EllipticEnvelope#

class sklearn.covariance.EllipticEnvelope(*, store_precision=True, assume_centered=False, support_fraction=None, contamination=0.1, random_state=None)[source]#

An object for detecting outliers in a Gaussian distributed dataset.

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...])

correct_covariance(data)[source]#

Apply a correction to raw Minimum Covariance Determinant estimates.

Correction using the empirical correction factor suggested by Rousseeuw and Van Driessen in [RVD].

Parameters:

dataarray-like of shape (n_samples, n_features): The data matrix, with p features and n samples. The data set must be the one which was used to compute the raw estimates.

Returns:

covariance_correctedndarray of shape (n_features, n_features): Corrected robust covariance estimate.

References

[RVD]

A Fast Algorithm for the Minimum Covariance Determinant Estimator, 1999, American Statistical Association and the American Society for Quality, TECHNOMETRICS

decision_function(X)[source]#

Compute the decision function of the given observations.

Parameters:

Xarray-like of shape (n_samples, n_features): The data matrix.

Returns:

decisionndarray 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.

error_norm(comp_cov, norm='frobenius', scaling=True, squared=True)[source]#

Compute the Mean Squared Error between two covariance estimators.

Parameters:

comp_covarray-like of shape (n_features, n_features): The covariance to compare with.
norm{“frobenius”, “spectral”}, default=”frobenius”: The type of norm used to compute the error. Available error types: - ‘frobenius’ (default): sqrt(tr(A^t.A)) - ‘spectral’: sqrt(max(eigenvalues(A^t.A)) where A is the error (comp_cov - self.covariance_).
scalingbool, default=True: If True (default), the squared error norm is divided by n_features. If False, the squared error norm is not rescaled.
squaredbool, default=True: Whether to compute the squared error norm or the error norm. If True (default), the squared error norm is returned. If False, the error norm is returned.

Returns:

resultfloat: The Mean Squared Error (in the sense of the Frobenius norm) between self and comp_cov covariance estimators.

fit(X, y=None)[source]#

Fit the EllipticEnvelope model.

Parameters:

Xarray-like of shape (n_samples, n_features): Training data.
yIgnored: Not used, present for API consistency by convention.

Returns:

selfobject: Returns the instance itself.

fit_predict(X, y=None, **kwargs)[source]#

Perform fit on X and returns labels for X.

Returns -1 for outliers and 1 for inliers.

Parameters:

X{array-like, sparse matrix} of shape (n_samples, n_features): The input samples.
yIgnored: Not used, present for API consistency by convention.
**kwargsdict: Arguments to be passed to fit.

Added in version 1.4.

Returns:

yndarray of shape (n_samples,): 1 for inliers, -1 for outliers.

get_metadata_routing()[source]#

Get metadata routing of this object.

Please check User Guide on how the routing mechanism works.

Returns:

routingMetadataRequest: A MetadataRequest encapsulating routing information.

get_params(deep=True)[source]#

Get parameters for this estimator.

Parameters:

deepbool, default=True: If True, will return the parameters for this estimator and contained subobjects that are estimators.

Returns:

paramsdict: Parameter names mapped to their values.

get_precision()[source]#

Getter for the precision matrix.

Returns:

precision_array-like of shape (n_features, n_features): The precision matrix associated to the current covariance object.

mahalanobis(X)[source]#

Compute the squared Mahalanobis distances of given observations.

Parameters:

Xarray-like of shape (n_samples, n_features): The observations, the Mahalanobis distances of the which we compute. Observations are assumed to be drawn from the same distribution than the data used in fit.

Returns:

distndarray of shape (n_samples,): Squared Mahalanobis distances of the observations.

predict(X)[source]#

Predict labels (1 inlier, -1 outlier) of X according to fitted model.

Parameters:

Xarray-like of shape (n_samples, n_features): The data matrix.

Returns:

is_inlierndarray of shape (n_samples,): Returns -1 for anomalies/outliers and +1 for inliers.

reweight_covariance(data)[source]#

Re-weight raw Minimum Covariance Determinant estimates.

Re-weight observations using Rousseeuw’s method (equivalent to deleting outlying observations from the data set before computing location and covariance estimates) described in [RVDriessen].

Parameters:

dataarray-like of shape (n_samples, n_features): The data matrix, with p features and n samples. The data set must be the one which was used to compute the raw estimates.

Returns:

location_reweightedndarray of shape (n_features,): Re-weighted robust location estimate.
covariance_reweightedndarray of shape (n_features, n_features): Re-weighted robust covariance estimate.
support_reweightedndarray of shape (n_samples,), dtype=bool: A mask of the observations that have been used to compute the re-weighted robust location and covariance estimates.

References

[RVDriessen]

A Fast Algorithm for the Minimum Covariance Determinant Estimator, 1999, American Statistical Association and the American Society for Quality, TECHNOMETRICS

score(X, y, sample_weight=None)[source]#

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:

Xarray-like of shape (n_samples, n_features): Test samples.
yarray-like of shape (n_samples,) or (n_samples, n_outputs): True labels for X.
sample_weightarray-like of shape (n_samples,), default=None: Sample weights.

Returns:

scorefloat: Mean accuracy of self.predict(X) w.r.t. y.

score_samples(X)[source]#

Compute the negative Mahalanobis distances.

Parameters:

Xarray-like of shape (n_samples, n_features): The data matrix.

Returns:

negative_mahal_distancesarray-like of shape (n_samples,): Opposite of the Mahalanobis distances.

set_params(**params)[source]#

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as Pipeline). The latter have parameters of the form <component>__<parameter> so that it’s possible to update each component of a nested object.

Parameters:

**paramsdict: Estimator parameters.

Returns:

selfestimator instance: Estimator instance.

Gallery examples#

Outlier detection on a real data set

Comparing anomaly detection algorithms for outlier detection on toy datasets