"""
Class for outlier detection.
This class provides a framework for outlier detection. It consists in
several methods that can be added to a covariance estimator in order to
assess the outlying-ness of the observations of a data set.
Such a "outlier detector" object is proposed constructed from a robust
covariance estimator (the Minimum Covariance Determinant).
"""
# Author: Virgile Fritsch <virgile.fritsch@inria.fr>
#
# License: BSD 3 clause
import numpy as np
import scipy as sp
from . import MinCovDet
from ..utils.validation import check_is_fitted, check_array
from ..metrics import accuracy_score
class EllipticEnvelope(MinCovDet):
"""An object for detecting outliers in a Gaussian distributed dataset.
Read more in the :ref:`User Guide <outlier_detection>`.
Parameters
----------
store_precision : boolean, optional (default=True)
Specify if the estimated precision is stored.
assume_centered : boolean, optional (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 in (0., 1.), optional (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_sample + n_features + 1] / 2`.
contamination : float in (0., 0.5), optional (default=0.1)
The amount of contamination of the data set, i.e. the proportion
of outliers in the data set.
random_state : int, RandomState instance or None, optional (default=None)
The seed of the pseudo random number generator to use when shuffling
the data. 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
----------
location_ : array-like, shape (n_features,)
Estimated robust location
covariance_ : array-like, shape (n_features, n_features)
Estimated robust covariance matrix
precision_ : array-like, shape (n_features, n_features)
Estimated pseudo inverse matrix.
(stored only if store_precision is True)
support_ : array-like, shape (n_samples,)
A mask of the observations that have been used to compute the
robust estimates of location and shape.
See Also
--------
EmpiricalCovariance, MinCovDet
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)
"""
def __init__(self, store_precision=True, assume_centered=False,
support_fraction=None, contamination=0.1,
random_state=None):
super(EllipticEnvelope, self).__init__(
store_precision=store_precision,
assume_centered=assume_centered,
support_fraction=support_fraction,
random_state=random_state)
self.contamination = contamination
[docs] def fit(self, X, y=None):
"""Fit the EllipticEnvelope model with X.
Parameters
----------
X : numpy array or sparse matrix of shape [n_samples, n_features]
Training data
y : (ignored)
"""
super(EllipticEnvelope, self).fit(X)
self.threshold_ = sp.stats.scoreatpercentile(
self.dist_, 100. * (1. - self.contamination))
return self
[docs] def decision_function(self, X, raw_values=False):
"""Compute the decision function of the given observations.
Parameters
----------
X : array-like, shape (n_samples, n_features)
raw_values : bool
Whether or not to consider raw Mahalanobis distances as the
decision function. Must be False (default) for compatibility
with the others outlier detection tools.
Returns
-------
decision : array-like, shape (n_samples, )
Decision function of the samples.
It is equal to the Mahalanobis distances if `raw_values`
is True. By default (``raw_values=False``), it is equal
to the cubic root of the shifted Mahalanobis distances.
In that case, the threshold for being an outlier is 0, which
ensures a compatibility with other outlier detection tools
such as the One-Class SVM.
"""
check_is_fitted(self, 'threshold_')
X = check_array(X)
mahal_dist = self.mahalanobis(X)
if raw_values:
decision = mahal_dist
else:
transformed_mahal_dist = mahal_dist ** 0.33
decision = self.threshold_ ** 0.33 - transformed_mahal_dist
return decision
[docs] def predict(self, X):
"""Outlyingness of observations in X according to the fitted model.
Parameters
----------
X : array-like, shape = (n_samples, n_features)
Returns
-------
is_outliers : array, shape = (n_samples, ), dtype = bool
For each observation, tells whether or not it should be considered
as an outlier according to the fitted model.
threshold : float,
The values of the less outlying point's decision function.
"""
check_is_fitted(self, 'threshold_')
X = check_array(X)
is_inlier = -np.ones(X.shape[0], dtype=int)
if self.contamination is not None:
values = self.decision_function(X, raw_values=True)
is_inlier[values <= self.threshold_] = 1
else:
raise NotImplementedError("You must provide a contamination rate.")
return is_inlier
[docs] def score(self, X, y, sample_weight=None):
"""Returns 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, shape = (n_samples, n_features)
Test samples.
y : array-like, shape = (n_samples,) or (n_samples, n_outputs)
True labels for X.
sample_weight : array-like, shape = (n_samples,), optional
Sample weights.
Returns
-------
score : float
Mean accuracy of self.predict(X) wrt. y.
"""
return accuracy_score(y, self.predict(X), sample_weight=sample_weight)
