On Kernel Fuzzy <i>c</i>-Means for Data with Tolerance Using Explicit Mapping for Kernel Data   Analysis

Yuchi Kanzawa; Yasunori Endo; Sadaaki Miyamoto

doi:10.20965/jaciii.2012.p0162

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JACIII Vol.16 No.1 pp. 162-168

doi: 10.20965/jaciii.2012.p0162

(2012)

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On Kernel Fuzzy c-Means for Data with Tolerance Using Explicit Mapping for Kernel Data Analysis

Yuchi Kanzawa^*, Yasunori Endo^,
and Sadaaki Miyamoto^

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

^**University of Tsukuba

Received:

January 15, 2011

Accepted:

October 3, 2011

Published:

January 20, 2012

Keywords:

fuzzy c-means, kernel data analysis, explicit mapping, tolerance

Abstract

While explicit mapping is generally unknown for kernel data analysis, its inner product should be known. Although we proposed a kernel fuzzy c-means algorithm for data with tolerance, cluster centers and tolerance in higher dimensional space have not been seen. Contrary to this common assumption, explicit mapping has been introduced and the situation of kernel fuzzy c-means in higher dimensional space has been described via kernel principal component analysis using explicit mapping. In this paper, cluster centers and the tolerance of kernel fuzzy c-means for data with tolerance are described via kernel principal component analysis using explicit mapping.

Cite this article as:

Y. Kanzawa, Y. Endo, and S. Miyamoto, “On Kernel Fuzzy c-Means for Data with Tolerance Using Explicit Mapping for Kernel Data Analysis,” J. Adv. Comput. Intell. Intell. Inform., Vol.16 No.1, pp. 162-168, 2012.

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References

[1] J. C. Bezdek, “Pattern Recognition with Fuzzy Objective Function Algorithms,” Plenun, New York, 1981.
[2] S. Miyamoto and K. Umayahara, “Methods in Hard and Fuzzy Clustering,” in: Z.-Q. Liu and S. Miyamoto (Eds.), Soft Computing and Human-Centered Machines, Springer-Verlag Tokyo, 2000.
[3] S. Miyamoto and D. Suizu, “Fuzzy c-Means Clustering Using Kernel Functions in Support Vector Machines,” J. Advanced Computational Intelligence and Intelligent Informatics, Vol.7, No.1, pp. 25-30, 2003.
[4] V. N. Vapnik, “Statistical Learning Theory,” Wiley, New York, 1998.
[5] 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.
[6] 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.
[7] R. Murata, Y. Endo, H. Haruyama, and S. Miyamoto, “On Fuzzy c-Means for Data with Tolerance,” J. of Advanced Computational Intelligence and Intelligent Informatics, Vol.10, No.5, pp. 673-681, 2006.
[8] Y. Kanzawa, Y. Endo, and S. Miyamoto, “Fuzzy c-Means for Data with Tolerance using Kernel Functions,” IEICE Trans., Fund., Vol.E91-A, No.9, pp. 2520-2534, 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] S. Miyamoto and K. Umayahara, “Methods in Hard and Fuzzy Clustering,” in: Z.-Q. Liu and S. Miyamoto (Eds.), Soft Computing and Human-Centered Machines, Springer-Verlag Tokyo, 2000.

[3] [3] S. Miyamoto and D. Suizu, “Fuzzy c-Means Clustering Using Kernel Functions in Support Vector Machines,” J. Advanced Computational Intelligence and Intelligent Informatics, Vol.7, No.1, pp. 25-30, 2003.

[4] [4] V. N. Vapnik, “Statistical Learning Theory,” Wiley, New York, 1998.

[5] [5] 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.

[6] [6] 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.

[7] [7] R. Murata, Y. Endo, H. Haruyama, and S. Miyamoto, “On Fuzzy c-Means for Data with Tolerance,” J. of Advanced Computational Intelligence and Intelligent Informatics, Vol.10, No.5, pp. 673-681, 2006.

[8] [8] Y. Kanzawa, Y. Endo, and S. Miyamoto, “Fuzzy c-Means for Data with Tolerance using Kernel Functions,” IEICE Trans., Fund., Vol.E91-A, No.9, pp. 2520-2534, 2008.

On Kernel Fuzzy c-Means for Data with Tolerance Using Explicit Mapping for Kernel Data Analysis

Yuchi Kanzawa*, Yasunori Endo**, and Sadaaki Miyamoto**

Yuchi Kanzawa^*, Yasunori Endo^,
and Sadaaki Miyamoto^