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# Author: Virgile Fritsch <virgile.fritsch@inria.fr>
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#
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# License: BSD 3 clause
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from numbers import Real
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import numpy as np
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from ..base import OutlierMixin, _fit_context
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from ..metrics import accuracy_score
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from ..utils._param_validation import Interval
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from ..utils.validation import check_is_fitted
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from ._robust_covariance import MinCovDet
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class EllipticEnvelope(OutlierMixin, MinCovDet):
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"""An object for detecting outliers in a Gaussian distributed dataset.
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Read more in the :ref:`User Guide <outlier_detection>`.
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Parameters
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----------
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store_precision : bool, default=True
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Specify if the estimated precision is stored.
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assume_centered : bool, default=False
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If True, the support of robust location and covariance estimates
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is computed, and a covariance estimate is recomputed from it,
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without centering the data.
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Useful to work with data whose mean is significantly equal to
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zero but is not exactly zero.
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If False, the robust location and covariance are directly computed
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with the FastMCD algorithm without additional treatment.
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support_fraction : float, default=None
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The proportion of points to be included in the support of the raw
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MCD estimate. If None, the minimum value of support_fraction will
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be used within the algorithm: `(n_samples + n_features + 1) / 2 * n_samples`.
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Range is (0, 1).
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contamination : float, default=0.1
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The amount of contamination of the data set, i.e. the proportion
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of outliers in the data set. Range is (0, 0.5].
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random_state : int, RandomState instance or None, default=None
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Determines the pseudo random number generator for shuffling
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the data. Pass an int for reproducible results across multiple function
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calls. See :term:`Glossary <random_state>`.
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Attributes
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----------
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location_ : ndarray of shape (n_features,)
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Estimated robust location.
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covariance_ : ndarray of shape (n_features, n_features)
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Estimated robust covariance matrix.
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precision_ : ndarray of shape (n_features, n_features)
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Estimated pseudo inverse matrix.
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(stored only if store_precision is True)
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support_ : ndarray of shape (n_samples,)
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A mask of the observations that have been used to compute the
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robust estimates of location and shape.
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offset_ : float
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Offset used to define the decision function from the raw scores.
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We have the relation: ``decision_function = score_samples - offset_``.
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The offset depends on the contamination parameter and is defined in
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such a way we obtain the expected number of outliers (samples with
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decision function < 0) in training.
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.. versionadded:: 0.20
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raw_location_ : ndarray of shape (n_features,)
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The raw robust estimated location before correction and re-weighting.
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raw_covariance_ : ndarray of shape (n_features, n_features)
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The raw robust estimated covariance before correction and re-weighting.
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raw_support_ : ndarray of shape (n_samples,)
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A mask of the observations that have been used to compute
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the raw robust estimates of location and shape, before correction
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and re-weighting.
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dist_ : ndarray of shape (n_samples,)
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Mahalanobis distances of the training set (on which :meth:`fit` is
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called) observations.
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n_features_in_ : int
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Number of features seen during :term:`fit`.
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.. versionadded:: 0.24
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feature_names_in_ : ndarray of shape (`n_features_in_`,)
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Names of features seen during :term:`fit`. Defined only when `X`
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has feature names that are all strings.
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.. versionadded:: 1.0
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See Also
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--------
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EmpiricalCovariance : Maximum likelihood covariance estimator.
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GraphicalLasso : Sparse inverse covariance estimation
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with an l1-penalized estimator.
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LedoitWolf : LedoitWolf Estimator.
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MinCovDet : Minimum Covariance Determinant
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(robust estimator of covariance).
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OAS : Oracle Approximating Shrinkage Estimator.
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ShrunkCovariance : Covariance estimator with shrinkage.
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Notes
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-----
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Outlier detection from covariance estimation may break or not
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perform well in high-dimensional settings. In particular, one will
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always take care to work with ``n_samples > n_features ** 2``.
