Maximum-Margin Model for Nearest Prototype Classifiers

In this paper, we study nearest prototype classifiers, which classify data instances into the classes to which their nearest prototypes belong. We propose a maximum-margin model for nearest prototype classifiers. To provide the margin, we define a class-wise discriminant function for instances by the negatives of distances of their nearest prototypes of the class. Then, we define the margin by the minimum of differences between the discriminant function values of instances with respect to the classes they belong to and the values of the other classes. The optimization problem corresponding to the maximum-margin model is a difference of convex functions (DC) program. It is solved using a DC algorithm, which is a k-means-like algorithm, i.e., the members and positions of prototypes are alternately optimized. Through a numerical study, we analyze the effects of hyperparameters of the maximum-margin model, especially considering the classification performance.