Abstract
Detecting clusters of different sizes represents a serious difficulty for all c-means clustering models. This study investigates the set of various modified fuzzy c-means clustering algorithms within the bounds of the probabilistic constraint, from the point of view of their sensitivity to cluster sizes. Two numerical frameworks are constructed, one of them addressing clusters of different cardinalities but relatively similar diameter, while the other manipulating with both cluster cardinality and diameter. The numerical evaluations have shown the existence of algorithms that can effectively handle both cases. However, these are difficult to automatically adjust to the input data through their parameters.
The work of S.M. Szilágyi was supported by the János Bolyai Fellowship Program of the Hungarian Academy of Sciences.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Dunn, J.C.: A fuzzy relative of the isodata process and its use in detecting compact well-separated clusters. Cybern. Syst. 3(3), 32–57 (1973)
Bezdek, J.C.: Pattern recognition with fuzzy objective function algorithms. Plenum, New York (1981)
Komazaki, Y., Miyamoto, S.: Variables for Controlling Cluster Sizes on Fuzzy c-Means. In: Torra, V., Narukawa, Y., Navarro-Arribas, G., Megías, D. (eds.) MDAI 2013. LNCS, vol. 8234, pp. 192–203. Springer, Heidelberg (2013)
Anderson, E.: The irises of the Gaspe peninsula. Bull. Am. Iris Soc. 59, 2–5 (1935)
Fan, J.L., Zhen, W.Z., Xie, W.X.: Suppressed fuzzy \(c\)-means clustering algorithm. Patt. Recogn. Lett. 24, 1607–1612 (2003)
Szilágyi, L., Szilágyi, S.M.: Generalization rules for the suppressed fuzzy \(c\)-means clustering algorithm. Neurocomput. 139, 298–309 (2014)
Höppner, F., Klawonn, F.: Improved fuzzy partition for fuzzy regression models. Int. J. Approx. Reason. 5, 599–613 (2003)
Zhu, L., Chung, F.L., Wang, S.: Generalized fuzzy \(c\)-means clustering algorithm with improved fuzzy partition. IEEE Trans. Syst. Man Cybern. B. 39, 578–591 (2009)
Miyamoto, S., Kurosawa, N.: Controlling cluster volume sizes in fuzzy \(c\)-means clustering. In: SCIS and ISIS, Yokohama, Japan, pp. 1–4 (2004)
Yang, M.S.: On a class of fuzzy classification maximum likelihood procedures. Fuzzy Sets Syst. 57(3), 365–375 (1993)
Noordam, J., Van Den Broek, W., Buydens, L.: Multivariate image segmentation with cluster size insensitive fuzzy \(c\)-means. Chemom. Intell. Lab. Syst. 64(1), 65–78 (2002)
Lin, P.L., Huang, P.W., Kuo, C.H., Lai, Y.H.: A size-insensitive integrity-based fuzzy \(c\)-means method for data clustering. Patt. Recogn. 47(5), 2024–2056 (2014)
Szilágyi, L.: A Unified Theory of Fuzzy c-Means Clustering Models with Improved Partition. In: Torra, V., Narukawa, T. (eds.) MDAI 2015. LNCS, vol. 9321, pp. 129–140. Springer, Heidelberg (2015)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing AG
About this paper
Cite this paper
Szilágyi, L., Szilágyi, S.M., Enăchescu, C. (2016). A Study on Cluster Size Sensitivity of Fuzzy c-Means Algorithm Variants. In: Hirose, A., Ozawa, S., Doya, K., Ikeda, K., Lee, M., Liu, D. (eds) Neural Information Processing. ICONIP 2016. Lecture Notes in Computer Science(), vol 9948. Springer, Cham. https://doi.org/10.1007/978-3-319-46672-9_53
Download citation
DOI: https://doi.org/10.1007/978-3-319-46672-9_53
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-46671-2
Online ISBN: 978-3-319-46672-9
eBook Packages: Computer ScienceComputer Science (R0)