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 Gaussiandistributed data, but could still be relevant on data drawn from a unimodal, symmetric distribution. It is not meant to be used with multimodal 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 multimodal datasets.
Read more in the User Guide.
 Parameters
 store_precisionbool
Specify if the estimated precision is stored.
 assume_centeredbool
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, 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
 random_stateint, RandomState instance or None, optional (default=None)
If int, random_state is the seed used by the random number generator; If RandomState instance, random_state is the random number generator; If None, the random number generator is the RandomState instance used by
np.random
.
 Attributes
 raw_location_arraylike, shape (n_features,)
The raw robust estimated location before correction and reweighting.
 raw_covariance_arraylike, shape (n_features, n_features)
The raw robust estimated covariance before correction and reweighting.
 raw_support_arraylike, 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 reweighting.
 location_arraylike, shape (n_features,)
Estimated robust location
 covariance_arraylike, shape (n_features, n_features)
Estimated robust covariance matrix
 precision_arraylike, shape (n_features, n_features)
Estimated pseudo inverse matrix. (stored only if store_precision is True)
 support_arraylike, shape (n_samples,)
A mask of the observations that have been used to compute the robust estimates of location and shape.
 dist_arraylike, shape (n_samples,)
Mahalanobis distances of the training set (on which
fit
is called) observations.
References
 R9f63e655f7bdRouseeuw1984
P. J. Rousseeuw. Least median of squares regression. J. Am Stat Ass, 79:871, 1984.
 R9f63e655f7bdRousseeuw
A Fast Algorithm for the Minimum Covariance Determinant Estimator, 1999, American Statistical Association and the American Society for Quality, TECHNOMETRICS
 R9f63e655f7bdButlerDavies
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, 13851400
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
(self, data)Apply a correction to raw Minimum Covariance Determinant estimates.
error_norm
(self, comp_cov[, norm, scaling, …])Computes the Mean Squared Error between two covariance estimators.
fit
(self, X[, y])Fits a Minimum Covariance Determinant with the FastMCD algorithm.
get_params
(self[, deep])Get parameters for this estimator.
get_precision
(self)Getter for the precision matrix.
mahalanobis
(self, X)Computes the squared Mahalanobis distances of given observations.
reweight_covariance
(self, data)Reweight raw Minimum Covariance Determinant estimates.
score
(self, X_test[, y])Computes the loglikelihood of a Gaussian data set with
self.covariance_
as an estimator of its covariance matrix.set_params
(self, \*\*params)Set the parameters of this estimator.

__init__
(self, store_precision=True, assume_centered=False, support_fraction=None, random_state=None)[source]¶ Initialize self. See help(type(self)) for accurate signature.

correct_covariance
(self, 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
 dataarraylike, 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_correctedarraylike, 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
(self, 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_covarraylike of shape (n_features, n_features)
The covariance to compare with.
 normstr
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
If True (default), the squared error norm is divided by n_features. If False, the squared error norm is not rescaled.
 squaredbool
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
 The Mean Squared Error (in the sense of the Frobenius norm) between
self
andcomp_cov
covariance estimators.

fit
(self, X, y=None)[source]¶ Fits a Minimum Covariance Determinant with the FastMCD algorithm.
 Parameters
 Xarraylike 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
not used, present for API consistence purpose.
 Returns
 selfobject

get_params
(self, 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
(self)[source]¶ Getter for the precision matrix.
 Returns
 precision_arraylike
The precision matrix associated to the current covariance object.

mahalanobis
(self, X)[source]¶ Computes the squared Mahalanobis distances of given observations.
 Parameters
 Xarraylike 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
 distarray, shape = [n_samples,]
Squared Mahalanobis distances of the observations.

reweight_covariance
(self, data)[source]¶ Reweight raw Minimum Covariance Determinant estimates.
Reweight observations using Rousseeuw’s method (equivalent to deleting outlying observations from the data set before computing location and covariance estimates) described in [RVDriessen].
 Parameters
 dataarraylike, 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_reweightedarraylike, shape (n_features, )
Reweighted robust location estimate.
 covariance_reweightedarraylike, shape (n_features, n_features)
Reweighted robust covariance estimate.
 support_reweightedarraylike, type boolean, shape (n_samples,)
A mask of the observations that have been used to compute the reweighted 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
(self, X_test, y=None)[source]¶ Computes the loglikelihood of a Gaussian data set with
self.covariance_
as an estimator of its covariance matrix. Parameters
 X_testarraylike 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).
 y
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
(self, **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.