Abstract
In this paper, an asymmetric version of the k-means clustering algorithm is proposed. The asymmetry arises caused by the use of asymmetric dissimilarities in the k-means algorithm. Application of asymmetric measures of dissimilarity is motivated with a basic nature of the k-means algorithm, which uses dissimilarities in an asymmetric manner. Clusters centroids are treated as the dominance points governing the asymmetric relationships in the entire cluster analysis. The results of experimental study on the real data have shown the superiority of asymmetric dissimilarities employed for the k-means method over their symmetric counterparts.
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
Steinhaus, H.: Sur la Division des Corp Matériels en Parties. Bulletin de l’Académie Polonaise des Sciences, C1. III 4(12), 801–804 (1956)
MacQueen, J.: Some Methods for Classification and Analysis of Multivariate Observations. In: Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, vol. 1, pp. 281–297 (1967)
Kanungo, T., Mount, D.M., Netanyahu, N.S., Piatko, C.D., Silverman, R., Wu, A.Y.: An Efficient k-Means Clustering Algorithm: Analysis and Implemetation. IEEE Transactions on Pattern Analysis and Machine Intelligence 24(7), 881–892 (2002)
Biau, G., Devroye, L., Lugosi, G.: On the Performance of Clustering in Hilbert Spaces. IEEE Transactions on Information Theory 54(2), 781–790 (2008)
Olszewski, D., Kolodziej, M., Twardy, M.: A Probabilistic Component for K-Means Algorithm and its Application to Sound Recognition. Przeglad Elektrotechniczny 86(6), 185–190 (2010)
Okada, A., Imaizumi, T.: Asymmetric Multidimensional Scaling of Two-Mode Three-Way Proximities. Journal of Classification 14(2), 195–224 (1997)
Okada, A.: An Asymmetric Cluster Analysis Study of Car Switching Data. In: Data Analysis. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Heidelberg (2000)
Okada, A., Imaizumi, T.: Multidimensional Scaling of Asymmetric Proximities with a Dominance Point. In: Advances in Data Analysis. Studies in Classification, Data Analysis, and Knowledge Organization, pp. 307–318. Springer, Heidelberg (2007)
Goldberger, A.L., Amaral, L.A.N., Glass, L., Hausdorff, J.M., Ivanov, P.C., Mark, R.G., Mietus, J.E., Moody, G.B., Peng, C.K., Stanley, H.E.: PhysioBank, PhysioToolkit, and PhysioNet: Components of a new research resource for complex physiologic signals. Circulation 101(23), e215–e220 (2000), circulation Electronic Pages: http://circ.ahajournals.org/cgi/content/full/101/23/e215
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Olszewski, D. (2011). Asymmetric k-Means Algorithm. In: Dobnikar, A., Lotrič, U., Šter, B. (eds) Adaptive and Natural Computing Algorithms. ICANNGA 2011. Lecture Notes in Computer Science, vol 6594. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20267-4_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-20267-4_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-20266-7
Online ISBN: 978-3-642-20267-4
eBook Packages: Computer ScienceComputer Science (R0)