pyod/models/mad.py
# -*- coding: utf-8 -*-
"""
Median Absolute deviation (MAD) Algorithm.
Strictly for Univariate Data.
"""
# Author: Yahya Almardeny <almardeny@gmail.com>
# License: BSD 2 clause
from __future__ import division
from __future__ import print_function
import numpy as np
from sklearn.utils import check_array
from .base import BaseDetector
def _check_dim(X):
"""
Internal function to assert univariate data
"""
if X.shape[1] != 1:
raise ValueError('MAD algorithm is just for univariate data. '
'Got Data with {} Dimensions.'.format(X.shape[1]))
class MAD(BaseDetector):
"""Median Absolute Deviation: for measuring the distances between
data points and the median in terms of median distance.
See :cite:`iglewicz1993detect` for details.
Parameters
----------
threshold : float, optional (default=3.5)
The modified z-score to use as a threshold. Observations with
a modified z-score (based on the median absolute deviation) greater
than this value will be classified as outliers.
Attributes
----------
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.
threshold_ : float
The modified z-score to use as a threshold. Observations with
a modified z-score (based on the median absolute deviation) greater
than this value will be classified as outliers.
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, threshold=3.5, contamination=0.1):
super(MAD, self).__init__(contamination=contamination)
if not isinstance(threshold, (float, int)):
raise TypeError(
'threshold must be a number. Got {}'.format(type(threshold)))
self.threshold = threshold
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. Note that `n_features` must equal 1.
y : Ignored
Not used, present for API consistency by convention.
Returns
-------
self : object
Fitted estimator.
"""
X = check_array(X, ensure_2d=False, force_all_finite=False)
_check_dim(X)
self._set_n_classes(y)
self.threshold_ = self.threshold
self.median_ = None # reset median after each call
self.median_diff_ = None # reset median_diff after each call
self.decision_scores_ = self.decision_function(X)
self._process_decision_scores()
return self
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.
Note that `n_features` must equal 1.
Returns
-------
anomaly_scores : numpy array of shape (n_samples,)
The anomaly score of the input samples.
"""
X = check_array(X, ensure_2d=False, force_all_finite=False)
_check_dim(X)
return self._mad(X)
def _mad(self, X):
"""
Apply the robust median absolute deviation (MAD)
to measure the distances of data points from the median.
Returns
-------
numpy array containing modified Z-scores of the observations.
The greater the score, the greater the outlierness.
"""
obs = np.reshape(X, (-1, 1))
# `self.median` will be None only before `fit()` is called
self.median_ = np.nanmedian(obs) if self.median_ is None else self.median_
diff = np.abs(obs - self.median_)
self.median_diff_ = np.nanmedian(diff) if self.median_diff_ is None else self.median_diff_
return np.nan_to_num(np.ravel(0.6745 * diff / self.median_diff_))
def _process_decision_scores(self):
"""This overrides PyOD base class function in order to use the
proper `threshold_` which is quite different in the base class.
Internal function to calculate key attributes:
- labels_: binary labels of training data.
- _mu: mean of decision scores.
- _sigma: standard deviation of decision scores.
Returns
-------
self
"""
self.labels_ = (self.decision_scores_ > self.threshold).astype('int').ravel()
# calculate for predict_proba()
self._mu = np.nanmean(self.decision_scores_)
self._sigma = np.nanstd(self.decision_scores_)
return self