Abstract
Several validity indices have been designed to evaluate solutions obtained by clustering algorithms. Traditional indices are generally designed to evaluate center-based clustering, where clusters are assumed to be of globular shapes with defined centers or representatives. Therefore they are not suitable to evaluate clusters of arbitrary shapes, sizes and densities, where clusters have no defined centers or representatives. In this work, HS (Homogeneity Separateness) validity measure based on a different shape is proposed. It is suitable for clusters of any shapes, sizes and/or of different densities. The main concepts of the proposed measure are explained and experimental results on both synthetic and real life data set that support the proposed measure are given.
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
Hartigan, J.A.: Clustering Algorithms. Wiley Series in Probability and Mathematical statistics (1975)
Milligan, G.W., Cooper, M.C.: An examination of procedures for determining the number of clusters in a data set. Psychimetrika 50, 159–179 (1985)
Dubes, R., Jain, A.K.: Validity studies in clustering methodologies. Pattern Recognition 11, 235–253 (1979)
Chou, C.-H., Su, M.-C., Lai, E.: A new cluster validity measure and its application to image compression. Pattern Anal. Applic. 7, 205–220 (2004), doi:10.1007/s10044-004-0218-1
Gath, I., Geva, A.B.: Unsupervised optimal fuzzy clustering. IEEE Trans. Pattern Anal. Machine Intell. 11, 773–781 (1989)
Gustafson, D.E., Kessel, W.C.: Fuzzy clustering with a fuzzy covariance matrix. In: Proceedings of the IEEE Conference on Decision and Control, San Diego, pp. 761–766 (January 1979)
Halkidi, M., Vazirgiannis, M.: Clustering validity assessment: Finding the optimal partitioning of a data set. In: Proc. IEEE ICDM, San Jose, CA, pp. 187–194 (2001)
Babuška, R., van der Veen, P.J., Kaymak, U.: Improved Covariance Estimation for Gustafson-Kessel Clustering, 0-7803-7280-8/02/$10.00 ©2002. IEEE (2002)
Prim, R.: Shortest connection networks and some generalization. Bell Systems Technical Journal 36, 1389–1401 (1957)
Kruskal, J.: On the shortest spanning subtree and the travelling salesman problem. In: Proceedings of the American Mathematical Society, pp. 48–50 (1956)
Nesetril, J., Milkova, E., Nesetrilova, H.: Otakar boruvka on minimum spanning tree problem: Translation of both the 1926 papers, comments, history. DMATH: Discrete Mathematics 233 (2001)
Zahn, C.: Graph-theoretical methods for detecting and describing gestalt clusters. IEEE Transactions on Computers C-20, 68–86 (1971)
Preparata, F., Shamos, M.: Computational Geometry: An Introduction. Springer, Newyork (1985)
Asano, T., Bhattacharya, B., Keil, M., Yao, F.: Clustering Algorithms based on minimum and maximum spanning trees. In: Proceedings of the 4th Annual Symposium on Computational Geometry, pp. 252–257 (1988)
Dunn, J.C.: A Fuzzy Relative of the ISODATA Process and its Use in Detecting Compact Well-Separated Clusters. Journal Cybern. 3(3), 32–57 (1973)
Davies, D.L., Bouldin, D.W.: A cluster separation measure. IEEE Trans. Pattern Analysis and Machine Intelligence 1(4), 224–227 (1979)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Murty, M.R., Murthy, J.V.R., Reddy, P.V.G.D.P., Naik, A., Satapathy, S.C. (2014). Homogeneity Separateness: A New Validity Measure for Clustering Problems. In: Satapathy, S., Avadhani, P., Udgata, S., Lakshminarayana, S. (eds) ICT and Critical Infrastructure: Proceedings of the 48th Annual Convention of Computer Society of India- Vol I. Advances in Intelligent Systems and Computing, vol 248. Springer, Cham. https://doi.org/10.1007/978-3-319-03107-1_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-03107-1_1
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-03106-4
Online ISBN: 978-3-319-03107-1
eBook Packages: EngineeringEngineering (R0)