This paper presents a fuzzy proportional membership model for clustering
(FCPM). Unlike the other clustering models, FCPM requires that each entity may
express an extent of each prototype, which makes its criterion to loose the conventional
prototype-additive structure. The methods for fitting the model at different
fuzziness parameter values are presented. Because of the complexity of the clustering
criterion, minimization of the errors requires the gradient projection method
(GPM).We discuss how to find the projection of a vector on the simplex of the fuzzy
membership vectors and how the stepsize length of the GPM had been fixed. The
properties of the clusters found with the FCPM are discussed. Especially appealing
seems the property to keep the extremal cluster prototypes stable even after addition
of many entities around the grand mean.
