CLUSCALE ("CLUstering and multidimensional SCAL[E]ing"): A Three-Way Hybrid Model Incorporating Overlapping Clustering and Multidimensional Scaling Structure

• Published in: Journal of classification Vol. 23; no. 2; pp. 269 - 299
• Main Authors: Chaturvedi, Anil, Carroll, J. Douglas
• Format: Journal Article
• Language: English
• Published: New York, NY Springer 01.09.2006; Springer Nature B.V
• Subjects: Algorithmics. Computability. Computer arithmetics; Applied sciences; Automatic classification; CLUSCALE; Computer applications; Computer science; control theory; systems; Exact sciences and technology; Expert systems; Knowledge representation; Mathematical programming; Mathematics; Multivariate analysis; Operational research and scientific management; Operational research. Management science; Optimization. Search problems; Parameter estimation; Probability and statistics; Scaling; Sciences and techniques of general use; Statistics; Studies; Theoretical computing; Cluster analysis; Metric analysis; Cluster analysis (statistics); Overlap; Multivariate analysis; Multidimensional scaling; Multi-linear model; Heterogeneity; Discrete parameter modeling; INDCLUS; Three way analysis of variance; Hybrid model; CLUSCALE; MDS; INDSCAL; Analysis of correlation data; Data analysis; Analysis of covariance data; Covariance analysis; Nonlinear optimization; Mixed integer programming; Variance decomposition; Integer programming; Correlation analysis; Tri-linear model; Overlapping clusters; Metric; Perceptual mapping' 3-way' Three-way analysis
• ISSN: 0176-4268; 1432-1343
• DOI: 10.1007/s00357-006-0016-0

Traditional techniques of perceptual mapping hypothesize that stimuli are differentiated in a common perceptual space of quantitative attributes. This paper enhances traditional perceptual mapping techniques such as multidimensional scaling (MDS) which assume only continuously valued dimensions by presenting a model and methodology called CLUSCALE for capturing stimulus differentiation due to perceptions that are qualitative, in addition to quantitative or continuously varying perceptual attributes or dimensions. It provides models and OLS parameter estimation procedures for both a two-way and a three-way version of this general model. Since the two-way version of the model and method has already been discussed by Chaturvedi and Carroll (2000), and a stochastic variant discussed by Navarro and Lee (2003), we shall deal in this paper almost entirely with the three-way version of this model. We recommend the use of the three-way approach over the two-way approach, since the three-way approach both accounts for and takes advantage of the heterogeneity in subjects' perceptions of stimuli to provide maximal information; i.e., it explicitly deals with individual differences among subjects.[PUBLICATION ABSTRACT]