# Author: Virgile Fritsch # # License: BSD 3 clause import numpy as np from numbers import Real from . import MinCovDet from ..utils._param_validation import Interval from ..utils.validation import check_is_fitted from ..metrics import accuracy_score from ..base import OutlierMixin class EllipticEnvelope(OutlierMixin, MinCovDet): """An object for detecting outliers in a Gaussian distributed dataset. Read more in the :ref:`User Guide `. Parameters ---------- store_precision : bool, default=True Specify if the estimated precision is stored. assume_centered : bool, default=False 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, default=None The proportion of points to be included in the support of the raw MCD estimate. If None, the minimum value of support_fraction will be used within the algorithm: `[n_sample + n_features + 1] / 2`. Range is (0, 1). contamination : float, default=0.1 The amount of contamination of the data set, i.e. the proportion of outliers in the data set. Range is (0, 0.5]. random_state : int, RandomState instance or None, default=None Determines the pseudo random number generator for shuffling the data. Pass an int for reproducible results across multiple function calls. See :term:`Glossary `. Attributes ---------- location_ : ndarray of shape (n_features,) Estimated robust location. covariance_ : ndarray of shape (n_features, n_features) Estimated robust covariance matrix. precision_ : ndarray of shape (n_features, n_features) Estimated pseudo inverse matrix. (stored only if store_precision is True) support_ : ndarray of shape (n_samples,) A mask of the observations that have been used to compute the robust estimates of location and shape. offset_ : float Offset used to define the decision function from the raw scores. We have the relation: ``decision_function = score_samples - offset_``. The offset depends on the contamination parameter and is defined in such a way we obtain the expected number of outliers (samples with decision function < 0) in training. .. versionadded:: 0.20 raw_location_ : ndarray of shape (n_features,) The raw robust estimated location before correction and re-weighting. raw_covariance_ : ndarray of shape (n_features, n_features) The raw robust estimated covariance before correction and re-weighting. raw_support_ : ndarray of shape (n_samples,) A mask of the observations that have been used to compute the raw robust estimates of location and shape, before correction and re-weighting. dist_ : ndarray of shape (n_samples,) Mahalanobis distances of the training set (on which :meth:`fit` is called) observations. n_features_in_ : int Number of features seen during :term:`fit`. .. versionadded:: 0.24 feature_names_in_ : ndarray of shape (`n_features_in_`,) Names of features seen during :term:`fit`. Defined only when `X` has feature names that are all strings. .. versionadded:: 1.0 See Also -------- EmpiricalCovariance : Maximum likelihood covariance estimator. GraphicalLasso : Sparse inverse covariance estimation with an l1-penalized estimator. LedoitWolf : LedoitWolf Estimator. MinCovDet : Minimum Covariance Determinant (robust estimator of covariance). OAS : Oracle Approximating Shrinkage Estimator. ShrunkCovariance : Covariance estimator with shrinkage. 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) Examples -------- >>> import numpy as np >>> from sklearn.covariance import EllipticEnvelope >>> true_cov = np.array([[.8, .3], ... [.3, .4]]) >>> X = np.random.RandomState(0).multivariate_normal(mean=[0, 0], ... cov=true_cov, ... size=500) >>> cov = EllipticEnvelope(random_state=0).fit(X) >>> # predict returns 1 for an inlier and -1 for an outlier >>> cov.predict([[0, 0], ... [3, 3]]) array([ 1, -1]) >>> cov.covariance_ array([[0.7411..., 0.2535...], [0.2535..., 0.3053...]]) >>> cov.location_ array([0.0813... , 0.0427...]) """ _parameter_constraints: dict = { **MinCovDet._parameter_constraints, "contamination": [Interval(Real, 0, 0.5, closed="right")], } def __init__( self, *, store_precision=True, assume_centered=False, support_fraction=None, contamination=0.1, random_state=None, ): super().__init__( store_precision=store_precision, assume_centered=assume_centered, support_fraction=support_fraction, random_state=random_state, ) self.contamination = contamination def fit(self, X, y=None): """Fit the EllipticEnvelope model. Parameters ---------- X : array-like of shape (n_samples, n_features) Training data. y : Ignored Not used, present for API consistency by convention. Returns ------- self : object Returns the instance itself. """ # `_validate_params` is called in `MinCovDet` super().fit(X) self.offset_ = np.percentile(-self.dist_, 100.0 * self.contamination) return self def decision_function(self, X): """Compute the decision function of the given observations. Parameters ---------- X : array-like of shape (n_samples, n_features) The data matrix. Returns ------- decision : ndarray of shape (n_samples,) Decision function of the samples. It is equal to the shifted Mahalanobis distances. The threshold for being an outlier is 0, which ensures a compatibility with other outlier detection algorithms. """ check_is_fitted(self) negative_mahal_dist = self.score_samples(X) return negative_mahal_dist - self.offset_ def score_samples(self, X): """Compute the negative Mahalanobis distances. Parameters ---------- X : array-like of shape (n_samples, n_features) The data matrix. Returns ------- negative_mahal_distances : array-like of shape (n_samples,) Opposite of the Mahalanobis distances. """ check_is_fitted(self) return -self.mahalanobis(X) def predict(self, X): """ Predict labels (1 inlier, -1 outlier) of X according to fitted model. Parameters ---------- X : array-like of shape (n_samples, n_features) The data matrix. Returns ------- is_inlier : ndarray of shape (n_samples,) Returns -1 for anomalies/outliers and +1 for inliers. """ values = self.decision_function(X) is_inlier = np.full(values.shape[0], -1, dtype=int) is_inlier[values >= 0] = 1 return is_inlier def score(self, X, y, sample_weight=None): """Return the mean accuracy on the given test data and labels. In multi-label classification, this is the subset accuracy which is a harsh metric since you require for each sample that each label set be correctly predicted. Parameters ---------- X : array-like of shape (n_samples, n_features) Test samples. y : array-like of shape (n_samples,) or (n_samples, n_outputs) True labels for X. sample_weight : array-like of shape (n_samples,), default=None Sample weights. Returns ------- score : float Mean accuracy of self.predict(X) w.r.t. y. """ return accuracy_score(y, self.predict(X), sample_weight=sample_weight)