Relational Fuzzy <i>c</i>-Lines   Clustering Derived from Kernelization of Fuzzy <i>c</i>-Lines

Yuchi Kanzawa

doi:10.20965/jaciii.2014.p0175

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JACIII Vol.18 No.2 pp. 175-181

doi: 10.20965/jaciii.2014.p0175

(2014)

Paper:

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Relational Fuzzy c-Lines Clustering Derived from Kernelization of Fuzzy c-Lines

Yuchi Kanzawa

Shibaura Institute of Technology, 3-7-5 Toyosu, Koto, Tokyo 135-8548, Japan

Received:

October 1, 2013

Accepted:

January 13, 2014

Published:

March 20, 2014

Keywords:

relational fuzzy clustering, kernel fuzzy clustering

Abstract

In this paper, two linear fuzzy clustering algorithms are proposed for relational data based on kernel fuzzy c-means, in which the prototypes of clusters are given by lines spanned in a feature space defined by the kernel which is derived from a given relational data. The proposed algorithms contrast the conventional method in which the prototypes of clusters are given by lines spanned by two representative objects. Through numerical examples, it is shown that the proposed algorithms can capture local sub-structures in relational data.

Cite this article as:

Y. Kanzawa, “Relational Fuzzy c-Lines Clustering Derived from Kernelization of Fuzzy c-Lines,” J. Adv. Comput. Intell. Intell. Inform., Vol.18 No.2, pp. 175-181, 2014.

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References

[1] J. C. Bezdek, “Pattern Recognition with Fuzzy Objective Function Algorithms,” Plenun, New York, 1981.
[2] K. Honda and H. Ichihashi, “Linear Fuzzy Clustering Techniques with Missing Values and Their Application to Local Principal Component Analysis,” IEEE Trans. Fuzzy Systems, Vol.12, No.2, pp. 183-193, 2004.
[3] K. Honda and H. Ichihashi, “Component-wise Robust Linear Fuzzy Clustering for Collaborative Filtering,” Int. J. of Approximate Reasoning, Vol.37, No.2, pp. 127-144, 2004.
[4] R. J. Hathaway, J. W. Davenport, and J. C. Bezdek, “Relational Duals of the c-means Clustering Algorithms,” Pattern Recognition, Vol.22, No.2, pp. 205-212, 1989.
[5] N. Haga, K. Honda, H. Ichihashi, and A. Notsu, “Linear Fuzzy Clustering of Relational Data Based on Extended Fuzzy c-Medoids,” Proc. FUZZ-IEEE, pp. 366-371, 2008.
[6] T. Yamamoto, K. Honda, A. Notsu, and H. Ichihashi, “Non-Euclidean Extension of FCMdd-Based Linear Clustering for Relational Data,” J. of Advanced Computational Intelligence and Intelligent Informatics, Vol.15, No.8, pp. 1050-1056, 2011.
[7] S. Miyamoto and D. Suizu, “Fuzzy c-Means Clustering Using Kernel Functions in Support Vector Machines,” J. of Advanced Computational Intelligence and Intelligent Informatics, Vol.7, No.1, pp. 25-30, 2003.
[8] V. N. Vapnik, “Statistical Learning Theory,” Wiley, New York, 1998.
[9] S.Miyamoto, Y. Kawasaki, and K. Sawazaki, “An Explicit Mapping for Kernel Data Analysis and Application to Text Analysis,” Proc. IFSA-EUSFLAT 2009, pp. 618-623, 2009.
[10] S. Miyamoto and K. Sawazaki, “An Explicit Mapping for Kernel Data Analysis and Application to c-Means Clustering,” Proc. NOLTA 2009, pp. 556-559, 2009.
[11] D. E. Gustafson and W. Kessel, “Fuzzy Clustering with a Fuzzy Covariance Matrix,” Proc. IEEE-CDC, Vol.2, pp. 761-766, 1979.
[12] G. Ekman, “Dimensions of Color Vision,” J. of Psychology, Vol.38, pp. 467-474, 1954.
[13] H. Wada, K. Honda, A. Notsu, and H. Ichihashi, “Document map construction and keyword selection based on local PCA,” Proc. of Joint 4th Int. Conf. on Soft Computing and Intelligent Systems and 9th Int. Symposium on Advanced Intelligent Systems, pp. 682-685, 2008.

This article is published under a Creative Commons Attribution-NoDerivatives 4.0 Internationa License.

[1] [1] J. C. Bezdek, “Pattern Recognition with Fuzzy Objective Function Algorithms,” Plenun, New York, 1981.

[2] [2] K. Honda and H. Ichihashi, “Linear Fuzzy Clustering Techniques with Missing Values and Their Application to Local Principal Component Analysis,” IEEE Trans. Fuzzy Systems, Vol.12, No.2, pp. 183-193, 2004.

[3] [3] K. Honda and H. Ichihashi, “Component-wise Robust Linear Fuzzy Clustering for Collaborative Filtering,” Int. J. of Approximate Reasoning, Vol.37, No.2, pp. 127-144, 2004.

[4] [4] R. J. Hathaway, J. W. Davenport, and J. C. Bezdek, “Relational Duals of the c-means Clustering Algorithms,” Pattern Recognition, Vol.22, No.2, pp. 205-212, 1989.

[5] [5] N. Haga, K. Honda, H. Ichihashi, and A. Notsu, “Linear Fuzzy Clustering of Relational Data Based on Extended Fuzzy c-Medoids,” Proc. FUZZ-IEEE, pp. 366-371, 2008.

[6] [6] T. Yamamoto, K. Honda, A. Notsu, and H. Ichihashi, “Non-Euclidean Extension of FCMdd-Based Linear Clustering for Relational Data,” J. of Advanced Computational Intelligence and Intelligent Informatics, Vol.15, No.8, pp. 1050-1056, 2011.

[7] [7] S. Miyamoto and D. Suizu, “Fuzzy c-Means Clustering Using Kernel Functions in Support Vector Machines,” J. of Advanced Computational Intelligence and Intelligent Informatics, Vol.7, No.1, pp. 25-30, 2003.

[8] [8] V. N. Vapnik, “Statistical Learning Theory,” Wiley, New York, 1998.

[9] [9] S.Miyamoto, Y. Kawasaki, and K. Sawazaki, “An Explicit Mapping for Kernel Data Analysis and Application to Text Analysis,” Proc. IFSA-EUSFLAT 2009, pp. 618-623, 2009.

[10] [10] S. Miyamoto and K. Sawazaki, “An Explicit Mapping for Kernel Data Analysis and Application to c-Means Clustering,” Proc. NOLTA 2009, pp. 556-559, 2009.

[11] [11] D. E. Gustafson and W. Kessel, “Fuzzy Clustering with a Fuzzy Covariance Matrix,” Proc. IEEE-CDC, Vol.2, pp. 761-766, 1979.

[12] [12] G. Ekman, “Dimensions of Color Vision,” J. of Psychology, Vol.38, pp. 467-474, 1954.

[13] [13] H. Wada, K. Honda, A. Notsu, and H. Ichihashi, “Document map construction and keyword selection based on local PCA,” Proc. of Joint 4th Int. Conf. on Soft Computing and Intelligent Systems and 9th Int. Symposium on Advanced Intelligent Systems, pp. 682-685, 2008.