.. DO NOT EDIT. .. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. .. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: .. "auto_examples/miscellaneous/plot_anomaly_comparison.py" .. LINE NUMBERS ARE GIVEN BELOW. .. only:: html .. note:: :class: sphx-glr-download-link-note :ref:`Go to the end ` to download the full example code or to run this example in your browser via JupyterLite or Binder .. 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. The :class:`sklearn.linear_model.SGDOneClassSVM` is an implementation of the One-Class SVM based on stochastic gradient descent (SGD). Combined with kernel approximation, this estimator can be used to approximate the solution of a kernelized :class:`sklearn.svm.OneClassSVM`. We note that, although not identical, the decision boundaries of the :class:`sklearn.linear_model.SGDOneClassSVM` and the ones of :class:`sklearn.svm.OneClassSVM` are very similar. The main advantage of using :class:`sklearn.linear_model.SGDOneClassSVM` is that it scales linearly with the number of samples. :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 64-191 .. image-sg:: /auto_examples/miscellaneous/images/sphx_glr_plot_anomaly_comparison_001.png :alt: Robust covariance, One-Class SVM, One-Class SVM (SGD), Isolation Forest, Local Outlier Factor :srcset: /auto_examples/miscellaneous/images/sphx_glr_plot_anomaly_comparison_001.png :class: sphx-glr-single-img .. code-block:: Python # Author: Alexandre Gramfort # Albert Thomas # License: BSD 3 clause import time import matplotlib import matplotlib.pyplot as plt import numpy as np from sklearn import svm from sklearn.covariance import EllipticEnvelope from sklearn.datasets import make_blobs, make_moons from sklearn.ensemble import IsolationForest from sklearn.kernel_approximation import Nystroem from sklearn.linear_model import SGDOneClassSVM from sklearn.neighbors import LocalOutlierFactor from sklearn.pipeline import make_pipeline 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. # the SGDOneClassSVM must be used in a pipeline with a kernel approximation # to give similar results to the OneClassSVM anomaly_algorithms = [ ( "Robust covariance", EllipticEnvelope(contamination=outliers_fraction, random_state=42), ), ("One-Class SVM", svm.OneClassSVM(nu=outliers_fraction, kernel="rbf", gamma=0.1)), ( "One-Class SVM (SGD)", make_pipeline( Nystroem(gamma=0.1, random_state=42, n_components=150), SGDOneClassSVM( nu=outliers_fraction, shuffle=True, fit_intercept=True, random_state=42, tol=1e-6, ), ), ), ( "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, 0.3], **blobs_params)[0], 4.0 * ( make_moons(n_samples=n_samples, noise=0.05, random_state=0)[0] - np.array([0.5, 0.25]) ), 14.0 * (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 + 4, 12.5)) plt.subplots_adjust( left=0.02, right=0.98, bottom=0.001, top=0.96, wspace=0.05, hspace=0.01 ) 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( 0.99, 0.01, ("%.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 3.060 seconds) .. _sphx_glr_download_auto_examples_miscellaneous_plot_anomaly_comparison.py: .. only:: html .. container:: sphx-glr-footer sphx-glr-footer-example .. container:: binder-badge .. image:: images/binder_badge_logo.svg :target: https://mybinder.org/v2/gh/scikit-learn/scikit-learn/main?urlpath=lab/tree/notebooks/auto_examples/miscellaneous/plot_anomaly_comparison.ipynb :alt: Launch binder :width: 150 px .. container:: lite-badge .. image:: images/jupyterlite_badge_logo.svg :target: ../../lite/lab/?path=auto_examples/miscellaneous/plot_anomaly_comparison.ipynb :alt: Launch JupyterLite :width: 150 px .. container:: sphx-glr-download sphx-glr-download-jupyter :download:`Download Jupyter notebook: plot_anomaly_comparison.ipynb ` .. container:: sphx-glr-download sphx-glr-download-python :download:`Download Python source code: plot_anomaly_comparison.py ` .. include:: plot_anomaly_comparison.recommendations .. only:: html .. rst-class:: sphx-glr-signature `Gallery generated by Sphinx-Gallery `_