Abstract
Based on the fuzzy c-means clustering method maximized with the Tsallis entropy, we have achieved its extension that assigns the q parameter of Tsallis entropy to each cluster as \(q_i\).
In this method, however, there remains three problems. That is, (1) determination \(q_i\) according to the data distribution, (2) occurrence of abnormal bias of \(q_i\), and (3) calculation termination condition of \(q_i\). In this article, we propose a new calculation method and a termination condition of \(q_i\), and show its effects by experiments.
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
Similar content being viewed by others
References
Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Prenum Press, New York (1981)
Li, R.P., Mukaidono, M.: A maximum entropy approach to fuzzy clustering. In: Proceedings of the 4th IEEE International Conference on Fuzzy Systems (FUZZ-IEEE/IFES 1995), pp. 2227–2232 (1995)
Miyamoto, S., Mukaidono, M.: Fuzzy c-means as a regularization and maximum entropy approach. In: Proceedings of the 7th International Fuzzy Systems Association World Congress, vol. II, pp. 86–92 (1997)
Rose, K., Gurewitz, E., Fox, B.C.: A deterministic annealing approach to clustering. Pattern Recogn. Lett. 11(9), 589–594 (1990)
De Luca, A., Termini, S.: A definition of a nonprobabilistic entropy in the setting of fuzzy sets theory. Inf. Control 20, 301–312 (1972)
Yasuda, M., Furuhashi, T., Matsuzaki, M., Okuma, S.: Fuzzy clustering using deterministic annealing method and its statistical mechanical characteristics. In: Proceedings of the 10th IEEE International Conference on Fuzzy Systems, P294 (2001)
Tsallis, C.: Possible generalization of Boltzmann-Gibbs statistics. J. Stat. Phys. 52, 479–487 (1988)
Abe, S., Okamoto, Y. (eds.): Nonextensive Statistical Mechanics and Its Applications. Springer (2001)
Gell-Mann, M., Tsallis, C. (eds.): Nonextensive Entropy - Interdisciplinary Applications. Oxford University Press, New York (2004)
Tsallis, C.: (ed.) Introduction to Nonextensive Statistical Mechanics. Springer (2009)
Menard, M., Courboulay, V., Dardignac, P.: Possibilistic and probabilistic fuzzy clustering: unification within the framework of the non-extensive thermostatistics. Pattern Recogn. 36, 1325–1342 (2003)
Yasuda, M.: Entropy maximization and very fast deterministic annealing approach to fuzzy c-means clustering. In: Proceedings of the Joint 5th International Conference on Soft Computing and 11th International Symposium on Intelligent Systems, SU-B1-3, pp. 1515–1520 (2010)
Yasuda, M.: Deterministic annealing approach to fuzzy c-means clustering based on entropy maximization. Advances in Fuzzy Systems, 960635 (2011)
Yasuda, M., Orito, Y.: Multi-q extension of Tsallis entropy based fuzzy c-means clustering. J. Adv. Comput. Intell. Intell. Inform. 18(3), 289–296 (2014)
Sloan Digital Sky Survey database (2010). http://classic.sdss.org/dr7/
Rosen, B.E.: Function optimization based on advanced simulated annealing. In: IEEE Workshop on Physics and Computation, PhysComp 1992, pp. 289–293 (1992)
De, T., Burnet, D.F., Chattopadhyay, A.K.: Clustering large number of extragalactic spectra of galaxies and quasars through canopies. Commun. Stat. - Theory Methods 45(9), 2638–2653 (2016)
Sanders, J., Kandrot, E.: CUDA by Example: An Introduction to General-Purpose GPU Programming. Addison-Wesley Professional, Boston (2010)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Yasuda, M. (2020). Determination of Multiple q Values for Tsallis-Entropy-Maximized-FCM. In: Liu, Y., Wang, L., Zhao, L., Yu, Z. (eds) Advances in Natural Computation, Fuzzy Systems and Knowledge Discovery. ICNC-FSKD 2019. Advances in Intelligent Systems and Computing, vol 1074. Springer, Cham. https://doi.org/10.1007/978-3-030-32456-8_83
Download citation
DOI: https://doi.org/10.1007/978-3-030-32456-8_83
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-32455-1
Online ISBN: 978-3-030-32456-8
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)