Abstract
In this paper we consider a problem of an unsupervised clustering of multidimensional numerical data. We propose a new method for determining an optimal number of clusters in a data set which is based on a parametric model of a Rate-Distortion curve. Theproposed method can be used in conjunction with any suitable clustering algorithm. It was tested with artificial and real numerical data sets and the results of experiments demonstrate empirically not only effectiveness of the method but also its ability to cope with “difficult” cases where other known methods failed.
This is a preview of subscription content, log in via an institution to check access.
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
Calinski, T., Harabasz, J.: A Dendrite Method for Cluster Analysis. Communication in Statistics 3, 1–27 (1974)
Dimitriadou, E., Dolnicar, S., Weingassel, A.: An Examination of Indexes for Determining the Number of Clusters in Binary Data Sets. Psychometrika 67, 137–160 (2002)
Frank, A., Asuncion, A.: UCI Machine Learning Repository. University of California, School of Information and Computer Science, Irvine, CA (2010), http://archive.ics.uci.edu/ml
Kanungo, T., Mount, D.M., Netanyahu, N.S., Piatko, C.D., Silverman, R., Wu, A.Y.: An Efficient k-Means Clustering Algorithm: Analysis and Implementation. IEEE Trans. Pattern Analysis and Machine Intelligence 24, 881–892 (2002)
Krzanowski, W.J., Lai, Y.T.: A Criterion for Determining the Number of Groups in a Data Set Using Sum-of-Squares Clustering. Biometrics 44, 23–34 (1984)
Milligan, G.W., Cooper, M.C.: An Examination of Procedures for Determining the Number of Clusters in a Data Set. Psychometrika 50, 159–179 (1985)
Salvador, S., Chan, P.: Determining the Number of Clusters/Segments in Hierarchical Clustering/Segmentation Algorithms. In: Proc. 16th IEEE Int. Conf. on Tools with Artificial Intelligence, pp. 576–584 (2004)
Sugar, C.A., James, G.M.: Finding the Number of Clusters in a Data Set: An Information Theoretic Approach. J. American Statist. Association 98, 750–763 (2003)
Tibshirani, R., Walther, G., Hastie, T.: Estimating the Number of Clusters in a Data Set via the Gap Statistics. J. R. Statist. Soc. 63, 411–423 (2001)
Vendramin, L., Campello, R.J.G.B., Hrushka, E.R.: Relative Clustering Validity Criteria: A Comparative Overview. Statistical Analysis and Data Mining 3, 209–235 (2010)
Xu, L.: Bayesian Ying-Yang machine, Clustering and Number of Clusters. Pattern Recognition Letters 18, 1167–1178 (1997)
Zhao, Q., Xu, M., Fränti, P.: Sum-of-Squares Based Cluster Validity Index and Significance Analysis. In: Kolehmainen, M., Toivanen, P., Beliczynski, B. (eds.) ICANNGA 2009. LNCS, vol. 5495, pp. 313–322. Springer, Heidelberg (2009)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kolesnikov, A., Trichina, E. (2012). Determining the Number of Clusters with Rate-Distortion Curve Modeling. In: Campilho, A., Kamel, M. (eds) Image Analysis and Recognition. ICIAR 2012. Lecture Notes in Computer Science, vol 7324. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31295-3_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-31295-3_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31294-6
Online ISBN: 978-3-642-31295-3
eBook Packages: Computer ScienceComputer Science (R0)