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

Authors:
Maurizio Vichi;Roberto Rocci;Henk A. L. Kiers
Affiliations:
University "La Sapienza", Rome, Italy;University "Tor Vergata", Rome, Italy;Heymans Institute (PA), The Netherlands, Germany
Venue:
Journal of Classification
Year:
2007

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Abstract

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.