A Robust One-Class Classification Model with Interval-Valued Data Based on Belief Functions and Minimax Strategy

A robust model for solving the one-class classification problem by interval-valued training data is proposed in the paper. It is based on using Dempster-Shafer theory for getting the lower and upper risk measures. The minimax or pessimistic strategy is applied to state an optimization problem in the framework of the modified support vector machine (SVM). The algorithm for computing optimal parameters of the classification function stems from extreme points of the convex polytope produced by the interval-valued elements of a training set. It is shown that the hard non-linear optimization problem is reduced to a finite number of standard SVMs.

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