Abstract
In this paper we investigate the problem of the determination of the number of clusters for symbolic objects described by multi-valued and modal variables. Three dissimilarity measures are selected in order to define distances on the set of symbolic objects. Methods for the determination of the number of clusters are applied to hierarchies of partitions produced by four hierarchical clustering methods, and to sets of partitions given by the symbolic clustering procedure SCLUST. Two real data sets are analysed.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Baker, F., and Hubert, L. (1975). “Measuring the Power of Hierarchical Cluster Analysis,” Journal of the American Statistical Association, 70, 31–38.
Beale, E. (1969). “Euclidean Cluster Analysis,” Bulletin of the International Statistical Institute, 43, 92–94.
Bock, H.-H., and Diday, E. (2000). Analysis of Symbolic Data. Exploratory Methods for Extracting Statistical Information from Complex Data. Springer-Verlag, Berlin.
Calinski, T., and Harabasz, J. (1974). “A Dendrite Method for Cluster Analysis,” Communications in Statistics, 3, 1–27.
Celeux, G., Diday, E., Govaert, G., Lechevallier, Y., and Ralan-Bondrainy, H. (1989). Classification Automatique des Données. Bordas.
Duda, R., and Hart, P. (1973). Pattern Classification and Scene Analysis. Wiley, New York.
Hubert, L., and Levin, J. (1976). “A General Statistical Framework for Assessing Categorical Clustering in Free Recall,” Psychological Bulletin, 83, 1072–1080.
Hardy, A., and Lallemand, P. (2002) “Determination of the Number of Clusters for Symbolic Objects Described by Interval Variables,” in Studies in Classification, Data Analysis and Knowledge Organisation, eds. K. Jajuga, et al., Berlin: Springer, pp. 311–318.
Milligan, G., and Cooper, M. “An Examination of Procedures for Determining the Number of Cluster in a Data Set,” Psychometrika, 50, 159–179.
Verde, R., de Carvalho, F., and Lechevallier, Y. (2000). “A Dynamical Clustering Algorithm for Multinominal Data,” Data Analysis, Classification, and Related Methods, eds. H. A. L. Kiers et al., Berlin: Springer, pp. 387–393.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Hardy, A., Lallemand, P. (2004). Clustering of Symbolic Objects Described by Multi-Valued and Modal Variables. In: Banks, D., McMorris, F.R., Arabie, P., Gaul, W. (eds) Classification, Clustering, and Data Mining Applications. Studies in Classification, Data Analysis, and Knowledge Organisation. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17103-1_31
Download citation
DOI: https://doi.org/10.1007/978-3-642-17103-1_31
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22014-5
Online ISBN: 978-3-642-17103-1
eBook Packages: Springer Book Archive