Generalized fuzzy c-means clustering strategies using Lp norm distances

Fuzzy c-means (FCM) isa useful clustering technique. Recent modifications of FCM using L-1 norm distances increase robustness to outliers. Object and relational data versions of FCM clustering are defined for the more general case where the L-p norm (p greater than or equal to 1) or semi-norm (0 < p < 1) is used as the measure of dissimilarity. We give simple (though computationally intensive) alternating optimization schemes for all object data cases of p > 0 in order to facilitate the empirical examination of the object data models. Both object and relational approaches are included in a numerical study.