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

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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.

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Authors and Affiliations

  1. Room 2C-553, Bell Laboratories, 600 Mountain Avenue, 07974, Murray Hill, NJ

    J. Douglas Carroll & Phipps Arabie

  2. Department of Psychology, University of Illinois, 603 East Daniel Street, 61820, Champaign, IL

    Phipps Arabie

Authors
  1. J. Douglas Carroll
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  2. Phipps Arabie
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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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