 clause

    import time

    import numpy as np
    import matplotlib
    import matplotlib.pyplot as plt

    from sklearn import svm
    from sklearn.datasets import make_moons, make_blobs
    from sklearn.covariance import EllipticEnvelope
    from sklearn.ensemble import IsolationForest
    from sklearn.neighbors import LocalOutlierFactor

    print(__doc__)

    matplotlib.rcParams['contour.negative_linestyle'] = 'solid'

    # Example settings
    n_samples = 300
    outliers_fraction = 0.15
    n_outliers = int(outliers_fraction * n_samples)
    n_inliers = n_samples - n_outliers

    # define outlier/anomaly detection methods to be compared
    anomaly_algorithms = [
        ("Robust covariance", EllipticEnvelope(contamination=outliers_fraction)),
        ("One-Class SVM", svm.OneClassSVM(nu=outliers_fraction, kernel="rbf",
                                          gamma=0.1)),
        ("Isolation Forest", IsolationForest(contamination=outliers_fraction,
                                             random_state=42)),
        ("Local Outlier Factor", LocalOutlierFactor(
            n_neighbors=35, contamination=outliers_fraction))]

    # Define datasets
    blobs_params = dict(random_state=0, n_samples=n_inliers, n_features=2)
    datasets = [
        make_blobs(centers=[[0, 0], [0, 0]], cluster_std=0.5,
                   **blobs_params)[0],
        make_blobs(centers=[[2, 2], [-2, -2]], cluster_std=[0.5, 0.5],
                   **blobs_params)[0],
        make_blobs(centers=[[2, 2], [-2, -2]], cluster_std=[1.5, .3],
                   **blobs_params)[0],
        4. * (make_moons(n_samples=n_samples, noise=.05, random_state=0)[0] -
              np.array([0.5, 0.25])),
        14. * (np.random.RandomState(42).rand(n_samples, 2) - 0.5)]

    # Compare given classifiers under given settings
    xx, yy = np.meshgrid(np.linspace(-7, 7, 150),
                         np.linspace(-7, 7, 150))

    plt.figure(figsize=(len(anomaly_algorithms) * 2 + 3, 12.5))
    plt.subplots_adjust(left=.02, right=.98, bottom=.001, top=.96, wspace=.05,
                        hspace=.01)

    plot_num = 1
    rng = np.random.RandomState(42)

    for i_dataset, X in enumerate(datasets):
        # Add outliers
        X = np.concatenate([X, rng.uniform(low=-6, high=6,
                           size=(n_outliers, 2))], axis=0)

        for name, algorithm in anomaly_algorithms:
            t0 = time.time()
            algorithm.fit(X)
            t1 = time.time()
            plt.subplot(len(datasets), len(anomaly_algorithms), plot_num)
            if i_dataset == 0:
                plt.title(name, size=18)

            # fit the data and tag outliers
            if name == "Local Outlier Factor":
                y_pred = algorithm.fit_predict(X)
            else:
                y_pred = algorithm.fit(X).predict(X)

            # plot the levels lines and the points
            if name != "Local Outlier Factor":  # LOF does not implement predict
                Z = algorithm.predict(np.c_[xx.ravel(), yy.ravel()])
                Z = Z.reshape(xx.shape)
                plt.contour(xx, yy, Z, levels=[0], linewidths=2, colors='black')

            colors = np.array(['#377eb8', '#ff7f00'])
            plt.scatter(X[:, 0], X[:, 1], s=10, color=colors[(y_pred + 1) // 2])

            plt.xlim(-7, 7)
            plt.ylim(-7, 7)
            plt.xticks(())
            plt.yticks(())
            plt.text(.99, .01, ('%.2fs' % (t1 - t0)).lstrip('0'),
                     transform=plt.gca().transAxes, size=15,
                     horizontalalignment='right')
            plot_num += 1

    plt.show()


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

   **Total running time of the script:** ( 0 minutes  3.404 seconds)


.. _sphx_glr_download_auto_examples_miscellaneous_plot_anomaly_comparison.py:


.. only :: html

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



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

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



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

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


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