A multi-class large margin classifier

Currently there are two approaches for a multi-class support vector classifier (SVC). One is to construct and combine several binary classifiers while the other is to directly consider all classes of data in one optimization formulation. For a K-class problem (K>2), the first approach has to construct at least K classifiers, and the second approach has to solve a much larger optimization problem proportional to K by the algorithms developed so far. In this paper, following the second approach, we present a novel multi-class large margin classifier (MLMC). This new machine can solve K-class problems in one optimization formulation without increasing the size of the quadratic programming (QP) problem proportional to K. This property allows us to construct just one classifier with as few variables in the QP problem as possible to classify multi-class data, and we can gain the advantage of speed from it especially when K is large. Our experiments indicate that MLMC almost works as well as (sometimes better than) many other multi-class SVCs for some benchmark data classification problems, and obtains a reasonable performance in face recognition application on the AR face database.