A general method for fuzzy partitioning and component analysis

A general method for two-mode simultaneous reduction of units and variables of a data matrix is introduced. It consists in a convex linear combination of Reduced K-Means (RKM) and Factorial K-Means (FKM). Both methodologies involve principal component analysis for variables and K-Means for units, even though RKM aims at maximizing the between-clusters deviance without imposing any condition on the within-clusters deviance, while FKM aims at minimizing the within-clusters deviance without imposing any condition on the between one. It follows that RKM and FKM complement each other. In order to take advantage of both methods a convex linear combination of RKM and FKM is proposed. Furthermore, the fuzzy approach to clustering is adopted because of its flexibility in handling the real world complexity and uncertainty. A fast Alternating Least Squares algorithm is introduced and its performance is investigated by simulated and real data.