Multiclass penalized likelihood pattern classification algorithm

Abstract

Penalized likelihood is a general approach whereby an objective function is defined, consisting of the log likelihood of the data minus some term penalizing non-smooth solutions. Subsequently, this objective function is maximized, yielding a solution that achieves some sort of trade-off between the faithfulness and the smoothness of the fit. In this paper we extend the penalized likelihood classification that we proposed in earlier work to the multi class case. The algorithms are based on using a penalty term based on the K-nearest neighbors and the likelihood of the training patterns' classifications. The algorithms are simple to implement, and result in a performance competitive with leading classifiers. © 2012 Springer-Verlag.