# Source code for pyod.models.mcd

```
# -*- coding: utf-8 -*-
"""Outlier Detection with Minimum Covariance Determinant (MCD)
"""
# Author: Yue Zhao <zhaoy@cmu.edu>
# License: BSD 2 clause
from __future__ import division
from __future__ import print_function
from sklearn.covariance import MinCovDet
from sklearn.utils.validation import check_is_fitted
from sklearn.utils.validation import check_array
from .base import BaseDetector
__all__ = ['MCD']
[docs]class MCD(BaseDetector):
"""Detecting outliers in a Gaussian distributed dataset using
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.
First fit a minimum covariance determinant model and then compute the
Mahalanobis distance as the outlier degree of the data
See :cite:`rousseeuw1999fast,hardin2004outlier` for details.
Parameters
----------
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. Used when fitting to
define the threshold on the decision function.
store_precision : bool
Specify if the estimated precision is stored.
assume_centered : bool
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, 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_state : int, 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_ : array-like, shape (n_features,)
The raw robust estimated location before correction and re-weighting.
raw_covariance_ : array-like, shape (n_features, n_features)
The raw robust estimated covariance before correction and re-weighting.
raw_support_ : array-like, 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_ : 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.
decision_scores_ : numpy array of shape (n_samples,)
The outlier scores of the training data.
The higher, the more abnormal. Outliers tend to have higher
scores. This value is available once the detector is
fitted. Mahalanobis distances of the training set (on which
`:meth:`fit` is called) observations.
threshold_ : float
The threshold is based on ``contamination``. It is the
``n_samples * contamination`` most abnormal samples in
``decision_scores_``. The threshold is calculated for generating
binary outlier labels.
labels_ : int, either 0 or 1
The binary labels of the training data. 0 stands for inliers
and 1 for outliers/anomalies. It is generated by applying
``threshold_`` on ``decision_scores_``.
"""
def __init__(self, contamination=0.1, store_precision=True,
assume_centered=False, support_fraction=None,
random_state=None):
super(MCD, self).__init__(contamination=contamination)
self.store_precision = store_precision
self.assume_centered = assume_centered
self.support_fraction = support_fraction
self.random_state = random_state
# noinspection PyIncorrectDocstring
[docs] def fit(self, X, y=None):
"""Fit detector. y is ignored in unsupervised methods.
Parameters
----------
X : numpy array of shape (n_samples, n_features)
The input samples.
y : Ignored
Not used, present for API consistency by convention.
Returns
-------
self : object
Fitted estimator.
"""
# Validate inputs X and y (optional)
X = check_array(X)
self._set_n_classes(y)
self.detector_ = MinCovDet(store_precision=self.store_precision,
assume_centered=self.assume_centered,
support_fraction=self.support_fraction,
random_state=self.random_state)
self.detector_.fit(X=X, y=y)
# Use mahalanabis distance as the outlier score
self.decision_scores_ = self.detector_.dist_
self._process_decision_scores()
return self
[docs] def decision_function(self, X):
"""Predict raw anomaly score of X using the fitted detector.
The anomaly score of an input sample is computed based on different
detector algorithms. For consistency, outliers are assigned with
larger anomaly scores.
Parameters
----------
X : numpy array of shape (n_samples, n_features)
The training input samples. Sparse matrices are accepted only
if they are supported by the base estimator.
Returns
-------
anomaly_scores : numpy array of shape (n_samples,)
The anomaly score of the input samples.
"""
check_is_fitted(self, ['decision_scores_', 'threshold_', 'labels_'])
X = check_array(X)
# Computer mahalanobis distance of the samples
return self.detector_.mahalanobis(X)
@property
def raw_location_(self):
"""The raw robust estimated location before correction and
re-weighting.
Decorator for scikit-learn MinCovDet attributes.
"""
return self.detector_.raw_location_
@property
def raw_covariance_(self):
"""The raw robust estimated location before correction and
re-weighting.
Decorator for scikit-learn MinCovDet attributes.
"""
return self.detector_.raw_covariance_
@property
def raw_support_(self):
"""A mask of the observations that have been used to compute
the raw robust estimates of location and shape, before correction
and re-weighting.
Decorator for scikit-learn MinCovDet attributes.
"""
return self.detector_.raw_support_
@property
def location_(self):
"""Estimated robust location.
Decorator for scikit-learn MinCovDet attributes.
"""
return self.detector_.location_
@property
def covariance_(self):
"""Estimated robust covariance matrix.
Decorator for scikit-learn MinCovDet attributes.
"""
return self.detector_.covariance_
@property
def precision_(self):
""" Estimated pseudo inverse matrix.
(stored only if store_precision is True)
Decorator for scikit-learn MinCovDet attributes.
"""
return self.detector_.precision_
@property
def support_(self):
"""A mask of the observations that have been used to compute
the robust estimates of location and shape.
Decorator for scikit-learn MinCovDet attributes.
"""
return self.detector_.support_
```