# -*- coding: utf-8 -*-
"""
Outlier detection based on Gaussian Mixture Model (GMM).
"""
# Author: Akira Tamamori <tamamori5917@gmail.com>
# License: BSD 2 clause
from __future__ import division, print_function
from sklearn.mixture import GaussianMixture
from sklearn.utils import check_array
from sklearn.utils.validation import check_is_fitted
from pyod.models.base import BaseDetector
from pyod.utils.utility import invert_order
[docs]
class GMM(BaseDetector):
"""Wrapper of scikit-learn Gaussian Mixture Model with more functionalities.
Unsupervised Outlier Detection.
See :cite:`aggarwal2015outlier` Chapter 2 for details.
Parameters
----------
n_components : int, default=1
The number of mixture components.
covariance_type : {'full', 'tied', 'diag', 'spherical'}, default='full'
String describing the type of covariance parameters to use.
tol : float, default=1e-3
The convergence threshold. EM iterations will stop when the
lower bound average gain is below this threshold.
reg_covar : float, default=1e-6
Non-negative regularization added to the diagonal of covariance.
Allows to assure that the covariance matrices are all positive.
max_iter : int, default=100
The number of EM iterations to perform.
n_init : int, default=1
The number of initializations to perform. The best results are kept.
init_params : {'kmeans', 'random'}, default='kmeans'
The method used to initialize the weights, the means and the
precisions.
weights_init : array-like of shape (n_components, ), default=None
The user-provided initial weights.
If it is None, weights are initialized using the `init_params` method.
means_init : array-like of shape (n_components, n_features), default=None
The user-provided initial means,
If it is None, means are initialized using the `init_params` method.
precisions_init : array-like, default=None
The user-provided initial precisions (inverse of the covariance
matrices).
If it is None, precisions are initialized using the 'init_params'
method.
random_state : int, RandomState instance or None, default=None
Controls the random seed given to the method chosen to initialize the
parameters.
warm_start : bool, default=False
If 'warm_start' is True, the solution of the last fitting is used as
initialization for the next call of fit().
verbose : int, default=0
Enable verbose output.
verbose_interval : int, default=10
Number of iteration done before the next print.
contamination : float in (0., 0.5), optional (default=0.1)
The amount of contamination of the data set.
Attributes
----------
weights_ : array-like of shape (n_components,)
The weights of each mixture components.
means_ : array-like of shape (n_components, n_features)
The mean of each mixture component.
covariances_ : array-like
The covariance of each mixture component.
precisions_ : array-like
The precision matrices for each component in the mixture.
precisions_cholesky_ : array-like
The cholesky decomposition of the precision matrices of each mixture
component.
converged_ : bool
True when convergence was reached in fit(), False otherwise.
n_iter_ : int
Number of step used by the best fit of EM to reach the convergence.
lower_bound_ : float
Lower bound value on the log-likelihood (of the training data with
respect to the model) of the best fit of EM.
decision_scores_ : numpy array of shape (n_samples,)
The outlier scores of the training data.
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,
n_components=1,
covariance_type="full",
tol=1e-3,
reg_covar=1e-6,
max_iter=100,
n_init=1,
init_params="kmeans",
weights_init=None,
means_init=None,
precisions_init=None,
random_state=None,
warm_start=False,
contamination=0.1,
):
super().__init__(contamination=contamination)
self.n_components = n_components
self.covariance_type = covariance_type
self.tol = tol
self.reg_covar = reg_covar
self.max_iter = max_iter
self.n_init = n_init
self.init_params = init_params
self.weights_init = weights_init
self.means_init = means_init
self.precisions_init = precisions_init
self.random_state = random_state
self.warm_start = warm_start
self.detector_ = None
self.decision_scores_ = None
[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.
sample_weight : array-like, shape (n_samples,)
Per-sample weights. Rescale C per sample. Higher weights
force the classifier to put more emphasis on these points.
Returns
-------
self : object
Fitted estimator.
"""
# validate inputs X and y (optional)
X = check_array(X)
self._set_n_classes(y)
self.detector_ = GaussianMixture(
n_components=self.n_components,
covariance_type=self.covariance_type,
tol=self.tol,
reg_covar=self.reg_covar,
max_iter=self.max_iter,
n_init=self.n_init,
init_params=self.init_params,
weights_init=self.weights_init,
means_init=self.means_init,
precisions_init=self.precisions_init,
random_state=self.random_state,
warm_start=self.warm_start,
)
self.detector_.fit(X=X, y=y)
# invert decision_scores_. Outliers comes with higher outlier scores
self.decision_scores_ = invert_order(self.detector_.score_samples(X))
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_"])
# Invert outlier scores. Outliers come with higher outlier scores
return invert_order(self.detector_.score_samples(X))
@property
def weights_(self):
"""The weights of each mixture components.
Decorator for scikit-learn Gaussian Mixture Model attributes.
"""
return self.detector_.weights_
@property
def means_(self):
"""The mean of each mixture component.
Decorator for scikit-learn Gaussian Mixture Model attributes.
"""
return self.detector_.means_
@property
def covariances_(self):
"""The covariance of each mixture component.
Decorator for scikit-learn Gaussian Mixture Model attributes.
"""
return self.detector_.covariances_
@property
def precisions_(self):
"""The precision matrices for each component in the mixture.
Decorator for scikit-learn Gaussian Mixture Model attributes.
"""
return self.detector_.precisions_
@property
def precisions_cholesky_(self):
"""The cholesky decomposition of the precision matrices
of each mixture component.
Decorator for scikit-learn Gaussian Mixture Model attributes.
"""
return self.detector_.precisions_cholesky_
@property
def converged_(self):
"""True when convergence was reached in fit(), False otherwise.
Decorator for scikit-learn Gaussian Mixture Model attributes.
"""
return self.detector_.converged_
@property
def n_iter_(self):
"""Number of step used by the best fit of EM to reach the convergence.
Decorator for scikit-learn Gaussian Mixture Model attributes.
"""
return self.detector_.n_iter_
@property
def lower_bound_(self):
"""Lower bound value on the log-likelihood of the best fit of EM.
Decorator for scikit-learn Gaussian Mixture Model attributes.
"""
return self.detector_.lower_bound_