FCM Clustering Based on IRLS and Mahalanobis Distances

Abstract

Classification procedures using normal populations predominate in statistical practice, since they have simplicity and reasonably high efficiency across a wide variety of population models. Although computing the posterior probabilities of the populations of each class after observing an object's feature vector is frequently useful for the purposes of identifying the less clear-cut assignment, the assignments to outlying observations tend to be near zero or one. A broad class of membership functions can be used in fuzzy c-means (FCM) clustering from the viewpoint of iteratively reweighted least-squares (IRLS) techniques. This paper clarifies the clustering characteristics of regular FCM, entropy regularized FCM and the proposed IRLS approaches. A new membership function and the IRLS approach enhance the classification procedure by truly less clear-cut assignments of memberships to the outlying observations.