Unsupervised Outlier Detection based on Random Projection Outlyingness (RPO).

rpo.py

# -*- coding: utf-8 -*-
"""Unsupervised Outlier Detection based on Random Projection Outlyingness (RPO).
"""
# Author: Akira Tamamori <tamamori5917@gmail.com>
# License: BSD 2 clause

from __future__ import division, print_function

import numpy as np
from pyod.models.base import BaseDetector
from scipy import stats
from sklearn.preprocessing import normalize
from sklearn.utils import check_array, check_random_state
from sklearn.utils.validation import check_is_fitted


class RPO(BaseDetector):
    """RPO class for outlier detection.

    Random Projection Outlyingness (RPO) is a measure of outlyingness of data point.

    In one-dimensional case, outlyingness from the center of the data distribution
    can be evaluated by using the median and the median absolute deviation.
    They are known to be less sensitive to outliers.

    The definition can be extended so that the outlyingness calculated for
    one-dimensional data can also be calculated for d-dimensional data.
    The d-dimensional projection axis is randomly sampled from the d-dimensional unit
    hypersphere, and the entire dataset is projected onto one-dimensional space.
    The outlyingness is then calculated over a one-dimensional dataset.

    Donoho, D. L., Gasko, M., et al. Breakdown properties of
    location estimates based on halfspace depth and projected
    outlyingness. The Annals of Statistics, 20(4):1803–1827, 1992.

    Parameters
    ----------
    n_projections :  int (0, n_samples), optional (default=100)
        The number of random projection axes.

    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.

    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
    ----------
    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 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, n_projections=100, random_state=None):
        super().__init__(contamination=contamination)
        self.n_projections = n_projections
        self.random_state = check_random_state(random_state)
        self.decision_scores_ = None
        self.proj_axes = None
        self.median = None
        self.median_dev = None

    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)

        # draw random axes on hypersphere
        self.proj_axes = self.random_state.randn(X.shape[1], self.n_projections)
        self.proj_axes = normalize(self.proj_axes)  # normalized vectors on hypersphere

        # project X onto random axis via inner product
        proj_data = X.dot(self.proj_axes)  # (n_samples, n_proj)

        self.median = np.median(proj_data, axis=0)  # (n_proj)
        self.median = np.expand_dims(self.median, axis=0)  # (1, n_proj)
        self.median_dev = stats.median_abs_deviation(proj_data, axis=0)  # (n_proj)
        self.median_dev = np.expand_dims(self.median_dev, axis=0)  # (1, n_proj)

        # compute random projection outlyingness
        self.decision_scores_ = np.max(
            np.abs(proj_data - self.median) / self.median_dev, axis=1
        )
        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.

        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)
        proj_data = X.dot(self.proj_axes)  # project X onto random axis
        anomaly_scores = np.max(
            np.abs(proj_data - self.median) / self.median_dev, axis=1
        )

        return anomaly_scores