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# `sklearn.covariance`.MinCovDet

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

  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_precision bool, default=True

      Specify if the estimated precision is stored.

    assume_centered bool, 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_fraction float, 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_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 Glossary.

  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.

    n_features_in_int

      Number of features seen during fit.

      New in version 0.24.

    feature_names_in_ndarray of shape (`n_features_in_`,)

      Names of features seen during fit. Defined only when `X` has feature names that are all strings.

      New in version 1.0.

  See also

  `EllipticEnvelope`

    An object for detecting outliers in a Gaussian distributed dataset.

  `EmpiricalCovariance`

    Maximum likelihood covariance estimator.

  `GraphicalLasso`

    Sparse inverse covariance estimation with an l1-penalized estimator.

  `GraphicalLassoCV`

    Sparse inverse covariance with cross-validated choice of the l1 penalty.

  `LedoitWolf`

    LedoitWolf Estimator.

  `OAS`

    Oracle Approximating Shrinkage Estimator.

  `ShrunkCovariance`

    Covariance estimator with shrinkage.

  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]) | Compute the Mean Squared Error between two covariance estimators.
  `fit`(X[, y]) | Fit a Minimum Covariance Determinant with the FastMCD algorithm.
  `get_metadata_routing`() | Get metadata routing of this object.
  `get_params`([deep]) | Get parameters for this estimator.
  `get_precision`() | Getter for the precision matrix.
  `mahalanobis`(X) | Compute the squared Mahalanobis distances of given observations.
  `reweight_covariance`(data) | Re-weight raw Minimum Covariance Determinant estimates.
  `score`(X_test[, y]) | Compute the log-likelihood of `X_test` under the estimated Gaussian model.
  `set_params`(**params) | Set the parameters of this estimator.
  `set_score_request`(*[, X_test]) | Request metadata passed to the `score` method.

  correct_covariance(data)

    Apply a correction to raw Minimum Covariance Determinant estimates.

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

    Parameters:
      data array-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_corrected ndarray 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)

    Compute the Mean Squared Error between two covariance estimators.

    Parameters:
      comp_cov array-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_)`.

      scaling bool, default=True

        If True (default), the squared error norm is divided by n_features. If False, the squared error norm is not rescaled.

      squared bool, 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:
      result float

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

  fit(X, y=None)

    Fit a Minimum Covariance Determinant with the FastMCD algorithm.

    Parameters:
      X array-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 consistency by convention.

    Returns:
      self object

        Returns the instance itself.

  get_metadata_routing()

    Get metadata routing of this object.

    Please check User Guide on how the routing mechanism works.

    Returns:
      routing MetadataRequest

        A `MetadataRequest` encapsulating routing information.

  get_params(deep=True)

    Get parameters for this estimator.

    Parameters:
      deep bool, default=True

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

    Returns:
      params dict

        Parameter names mapped to their values.

  get_precision()

    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)

    Compute the squared Mahalanobis distances of given observations.

    Parameters:
      X array-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:
      dist ndarray of shape (n_samples,)

        Squared Mahalanobis distances of the observations.

  reweight_covariance(data)

    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:
      data array-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_reweighted ndarray of shape (n_features,)

        Re-weighted robust location estimate.

      covariance_reweighted ndarray of shape (n_features, n_features)

        Re-weighted robust covariance estimate.

      support_reweighted ndarray 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)

    Compute the log-likelihood of `X_test` under the estimated Gaussian model.

    The Gaussian model is defined by its mean and covariance matrix which are represented respectively by `self.location_` and `self.covariance_`.

    Parameters:
      X_test array-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).

      y Ignored

        Not used, present for API consistency by convention.

    Returns:
      res float

        The log-likelihood of `X_test` with `self.location_` and `self.covariance_` as estimators of the Gaussian model mean and covariance matrix respectively.

  set_params(**params)

    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:
      **params dict

        Estimator parameters.

    Returns:
      self estimator instance

        Estimator instance.

  set_score_request(*, X_test: bool | None | str = '$UNCHANGED$') → MinCovDet

    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.

    New 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:
      X_test str, True, False, or None, default=sklearn.utils.metadata_routing.UNCHANGED

        Metadata routing for `X_test` parameter in `score`.

    Returns:
      self object

        The updated object.

## Examples using `sklearn.covariance.MinCovDet`

Robust covariance estimation and Mahalanobis distances relevance

Robust covariance estimation and Mahalanobis distances relevance

Robust vs Empirical covariance estimate

Robust vs Empirical covariance estimate