A new robust model of one-class classification by interval-valued training data using the triangular kernel

Abstract

A robust one-class classification model as an extension of Campbell and Bennett’s (C–B) novelty detection model on the case of interval-valued training data is proposed in the paper. It is shown that the dual optimization problem to a linear program in the C–B model has a nice property allowing to represent it as a set of simple linear programs. It is proposed also to replace the Gaussian kernel in the obtained linear support vector machines by the well-known triangular kernel which can be regarded as an approximation of the Gaussian kernel. This replacement allows us to get a finite set of simple linear optimization problems for dealing with interval-valued data. Numerical experiments with synthetic and real data illustrate performance of the proposed model.