Summary
A procedure is developed for clustering objects in a low-dimensional subspace of the column space of an objects by variables data matrix. The method is based on the K-means criterion and seeks the subspace that is maximally informative about the clustering structure in the data. In this low-dimensional representation, the objects, the variables and the cluster centroids are displayed jointly. The advantages of the new method are discussed, an efficient alternating least-squares algorithm is described, and the procedure is illustrated on some artificial data.
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References
ARABIE, P., and HUBERT, L. (in press): Cluster analysis in marketing research. In: R. P. Bagozzi (ed.): Handbook of marketing research. Blackwell, Oxford.
CHANG, W.-C. (1983): On using principal components before separating a mixture of two multivariate normal distributions. Applied Statistics, 32, 267–275.
DESARBO, W. S., HOWARD, D. J., and JEDIDI, K. (1991): Multiclus: A new method for simultaneously performing multidimensional scaling and cluster analysis. Psychometrika, 56, 121–136.
DESARBO, W. S., JEDIDI, K., COOL, K., and SCHENDEL, D. (1990): Simultaneous multidimensional unfolding and cluster analysis: An investigation of strategic groups. Marketing Letters, 2, 129–146.
DE SOETE, G., and HEISER, W. J. (1993): A latent class unfolding model for analyzing single stimulus preference ratings. Psychometrika, 58, 545–565.
DE SOETE, G. and WINSBERG, S. (1993): A latent class vector model for preference data. Journal of Classification, 10, 195–218.
DOYLE, P., and SAUNDERS, J. (1985): Market segmentation and positioning in specialized industrial markets. Journal of Marketing, 49, 24–32.
FURSE, D. H., PUNJ, G. N., and STEWART, D. W. (1984): A typology of individual search strategies among purchasers of new automobiles. Journal of Consumer Research, 10, 417–431.
GABRIEL, K. R. (1971): The biplot graphic display of matrices with application to principal component analysis. Biometrika, 58, 453–467.
HEISER, W. J. (1993): Clustering in low-dimensional space. In: O. Opitz, B. Lausen, and R. Klar (eds.): Information and classification. Springer-Verlag, Berlin, 162–173.
HUBERT, L., and ARABIE, P. (1985): Comparing partitions. Journal of Classification, 2, 193–218.
KRUSKAL, J. B. (1972): Linear transformation of multivariate data to reveal clustering. In: R. N. Shepard, A. K. Romney, and S. B. Nerlove (eds.): Multidimensional scaling. Theory and applications in the behavioral sciences. Seminar Press, New York, vol. 1, 179–191.
MACQUEEN, J. (1967): Some methods for classification and analysis of multivariate observations. In: L. M. LeCam and J. Neyman (eds.): 5th Berkeley Symposium on Mathematics, Statistics, and Probability. University of California Press, Berkeley, vol. 1, 281–298.
MILLIGAN, G. W. (1980): An examination of the effect of six types of error perturbation on fifteen clustering algorithms. Psychometrika, 45, 325–342.
VAN BUUREN, S., and HEISER, W. J. (1989): Clustering N objects into K groups under optimal scaling of variables. Psychometrika, 54, 699–706.
WINSBERG, S., and DE SOETE, G. (1993): A latent class approach to fitting the weighted Euclidean mode, Clascal. Psychometrika, 58, 315–330.
YOUNG, G. (1940): Maximum likelihood estimation and factor analysis. Psychometrika, 6, 49–53.
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© 1994 Springer-Verlag Berlin Heidelberg
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De Soete, G., Carroll, J.D. (1994). K-means clustering in a low-dimensional Euclidean space. In: Diday, E., Lechevallier, Y., Schader, M., Bertrand, P., Burtschy, B. (eds) New Approaches in Classification and Data Analysis. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-51175-2_24
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DOI: https://doi.org/10.1007/978-3-642-51175-2_24
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