A framework for imprecise robust one-class classification models

Abstract

A framework for constructing robust one-class classification models is proposed in the paper. It is based on Walley’s imprecise extensions of contaminated models which produce a set of probability distributions of data points instead of a single empirical distribution. The minimax and minimin strategies are used to choose an optimal probability distribution from the set and to construct optimal separating functions. It is shown that an algorithm for computing optimal parameters is determined by extreme points of the probability set and is reduced to a finite number of standard SVM tasks with weighted data points. Important special cases of the models, including pari-mutuel, constant odd-ratio, contaminated models and Kolmogorov–Smirnov bounds are studied. Experimental results with synthetic and real data illustrate the proposed models.