A multi-class learning method for multiconlitron using hybrid binary tree architecture

Abstract

Multiconlitron is a general geometric method for constructing piecewise linear classifiers, but it was initially designed only for two-class problem. In this paper, we propose a multi-class learning method of multiconlitron by using a hybrid binary tree architecture. At each internal node that does not generate leaf nodes, a hyperplane is first created as perpendicular bisectors of line segment linking centroids of the two farthest classes from each other. Then, according to the positive or negative sides on the hyperplane, all the inherited classes are divided into two groups for the next iteration. For an internal node that will generate leaf nodes, the multiconlitron is constructed by support multiconlitron algorithm, which can separate one class from the other class (or group). Generally, the approximate hyperplane by centroids can provide fast division in the early stages of the training phase, whereas the ensemble boundaries with multiconlitron will perform the final precise decision. As a result, a hybrid binary partition tree is created which represents a hierarchical division of given classes. Experimental results show that the proposed method is better than one-versus-one multiconlitron and directed acyclic graph multiconlitron, both in terms of classification effectiveness and computational time. Moreover, comparison with another tree-based multi-class piecewise linear classifier verifies its competitiveness and superiority.