An one-class classification support vector machine model by interval-valued training data

A modification of the well-known one-class classification support vector machine (OCC SVM) dealing with interval-valued or set-valued training data is proposed. Its main idea is to represent every interval of training data by a finite set of precise data with imprecise weights. This representation is based on replacement of the interval-valued expected risk produced by interval-valued data with the interval-valued expected risk produced by imprecise weights or sets of weights. In other words, the interval uncertainty is replaced with the imprecise weight or probabilistic uncertainty. It is shown how constraints for the imprecise weights are incorporated into dual quadratic programming problems which can be viewed as extensions of the well-known OCC SVM models. Numerical examples with synthetic and real interval-valued training data illustrate the proposed approach and investigate its properties.