Abstract
In the application of clustering methods to real world data sets, two problems frequently arise: (a) how can the various contributory variables in a specific battery be weighted so as to enhance some cluster structure that may be present, and (b) how can various alternative batteries be combined to produce a single clustering that “best” incorporates each contributory set. A new method is proposed (SYNCLUS, SYNthesizedCLUStering) for dealing with these two problems.
Similar content being viewed by others
Reference notes
DeSarbo, W. S. and Mahajan, V. (1982). Constrained classification,Working Paper, Bell Laboratories, Murray Hill, N.J.
Fowlkes, E. (1981). Variable selection in clustering,presented at Bell Laboratories Work Seminar, Murray Hill, N.J.
Fowlkes, E., Gnanadesikan, R., and Kettenring, J. R. (1982). Variable selection in clustering,Work in Progress, Bell Laboratories, Murray Hill, N.J.
Green, P. E. and Goldberg, S. M. (1981). The beta drug company case,Wharton-School Publication, University of Pennsylvania.
References
Arabie, P. A. and Carroll, J. D. (1980).MAPCLUS: A mathematical programming approach to fitting theADCLUS model,Psychometrika, 45, 211–235.
Arabie, P., Carroll, J. D. DeSarbo, W. S., and Wind, Y. (1981). Overlapping clustering: A new methodology for product positioning,Journal of Marketing Research, 18, pp. 000–000.
Art, D., Gnanadesikan, R., and Kettenring, J. R. (in press). Data-based metrics for cluster analysis,Utilitas Mathematica.
Carroll, J. D. and Arabie, P. A. (1983). INDCLUS: An individual differences generalization of the ADCLUS Model and the MAPCLUS Algorithm,Psychometrika, 48, 157–169.
DeSarbo, W. S. (1982). GENNCLUS: New models for general nonhierarchical clustering analysis,Psychometrika, 47, 449–475.
Friedman, H. P. and Rubin, J. (1967). On some invariant criteria for grouping data,Journal of the American Statistical Association, 62, 1159–1178.
Friedman, J. H. and Tukey, J. W. (1974). A projection pursuit algorithm for exploratory data analysis,IEEE Transactions on Computers, C-23, 881–890.
Garfinkle, R. S. and Nemhauser, G. L. (1972).Integer Programming, New York: J. Wiley and Sons.
Hartigan, J. A. (1975).Clustering Algorithms, New York: J. Wiley and Sons.
Hartigan, J. A. (1978). Asymptotic distributions for clustering criteria,Annals of Statistics, Vol. 6, No. 1, 117–131.
Kruskal, J. B. (1964a). Multidimensional scaling by optimizing goodness of fit to a nonmetric hypothesis,Psychometrika, 29, 1–27.
Kruskal, J. B. (1964b). Nonmetric multidimensional scaling: A numerical method,Psychometrika, 29, 115–129.
Kruskal, J. B. and Carroll, J. D. (1969). Geometrical models and badness-of-fit functions, inMultivariate Analysis III, edited by P. R. Krishnaiah, New York: Academic Press, 639–670.
Kruskal, J. B. (1972). Linear transformations of multivariate data to reveal clustering, inMultidimensional Scaling: Theory and Applications in the Behavioral Sciences, edited by Shepard, R. N., Romney, A. K., and Nerlove, S. B., New York: Seminar Press, 181–191.
MacQueen, J. (1967). Some methods for classification and analysis of multivariate observations,Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Vol. I, 231–297.
Morrison, D. G. (1967). Measurement problems in cluster analysis,Management Science, 13, 775–780.
Pollard, D. (1981). Strong consistency ofK-means clustering,Annals of Statistics, Vol. 9, No. 1, 135–140.
Rohlf, F. J. (1970). Adaptive hierarchical clustering schemes,Systematic Zoology, 19, 58–82.
Sneath, P. H. A. and Sokal, R. R. (1973).Numerical Taxonomy, San Francisco: W. H. Freeman and Co.
Späth, H. (1980).Cluster Analysis Algorithms, Chichester, England: Ellis Horwood Ltd.
Shepard, R. N. and Arabie, P. (1979). Additive clustering: representation of similarities as combination of discrete overlapping properties,Psychological Review, 86, 87–123.
Wind, Y. (1982).Product Policy: Concepts, Methods and Strategy, Reading, Mass.: Addison-Wesley.
Author information
Authors and Affiliations
Additional information
We wish to thank Anne Freeny and Deborah Art for their computer assistance, and Ed Fowlkes for his helpful technical discussion. We would also like to acknowledge the insightful and helpful comments from the editor and reviewers.
Rights and permissions
About this article
Cite this article
DeSarbo, W.S., Carroll, J.D., Clark, L.A. et al. Synthesized clustering: A method for amalgamating alternative clustering bases with differential weighting of variables. Psychometrika 49, 57–78 (1984). https://doi.org/10.1007/BF02294206
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02294206