Simultaneous Component and Clustering Models for Three-way Data: Within and Between Approaches

In this paper two techniques for units clustering and factorial dimensionality reduction of variables and occasions of a three-mode data set are discussed. These techniques can be seen as the simultaneous version of two procedures based on the sequential application of k-means and Tucker2 algorithms and vice versa. The two techniques, T3Clus and 3Fk-means, have been compared theoretically and empirically by a simulation study. In the latter, it has been noted that neither T3Clus nor 3Fk-means outperforms the other in every case. From these results rises the idea to combine the two techniques in a unique general model, named CT3Clus, having T3Clus and 3Fk-means as special cases. A simulation study follows to show the effectiveness of the proposal.