Summary
The CANDCLUS (for CANonical Decompositon CLUStering) model and method is described for analysis of multiway data arrays in terms of multilinear models in which some ways (or modes) are modeled by continuous parameters defining spatial dimensions, other ways/modes by discrete parameters defining cluster or other categorical structures, and still others by mixtures of continuous and discrete parameters defining “hybrid” models in which spatial dimensional structure is combined with cluster-like categorical structure. A generalization of CANDCLUS, called MUMCLUS (for MUltiMode CLUStering), whose two-way special case corresponds to DeSarbo’s GENNCLUS model, is also defined and discussed. Methods previously published for unconstrained fitting of the CANDCLUS/MUMCLUS family of models, based on a separability property observed by Chaturvedi, are extended to allow certain constraints on the discrete parameters—in particular a constraint that the cluster structure be a partition, and another that each entity in a particular mode may be a member of no more than C clusters. These constraints are implemented via an extended separability property (for vectors of discrete parameters, rather than for single parameters) which is defined. The possibility of fitting other constrained versions of these models within this general framework is discussed.
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References
Carroll, J. D. (1976): Spatial, non-spatial and hybrid models for scaling, Psychometrika, 41, 439–463.
Carroll, J. D. and Arabie, P. (in press): Multidimensional scaling, In: Handbook of Perception and Cognition. Volume 3: Measurement, Judgment and Decision Making,Birnbaum, M. H. (ed.), San Diego, CA: Academic Press.
Carroll, J. D. and Chang, J. J. (1970): Analysis of individual differences in multidimensional scaling via an N-way generalization of “Eckert-Young” decomposition, Psychometrika, 35, 283–319.
Carroll, J. D. and Chaturvedi, A. (1995): A general approach to clustering and multidimensional scaling of two-way, three-way, or higher way data, In: Geometric Representations of Perceptual Phenomena, Luce, R. D. et al. (eds.), 295–318, Mahwah, NJ: Erlbaum.
Carroll, J. D. et al. (1994): K-means,K-medians and K-modes: Special cases of partitioning multiway data. (Paper presented at meeting of the Classification Society of North America, Houston, TX. )
Carroll, J. D. and Pruzansky, S. (1980): Discrete and hybrid scaling models, In: Similarity and Choice, Lantermann et al., (eds.), 108–139, Bern: Hans Huber.
Carroll, J. D. and Pruzansky, S. (1984): The CANDECOMP-CANDELINC family of models and methods for multidimensional data analysis, In: Research Methods for Multimode Data Analysis, Law, H. G. et al. (eds.), 372–402, New York: Praeger.
Chaturvedi, A. and Carroll, J. D. (1994): An alternating combinatorial optimization approach to fitting the INDCLUS and generalized INDCLUS models, Journal of Classification, 11, 155–170.
Chaturvedi, A. et al. (1994): A feature based approach to market segmentation via overlapping K-centroids clustering. Manuscript submitted for publication.
Chaturvedi, A. et al. (1995): Two L1 norm procedures for fitting ADCLUS and INDCLUS. Manuscript submitted for publication.
Chaturvedi, A. et al. (1996): Market segmentation via K-modes clustering. (Paper presented at American Statistical Association Conference, Chicago, IL.
De Soete, G. and Carroll, J. D. (1996): Tree and other network models for representing proximity data, In: Clustering and Classification, Arabie, P. et al. (eds.), 157–197, River Edge, NJ• World Scientific.
DeSarbo, W. S (1982): GENNCLUS: New models for general nonhierarchical clustering analysis, Psychometrika, 47, 449–475.
ten Berge, J. M. F and Kiers, H. A. L. (1996): Some uniqueness results for PARAFAC2, Psychometrika, 61, 123–132.
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© 1998 Springer Japan
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Carroll, J.D., Chaturvedi, A. (1998). Fitting the CANDCLUS/MUMCLUS Models with Partitioning and Other Constraints. In: Hayashi, C., Yajima, K., Bock, HH., Ohsumi, N., Tanaka, Y., Baba, Y. (eds) Data Science, Classification, and Related Methods. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Tokyo. https://doi.org/10.1007/978-4-431-65950-1_55
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DOI: https://doi.org/10.1007/978-4-431-65950-1_55
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