Mutual Information Measures for Subclass Error-Correcting Output Codes Classification

Abstract

Error-Correcting Output Codes (ECOCs) reveal a common way to model multi-class classification problems. According to this state of the art technique, a multi-class problem is decomposed into several binary ones. Additionally, on the ECOC framework we can apply the subclasses technique (sub-ECOC), where by splitting the initial classes of the problem we aim to the creation of larger but easier to solve ECOC configurations. The multi-class problem’s decomposition is achieved via a searching procedure known as sequential forward floating search (SFFS). The SFFS algorithm in each step searches for the optimum binary separation of the classes that compose the multi-class problem. The separation decision is based on the maximization or minimization of a criterion function. The standard criterion used is the maximization of the mutual information (MI) between the bi-partitions created in each step of the SFFS. The materialization of the MI measure is achieved by a method called fast quadratic Mutual Information (FQMI). Although FQMI is quite accurate in modelling the MI, its computation is of high algorithmic complexity, which as a consequence makes the ECOC and sub-ECOC techniques applicable only on small datasets. In this paper we present some alternative separation criteria of reduced computational complexity that can be used in the SFFS algorithm. Furthermore, we compare the performance of these criteria over several multi-class classification problems.