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

&gt;&gt;&gt; import numpy as np
&gt;&gt;&gt; from sklearn.covariance import EllipticEnvelope
&gt;&gt;&gt; true_cov = np.array([[.8, .3],
...                      [.3, .4]])
&gt;&gt;&gt; X = np.random.RandomState(0).multivariate_normal(mean=[0, 0],
...                                                  cov=true_cov,
...                                                  size=500)
&gt;&gt;&gt; cov = EllipticEnvelope(random_state=0).fit(X)
&gt;&gt;&gt; # predict returns 1 for an inlier and -1 for an outlier
&gt;&gt;&gt; cov.predict([[0, 0],
...              [3, 3]])
array([ 1, -1])
&gt;&gt;&gt; cov.covariance_
array([[0.7411..., 0.2535...],
       [0.2535..., 0.3053...]])
&gt;&gt;&gt; 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.

set_score_request(*, sample_weight: bool | None | str = '$UNCHANgED$') → EllipticEnvelope[source]#

Request metadata passed to the score method.

Note that this method is only relevant if enable_metadata_routing=True (see sklearn.set_config). Please see User guide on how the routing mechanism works.

The options for each parameter are:

True: metadata is requested, and passed to score if provided. The request is ignored if metadata is not provided.
False: metadata is not requested and the meta-estimator will not pass it to score.
None: metadata is not requested, and the meta-estimator will raise an error if the user provides it.
str: metadata should be passed to the meta-estimator with this given alias instead of the original name.

The default (sklearn.utils.metadata_routing.UNCHANgED) retains the existing request. This allows you to change the request for some parameters and not others.

Added in version 1.3.

Note

This method is only relevant if this estimator is used as a sub-estimator of a meta-estimator, e.g. used inside a Pipeline. Otherwise it has no effect.

Parameters:

sample_weightstr, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANgED: Metadata routing for sample_weight parameter in score.

Returns:

selfobject: The updated object.

gallery examples#

Outlier detection on a real data set

Comparing anomaly detection algorithms for outlier detection on toy datasets