""" Class for outlier detection. This class provides a framework for outlier detection. It consists in several methods that can be added to a covariance estimator in order to assess the outlying-ness of the observations of a data set. Such a "outlier detector" object is proposed constructed from a robust covariance estimator (the Minimum Covariance Determinant). """ # Author: Virgile Fritsch # # License: BSD 3 clause import numpy as np import scipy as sp from . import MinCovDet from ..base import ClassifierMixin from ..utils.validation import check_is_fitted class OutlierDetectionMixin(object): """Set of methods for outliers detection with covariance estimators. Parameters ---------- contamination : float, 0. < contamination < 0.5 The amount of contamination of the data set, i.e. the proportion of outliers in the data set. Notes ----- Outlier detection from covariance estimation may break or not perform well in high-dimensional settings. In particular, one will always take care to work with ``n_samples > n_features ** 2``. """ def __init__(self, contamination=0.1): self.contamination = contamination def decision_function(self, X, raw_values=False): """Compute the decision function of the given observations. Parameters ---------- X : array-like, shape (n_samples, n_features) raw_values : bool Whether or not to consider raw Mahalanobis distances as the decision function. Must be False (default) for compatibility with the others outlier detection tools. Returns ------- decision : array-like, shape (n_samples, ) The values of the decision function for each observations. It is equal to the Mahalanobis distances if `raw_values` is True. By default (``raw_values=True``), it is equal to the cubic root of the shifted Mahalanobis distances. In that case, the threshold for being an outlier is 0, which ensures a compatibility with other outlier detection tools such as the One-Class SVM. """ check_is_fitted(self, 'threshold_') mahal_dist = self.mahalanobis(X) if raw_values: decision = mahal_dist else: check_is_fitted(self, 'threshold_') transformed_mahal_dist = mahal_dist ** 0.33 decision = self.threshold_ ** 0.33 - transformed_mahal_dist return decision def predict(self, X): """Outlyingness of observations in X according to the fitted model. Parameters ---------- X : array-like, shape = (n_samples, n_features) Returns ------- is_outliers : array, shape = (n_samples, ), dtype = bool For each observations, tells whether or not it should be considered as an outlier according to the fitted model. threshold : float, The values of the less outlying point's decision function. """ check_is_fitted(self, 'threshold_') is_inlier = -np.ones(X.shape[0], dtype=int) if self.contamination is not None: values = self.decision_function(X, raw_values=True) is_inlier[values <= self.threshold_] = 1 else: raise NotImplementedError("You must provide a contamination rate.") return is_inlier class EllipticEnvelope(ClassifierMixin, OutlierDetectionMixin, MinCovDet): """An object for detecting outliers in a Gaussian distributed dataset. Read more in the :ref:`User Guide `. Attributes ---------- `contamination` : float, 0. < contamination < 0.5 The amount of contamination of the data set, i.e. the proportion of \ outliers in the data set. location_ : array-like, shape (n_features,) Estimated robust location covariance_ : array-like, shape (n_features, n_features) Estimated robust covariance matrix precision_ : array-like, shape (n_features, n_features) Estimated pseudo inverse matrix. (stored only if store_precision is True) support_ : array-like, shape (n_samples,) A mask of the observations that have been used to compute the robust estimates of location and shape. Parameters ---------- store_precision : bool Specify if the estimated precision is stored. assume_centered : Boolean If True, the support of robust location and covariance estimates is computed, and a covariance estimate is recomputed from it, without centering the data. Useful to work with data whose mean is significantly equal to zero but is not exactly zero. If False, the robust location and covariance are directly computed with the FastMCD algorithm without additional treatment. support_fraction : float, 0 < support_fraction < 1 The proportion of points to be included in the support of the raw MCD estimate. Default is ``None``, which implies that the minimum value of support_fraction will be used within the algorithm: `[n_sample + n_features + 1] / 2`. contamination : float, 0. < contamination < 0.5 The amount of contamination of the data set, i.e. the proportion of outliers in the data set. See Also -------- EmpiricalCovariance, MinCovDet Notes ----- Outlier detection from covariance estimation may break or not perform well in high-dimensional settings. In particular, one will always take care to work with ``n_samples > n_features ** 2``. References ---------- .. [1] Rousseeuw, P.J., Van Driessen, K. "A fast algorithm for the minimum covariance determinant estimator" Technometrics 41(3), 212 (1999) """ def __init__(self, store_precision=True, assume_centered=False, support_fraction=None, contamination=0.1, random_state=None): MinCovDet.__init__(self, store_precision=store_precision, assume_centered=assume_centered, support_fraction=support_fraction, random_state=random_state) OutlierDetectionMixin.__init__(self, contamination=contamination) def fit(self, X, y=None): MinCovDet.fit(self, X) self.threshold_ = sp.stats.scoreatpercentile( self.dist_, 100. * (1. - self.contamination)) return self