Presupervised and post-supervised prototype classifier design

We extend the nearest prototype classifier to a generalized nearest prototype classifier (GNPC). The GNPC uses "soft" labeling of the prototypes in the classes, thereby encompassing a variety of classifiers. Based on how the prototypes are found we distinguish between presupervised and postsupervised GNPC designs. We derive the conditions for optimality (relative to the standard Bayes error rate) of two designs where prototypes represent: 1) the components of class-conditional mixture densities (presupervised design) or 2) the components of the unconditional mixture density (postsupervised design). An artificial data set and the "satimage" data set from the database ELENA are used to experimentally study the two approaches. A radial basis function (RBF) network is used as a representative of each GNPC type. Neither the theoretical nor the experimental results indicate clear reasons to prefer one of the approaches. The postsupervised GNPC design tends to be more robust and less accurate than the presupervised one.