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References
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----------
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.. [1] Rousseeuw, P.J., Van Driessen, K. "A fast algorithm for the
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minimum covariance determinant estimator" Technometrics 41(3), 212
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(1999)
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Examples
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--------
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>>> import numpy as np
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>>> from sklearn.covariance import EllipticEnvelope
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>>> true_cov = np.array([[.8, .3],
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... [.3, .4]])
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>>> X = np.random.RandomState(0).multivariate_normal(mean=[0, 0],
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... cov=true_cov,
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... size=500)
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>>> cov = EllipticEnvelope(random_state=0).fit(X)
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>>> # predict returns 1 for an inlier and -1 for an outlier
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>>> cov.predict([[0, 0],
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... [3, 3]])
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array([ 1, -1])
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>>> cov.covariance_
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array([[0.7411..., 0.2535...],
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[0.2535..., 0.3053...]])
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>>> cov.location_
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array([0.0813... , 0.0427...])
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"""
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_parameter_constraints: dict = {
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**MinCovDet._parameter_constraints,
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"contamination": [Interval(Real, 0, 0.5, closed="right")],
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}
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def __init__(
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self,
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*,
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store_precision=True,
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assume_centered=False,
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support_fraction=None,
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contamination=0.1,
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random_state=None,
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):
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super().__init__(
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store_precision=store_precision,
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assume_centered=assume_centered,
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support_fraction=support_fraction,
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random_state=random_state,
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)
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self.contamination = contamination
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@_fit_context(prefer_skip_nested_validation=True)
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def fit(self, X, y=None):
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"""Fit the EllipticEnvelope model.
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Parameters
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----------
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X : array-like of shape (n_samples, n_features)
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Training data.
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y : Ignored
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Not used, present for API consistency by convention.
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Returns
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-------
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self : object
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Returns the instance itself.
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"""
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super().fit(X)
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self.offset_ = np.percentile(-self.dist_, 100.0 * self.contamination)
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return self
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def decision_function(self, X):
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"""Compute the decision function of the given observations.
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Parameters
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----------
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X : array-like of shape (n_samples, n_features)
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The data matrix.
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Returns
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-------
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decision : ndarray of shape (n_samples,)
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Decision function of the samples.
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It is equal to the shifted Mahalanobis distances.
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The threshold for being an outlier is 0, which ensures a
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compatibility with other outlier detection algorithms.
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"""
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check_is_fitted(self)
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negative_mahal_dist = self.score_samples(X)
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return negative_mahal_dist - self.offset_
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def score_samples(self, X):
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"""Compute the negative Mahalanobis distances.
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Parameters
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----------
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X : array-like of shape (n_samples, n_features)
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The data matrix.
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Returns
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-------
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negative_mahal_distances : array-like of shape (n_samples,)
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Opposite of the Mahalanobis distances.
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"""
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check_is_fitted(self)
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return -self.mahalanobis(X)
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def predict(self, X):
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"""
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Predict labels (1 inlier, -1 outlier) of X according to fitted model.
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Parameters
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----------
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X : array-like of shape (n_samples, n_features)
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The data matrix.
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Returns
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-------
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is_inlier : ndarray of shape (n_samples,)
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Returns -1 for anomalies/outliers and +1 for inliers.
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"""
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values = self.decision_function(X)
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is_inlier = np.full(values.shape[0], -1, dtype=int)
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is_inlier[values >= 0] = 1
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return is_inlier
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def score(self, X, y, sample_weight=None):
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"""Return the mean accuracy on the given test data and labels.
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In multi-label classification, this is the subset accuracy
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which is a harsh metric since you require for each sample that
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each label set be correctly predicted.
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Parameters
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----------
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X : array-like of shape (n_samples, n_features)
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Test samples.
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y : array-like of shape (n_samples,) or (n_samples, n_outputs)
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True labels for X.
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sample_weight : array-like of shape (n_samples,), default=None
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Sample weights.
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Returns
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-------
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score : float
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Mean accuracy of self.predict(X) w.r.t. y.
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"""
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return accuracy_score(y, self.predict(X), sample_weight=sample_weight)
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