Simultaneous component and clustering models for three-way data: Within and between approaches. (English) Zbl 1144.62045

Vichi, Maurizio; Rocci, Roberto; Kiers, Henk A. L.

J. Classif. 24, No. 1, 71-98 (2007).

Summary: 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.

MSC:

62H30	Classification and discrimination; cluster analysis (statistical aspects)
65C60	Computational problems in statistics (MSC2010)
91C20	Clustering in the social and behavioral sciences

Keywords:

least squares estimation; three-way factorial \(k\)-means