A relational dual of the fuzzy possibilistic c-means algorithm

The hard, fuzzy and possibilistic c-means clustering algorithms are widely used for partitioning a set of n objects into c groups. There are cases, however, when more than one type of partition is necessary to correctly describe the belongingness of an object to a group. Previously, Pal, Pal and Bezdek listed some of these cases and proposed a method to simultaneously produce both memberships and typicalities for a set of vectorial object data: the fuzzy possibilistic c-means (FPCM) clustering algorithm. However, FPCM is not directly applicable when the data are represented by object-object relationships. In this paper, we reformulate FPCM so that it can work with A-norm relational data. Extensions and properties of the relational clustering algorithm are also considered.