Fuzzy classification function of entropy regularized fuzzy c-means algorithm for data with tolerance using kernel function

Yuchi Kanzawa; Yasunori Endo; Sadaaki Miyamoto

doi:10.1109/GRC.2008.4664765

Fuzzy classification function of entropy regularized fuzzy c-means algorithm for data with tolerance using kernel function

Yuchi Kanzawa, Yasunori Endo, Sadaaki Miyamoto

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

5 Citations (Scopus)

Abstract

In this paper, the fuzzy classification functions of the entropy regularized fuzzy c-means for data with tolerance using kernel functions are proposed. First, the standard clustering algorithm for data with tolerance using kernel functions are introduced. Second, the fuzzy classification function for fuzzy c-means without tolerance using kernel functions is discussed as the solution of a certain optimization problem. Third, the optimization problem is shown so that the solutions are the fuzzy classification function values for the entropy regularized fuzzy c-means algorithms using kernel functions with respect to data with tolerance. Fourth, Karush-Kuhn-Tucker conditions of the objective function is considered, and the iterative algorithm is proposed for the optimization problem. Some numerical examples are shown.

Original language	English
Title of host publication	2008 IEEE International Conference on Granular Computing, GRC 2008
Pages	350-355
Number of pages	6
DOIs	https://doi.org/10.1109/GRC.2008.4664765
Publication status	Published - 2008 Dec 30
Event	2008 IEEE International Conference on Granular Computing, GRC 2008 - Hangzhou, China Duration: 2008 Aug 26 → 2008 Aug 28

Publication series

Name	2008 IEEE International Conference on Granular Computing, GRC 2008

Conference

Conference	2008 IEEE International Conference on Granular Computing, GRC 2008
Country/Territory	China
City	Hangzhou
Period	08/8/26 → 08/8/28

ASJC Scopus subject areas

Artificial Intelligence
Computer Science Applications
Software

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10.1109/GRC.2008.4664765

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Kanzawa, Y., Endo, Y., & Miyamoto, S. (2008). Fuzzy classification function of entropy regularized fuzzy c-means algorithm for data with tolerance using kernel function. In 2008 IEEE International Conference on Granular Computing, GRC 2008 (pp. 350-355). [4664765] (2008 IEEE International Conference on Granular Computing, GRC 2008). https://doi.org/10.1109/GRC.2008.4664765

Fuzzy classification function of entropy regularized fuzzy c-means algorithm for data with tolerance using kernel function. / Kanzawa, Yuchi; Endo, Yasunori; Miyamoto, Sadaaki.
2008 IEEE International Conference on Granular Computing, GRC 2008. 2008. p. 350-355 4664765 (2008 IEEE International Conference on Granular Computing, GRC 2008).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Kanzawa, Y, Endo, Y & Miyamoto, S 2008, Fuzzy classification function of entropy regularized fuzzy c-means algorithm for data with tolerance using kernel function. in 2008 IEEE International Conference on Granular Computing, GRC 2008., 4664765, 2008 IEEE International Conference on Granular Computing, GRC 2008, pp. 350-355, 2008 IEEE International Conference on Granular Computing, GRC 2008, Hangzhou, China, 08/8/26. https://doi.org/10.1109/GRC.2008.4664765

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abstract = "In this paper, the fuzzy classification functions of the entropy regularized fuzzy c-means for data with tolerance using kernel functions are proposed. First, the standard clustering algorithm for data with tolerance using kernel functions are introduced. Second, the fuzzy classification function for fuzzy c-means without tolerance using kernel functions is discussed as the solution of a certain optimization problem. Third, the optimization problem is shown so that the solutions are the fuzzy classification function values for the entropy regularized fuzzy c-means algorithms using kernel functions with respect to data with tolerance. Fourth, Karush-Kuhn-Tucker conditions of the objective function is considered, and the iterative algorithm is proposed for the optimization problem. Some numerical examples are shown.",

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AB - In this paper, the fuzzy classification functions of the entropy regularized fuzzy c-means for data with tolerance using kernel functions are proposed. First, the standard clustering algorithm for data with tolerance using kernel functions are introduced. Second, the fuzzy classification function for fuzzy c-means without tolerance using kernel functions is discussed as the solution of a certain optimization problem. Third, the optimization problem is shown so that the solutions are the fuzzy classification function values for the entropy regularized fuzzy c-means algorithms using kernel functions with respect to data with tolerance. Fourth, Karush-Kuhn-Tucker conditions of the objective function is considered, and the iterative algorithm is proposed for the optimization problem. Some numerical examples are shown.

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Fuzzy classification function of entropy regularized fuzzy c-means algorithm for data with tolerance using kernel function

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