Fuzzy clustering in a reduced subspace

A general method for two-mode simultaneous reduction of observation units and variables of a data matrix is introduced. It consists in a compromise between the Reduced K-Means (RKM) and Factorial K-Means (FKM) procedures. Both methodologies involve principal component analysis for variables and K-Means for observation 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 the RKM and FKM loss functions is used. Furthermore, the fuzzy approach to clustering