Building Hybrid Fuzzy Classifier Trees by Additive/Subtractive Composition of Sets

Abstract

Especially for one-class classification problems, an accurate model of the class is necessary. Since the shape of a class might be arbitrarily complex, it is hard to choose an approach that is generic enough to cope with the variety of shapes, while delivering an interpretable model that remains as simple as possible and thus applicable in practice. In this article, this problem is tackled by combining convex building blocks both additively and subtractively in a tree-like structure. The convex building blocks are represented by multivariate membership functions that aggregate the respective parts of the learning data. During the learning process, proven methods from support vector machines and cluster analysis are employed in order to optimally find the structure of the tree. Several academic examples demonstrate the viability of the approach. © Springer International Publishing Switzerland 2014.