FCM Classifier Based on IRLS and Fuzzy Mahalanobis Distances

In many statistical clustering approaches, such as Gaussian mixture models (GMM) and deterministic annealing (DA), the resultant posterior probabilities of outliers, which correspond to cluster memberships of points that are far from all cluster centroids, tend to become clear-cut. The classifier based on normal distributions or normal mixtures such as probabilistic neural networks (PNN) also suffer from this deficit of entropy based methods. A novel membership function and a fuzzy clustering derived from the viewpoint of IRLS techniques resolves the problem of singularity in the regular fuzzy c-means (FCM) clustering. A FCM classifier using the membership function and Mahalanobis distances makes class memberships of outliers less clear-cut, which thus leads to a prudent and rational decision in many classification problems.