Selected Applications in Classifier Design

Abstract

In this final chapter we consider several fuzzy algorithms that effect partitions of feature space ℝ^p, enabling classification of unlabeled (future) observations, based on the decision functions which characterize the classifier. S25 describes the general problem in terms of a canonical classifier, and briefly discusses Bayesian statistical decision theory. In S26 estimation of the parameters of a mixed multivariate normal distribution via statistical (maximum likelihood) and fuzzy (c-means) methods is illustrated. Both methods generate very similar estimates of the optimal Bayesian classifier. S27 considers the utilization of the prototypical means generated by (A11.1) for characterization of a (single) nearest prototype classifier, and compares its empirical performance to the well-known k-nearest-neighbor family of deterministic classifiers. In S28, an implicit classifier design based on Ruspini’s algorithm is discussed and exemplified.