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Indclus: An individual differences generalization of the adclus model and the mapclus algorithm

Abstract

We present a new model and associated algorithm, INDCLUS, that generalizes the Shepard-Arabie ADCLUS (ADditive CLUStering) model and the MAPCLUS algorithm, so as to represent in a clustering solution individual differences among subjects or other sources of data. Like MAPCLUS, the INDCLUS generalization utilizes an alternating least squares method combined with a mathematical programming optimization procedure based on a penalty function approach to impose discrete (0,1) constraints on parameters defining cluster membership. All subjects in an INDCLUS analysis are assumed to have a common set of clusters, which are differentially weighted by subjects in order to portray individual differences. As such, INDCLUS provides a (discrete) clustering counterpart to the Carroll-Chang INDSCAL model for (continuous) spatial representations. Finally, we consider possible generalizations of the INDCLUS model and algorithm.

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Additional information

We are indebted to Seymour Rosenberg for making available the data from Rosenberg and Kim [1975]. Also, this work has benefited from the observations of S. A. Boorman, W. S. DeSarbo, G. Furnas, P. E. Green, L. J. Hubert, L. E. Jones, J. B. Kruskal, S. Pruzansky, D. Schmittlein, E. J. Shoben, S. D. Soli, and anonymous referees.

This research was supported in part by NSF Grant SES82 00441, LEAA Grant 78-NI-AX-0142, and NSF Grant SES80 04815.

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Carroll, J.D., Arabie, P. Indclus: An individual differences generalization of the adclus model and the mapclus algorithm. Psychometrika 48, 157–169 (1983). https://doi.org/10.1007/BF02294012

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Key words

  • additive clustering
  • nonhierarchical clustering
  • combinatorial optimization
  • three-way clustering
  • individual differences clustering