Abstract
Semi-supervised clustering uses partially labeled data, as often occurs in practical clustering, to obtain a better clustering result. One approach uses hard constraints which specify data that must and cannot be within the same cluster. In this chapter, we propose another approach to semi-supervised clustering with soft pairwise constraints. The clustering method used is fuzzy c-means (FCM), a commonly used fuzzy clustering method. Two previously proposed variants, entropy-regularized relational/kernel fuzzy c-means clustering and indefinite kernel fuzzy c-means clustering algorithm are modified to use the soft constraints. In addition, a method is discussed that propagates pairwise constraints when the given constraints are not sufficient for obtaining the desired clustering result. Using some numerical examples, it is shown that the proposed algorithms obtain better clustering results.
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, Plenum, New York, (1981).
Miyamoto, S. and Umayahara, K.: “Methods in Hard and Fuzzy Clustering,” in: Liu, Z.-Q. and Miyamoto, S. (eds), Soft Computing and Human-centered Machines, Springer-Verlag Tokyo, (2000).
Hathaway, R.J., Davenport, J.W. and Bezdek, J.C.: “Relational Duals of the \(c\)-means Clustering Algorithms,” Pattern Recognition, Vol. 22, No. 2, pp. 205–212, (1989).
Hathaway, R.J. and Bezdek, J.C.: “NERF C-means: Non-Euclidean Relational Fuzzy Clustering,” Pattern Recognition, Vol. 27, No. 3, pp. 429–437, (1994).
Kanzawa, Y.: “Entropy-Regularized Fuzzy Clustering for Non-Euclidean Relational Data and Indefinite Kernel Data,” JACIII, Vol. 16, No. 7, pp. 784–792, (2012).
Miyamoto, S. and Suizu, D.: “Fuzzy \(c\)-Means Clustering Using Kernel Functions in Support Vector Machines,” JACIII, Vol. 7, No. 1, pp. 25–30, (2003).
Miyamoto, S., Kawasaki, Y., and Sawazaki, K.: “An Explicit Mapping for Kernel Data Analysis and Application to Text Analysis,” Proc. IFSA-EUSFLAT 2009, pp. 618–623, (2009).
Kanzawa, Y., Endo, Y., and Miyamoto, S.: “Indefinite Kernel Fuzzy \(c\)-Means Clustering Algorithms,” Lecture Notes in Computer Science, Vol. 6408, pp. 116–128, (2010).
Bouchachia, A. and Pedrycz, W.: “Data Clustering with Partial Supervision,” Data Mining and Knowledge Discovery, Vol. 12, pp. 47–78, (2006).
Yamazaki, M., Miyamoto, S. and Lee, I.-J.: “Semi-supervised Clustering with Two Types of Additional Functions,” Proc. 24th Fuzzy System Symposium, 2E2-01, (2009).
Yamashiro, M., Endo, Y., Hamasuna, Y. and Miyamoto, S.: “A Study on Semi-supervised Fuzzy \(c\)-Means,” Proc. 24th Fuzzy System Symposium, 2E3-04, (2009).
Kanzawa, Y., Endo, Y. and Miyamoto, S.: “A Semi-Supervised Entropy Regularized Fuzzy \(c\)-Means,” Proc. 2009 International Symposium on Nonlinear Theory and Its Applications, pp. 564–567, (2009).
Wagstaff, K., Cardie, C., Rogers, S. and Schroedl, S.: “Constrained K-means Clustering with Background Knowledge,” Proc. Eighteenth International Conference on Machine-Learning, pp. 577–584, (2001).
Grira, N., Crucianu, M. and Boujemaa, N.: “Semi-supervised Image Database Categorization using Pairwise Constraints,” Proc. 2005 IEEE International Conference on Image Processing, Vol. 3, pp. 1228–1231, (2005).
Kanzawa, Y., Endo, Y. and Miyamoto, S: “Some Pairwise Constrained Semi-Supervised Fuzzy \(c\)-Means Clustering,” LNAI, Vol. 5681, pp. 268–281, (2009).
Kanzawa, Y., Endo, Y., and Miyamoto, S.: “Semi-Supervised Fuzzy c-Means Algorithm by Revising Dissimilarity Between Data,” JACIII, Vol. 15, No. 1, pp. 95–101, (2011).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Kanzawa, Y. (2017). Semi-supervised Fuzzy c-Means Algorithms by Revising Dissimilarity/Kernel Matrices. In: Torra, V., Dahlbom, A., Narukawa, Y. (eds) Fuzzy Sets, Rough Sets, Multisets and Clustering. Studies in Computational Intelligence, vol 671. Springer, Cham. https://doi.org/10.1007/978-3-319-47557-8_4
Download citation
DOI: https://doi.org/10.1007/978-3-319-47557-8_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-47556-1
Online ISBN: 978-3-319-47557-8
eBook Packages: EngineeringEngineering (R0)