A Flexible Classifier Design Framework Based on Multiobjective Programming

Abstract

We propose a multiobjective programming (MOP) framework for finding compromise solutions that are satisfactory for each of multiple competing performance criteria in a pattern classification task. The fundamental idea for our formulation of classifier learning, which we refer to as iterative constrained optimization (ICO), evolves around improving one objective while allowing the rest to degrade. This is achieved by the optimization of individual objectives with proper constraints on the remaining competing objectives. The constraint bounds are adjusted based on the objective functions obtained in the most recent iteration. An aggregated utility function is used to evaluate the acceptability of local changes in competing criteria, i.e., changes from one iteration to the next. Although many MOP approaches developed so far are formal and extensible to large number of competing objectives, their capabilities are examined only with two or three objectives. This is mainly because practical problems become significantly harder to manage when the number of objectives gets larger. We, however, illustrate the proposed framework in the context of automatic language identification (LID) of 12 languages and three dialects. This LID task requires the simultaneous minimization of the false-acceptance and false-rejection rates for each of the 15 languages/dialects, and, hence, is an MOP problem with a total of 30 competing objectives. In our experiments, we observed that the ICO-trained classifiers result in not only reduced error rates but also a good balance among the many competing objectives when compared to those classifiers that minimize an overall objective. We interpret our experimental findings as evidence for ICO offering a greater degree of freedom for classifier design.