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Indclus: An Individual differences Generalization of the Adclus Model and the Mapclus Algorithm

Published online by Cambridge University Press:  01 January 2025

J. Douglas Carroll  and
Phipps Arabie
J. Douglas Carroll*
Affiliation:
Bell Laboratories
Phipps Arabie
Affiliation:
Bell Laboratories University of Illinois at Champaign
*
Authors' addresses: J. Douglas Carroll, Room 2C-553, Bell Laboratories, 600 Mountain Avenue, Murray Hill, NJ 07974; Phipps Arabie, Department of Psychology, University of Illinois, 603 East Daniel Street, Champaign, IL 61820.
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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.

Keywords

additive clusteringnonhierarchical clusteringcombinatorial optimizationthree-way clusteringindividual differences clustering
Type
Original Paper
Information
Psychometrika , Volume 48 , Issue 2 , June 1983 , pp. 157 - 169
Copyright
Copyright © 1983 The Psychometric Society

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Footnotes

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.

References

Reference Notes

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