sklearn.covariance.MinCovDet

class sklearn.covariance.MinCovDet(*, store_precision=True, assume_centered=False, support_fraction=None, random_state=None)[source]

Minimum Covariance Determinant (MCD): robust estimator of covariance.

The Minimum Covariance Determinant covariance estimator is to be applied on Gaussian-distributed data, but could still be relevant on data drawn from a unimodal, symmetric distribution. It is not meant to be used with multi-modal data (the algorithm used to fit a MinCovDet object is likely to fail in such a case). One should consider projection pursuit methods to deal with multi-modal datasets.

Read more in the User Guide.

Parameters
store_precisionbool, default=True

Specify if the estimated precision is stored.

assume_centeredbool, default=False

If True, the support of the robust location and the 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_fractionfloat, default=None

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. The parameter must be in the range (0, 1).

random_stateint or RandomState instance, 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 <random_state>.

Attributes
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.

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.

dist_ndarray of shape (n_samples,)

Mahalanobis distances of the training set (on which fit is called) observations.

References

Rouseeuw1984

P. J. Rousseeuw. Least median of squares regression. J. Am Stat Ass, 79:871, 1984.

Rousseeuw

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

ButlerDavies

R. W. Butler, P. L. Davies and M. Jhun, Asymptotics For The Minimum Covariance Determinant Estimator, The Annals of Statistics, 1993, Vol. 21, No. 3, 1385-1400

Examples

>>> import numpy as np
>>> from sklearn.covariance import MinCovDet
>>> from sklearn.datasets import make_gaussian_quantiles
>>> real_cov = np.array([[.8, .3],
...                      [.3, .4]])
>>> rng = np.random.RandomState(0)
>>> X = rng.multivariate_normal(mean=[0, 0],
...                                   cov=real_cov,
...                                   size=500)
>>> cov = MinCovDet(random_state=0).fit(X)
>>> cov.covariance_
array([[0.7411..., 0.2535...],
       [0.2535..., 0.3053...]])
>>> cov.location_
array([0.0813... , 0.0427...])

Methods

correct_covariance(data)

Apply a correction to raw Minimum Covariance Determinant estimates.

error_norm(comp_cov[, norm, scaling, squared])

Computes the Mean Squared Error between two covariance estimators.

fit(X[, y])

Fits a Minimum Covariance Determinant with the FastMCD algorithm.

get_params([deep])

Get parameters for this estimator.

get_precision()

Getter for the precision matrix.

mahalanobis(X)

Computes the squared Mahalanobis distances of given observations.

reweight_covariance(data)

Re-weight raw Minimum Covariance Determinant estimates.

score(X_test[, y])

Computes the log-likelihood of a Gaussian data set with self.covariance_ as an estimator of its covariance matrix.

set_params(**params)

Set the parameters of this estimator.
__init__(*, store_precision=True, assume_centered=False, support_fraction=None, random_state=None)[source]

Initialize self. See help(type(self)) for accurate signature.

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

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

Computes the Mean Squared Error between two covariance estimators. (In the sense of the Frobenius norm).

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]

Fits a Minimum Covariance Determinant with the FastMCD algorithm.

Parameters
Xarray-like of shape (n_samples, n_features)

Training data, where n_samples is the number of samples and n_features is the number of features.

y: Ignored

Not used, present for API consistence purpose.

Returns
selfobject
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
paramsmapping of string to any

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]

Computes 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.

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_test, y=None)[source]

Computes the log-likelihood of a Gaussian data set with self.covariance_ as an estimator of its covariance matrix.

Parameters
X_testarray-like of shape (n_samples, n_features)

Test data of which we compute the likelihood, where n_samples is the number of samples and n_features is the number of features. X_test is assumed to be drawn from the same distribution than the data used in fit (including centering).

yIgnored

Not used, present for API consistence purpose.

Returns
resfloat

The likelihood of the data set with self.covariance_ as an estimator of its covariance matrix.

set_params(**params)[source]

Set the parameters of this estimator.

The method works on simple estimators as well as on nested objects (such as pipelines). 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
selfobject

Estimator instance.