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# Authors: The scikit-learn developers
# SPDX-License-Identifier: BSD-3-Clause
from numbers import Real
import numpy as np
from ..base import OutlierMixin, _fit_context
from ..metrics import accuracy_score
from ..utils._param_validation import Interval
from ..utils.validation import check_is_fitted
from ._robust_covariance import MinCovDet
class EllipticEnvelope(OutlierMixin, MinCovDet):
"""An object for detecting outliers in a Gaussian distributed dataset.
Read more in the :ref:`User Guide <outlier_detection>`.
Parameters
----------
store_precision : bool, default=True
Specify if the estimated precision is stored.
assume_centered : bool, default=False
If True, the support of robust location and 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. If None, the minimum value of support_fraction will
be used within the algorithm: `(n_samples + n_features + 1) / 2 * n_samples`.
Range is (0, 1).
contamination : float, default=0.1
The amount of contamination of the data set, i.e. the proportion
of outliers in the data set. Range is (0, 0.5].
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 :term:`Glossary <random_state>`.
Attributes
----------
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.
offset_ : float
Offset used to define the decision function from the raw scores.
We have the relation: ``decision_function = score_samples - offset_``.
The offset depends on the contamination parameter and is defined in
such a way we obtain the expected number of outliers (samples with
decision function < 0) in training.
.. versionadded:: 0.20
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.
dist_ : ndarray of shape (n_samples,)
Mahalanobis distances of the training set (on which :meth:`fit` is
called) observations.
n_features_in_ : int
Number of features seen during :term:`fit`.
.. versionadded:: 0.24
feature_names_in_ : ndarray of shape (`n_features_in_`,)
Names of features seen during :term:`fit`. Defined only when `X`
has feature names that are all strings.
.. versionadded:: 1.0
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
--------
>>> import numpy as np
>>> from sklearn.covariance import EllipticEnvelope
>>> true_cov = np.array([[.8, .3],
... [.3, .4]])
>>> X = np.random.RandomState(0).multivariate_normal(mean=[0, 0],
... cov=true_cov,
... size=500)
>>> cov = EllipticEnvelope(random_state=0).fit(X)
>>> # predict returns 1 for an inlier and -1 for an outlier
>>> cov.predict([[0, 0],
... [3, 3]])
array([ 1, -1])
>>> cov.covariance_
array([[0.7411..., 0.2535...],
[0.2535..., 0.3053...]])
>>> cov.location_
array([0.0813... , 0.0427...])
"""
_parameter_constraints: dict = {
**MinCovDet._parameter_constraints,
"contamination": [Interval(Real, 0, 0.5, closed="right")],
}
def __init__(
self,
*,
store_precision=True,
assume_centered=False,
support_fraction=None,
contamination=0.1,
random_state=None,
):
super().__init__(
store_precision=store_precision,
assume_centered=assume_centered,
support_fraction=support_fraction,
random_state=random_state,
)
self.contamination = contamination
@_fit_context(prefer_skip_nested_validation=True)
def fit(self, X, y=None):
"""Fit the EllipticEnvelope model.
Parameters
----------
X : array-like of shape (n_samples, n_features)
Training data.
y : Ignored
Not used, present for API consistency by convention.
Returns
-------
self : object
Returns the instance itself.
"""
super().fit(X)
self.offset_ = np.percentile(-self.dist_, 100.0 * self.contamination)
return self
def decision_function(self, X):
"""Compute the decision function of the given observations.
Parameters
----------
X : array-like of shape (n_samples, n_features)
The data matrix.
Returns
-------
decision : ndarray 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.
"""
check_is_fitted(self)
negative_mahal_dist = self.score_samples(X)
return negative_mahal_dist - self.offset_
def score_samples(self, X):
"""Compute the negative Mahalanobis distances.
Parameters
----------
X : array-like of shape (n_samples, n_features)
The data matrix.
Returns
-------
negative_mahal_distances : array-like of shape (n_samples,)
Opposite of the Mahalanobis distances.
"""
check_is_fitted(self)
return -self.mahalanobis(X)
def predict(self, X):
"""
Predict labels (1 inlier, -1 outlier) of X according to fitted model.
Parameters
----------
X : array-like of shape (n_samples, n_features)
The data matrix.
Returns
-------
is_inlier : ndarray of shape (n_samples,)
Returns -1 for anomalies/outliers and +1 for inliers.
"""
values = self.decision_function(X)
is_inlier = np.full(values.shape[0], -1, dtype=int)
is_inlier[values >= 0] = 1
return is_inlier
def score(self, X, y, sample_weight=None):
"""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
----------
X : array-like of shape (n_samples, n_features)
Test samples.
y : array-like of shape (n_samples,) or (n_samples, n_outputs)
True labels for X.
sample_weight : array-like of shape (n_samples,), default=None
Sample weights.
Returns
-------
score : float
Mean accuracy of self.predict(X) w.r.t. y.
"""
return accuracy_score(y, self.predict(X), sample_weight=sample_weight)
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