### 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 |
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Title of host publication | 2008 IEEE International Conference on Granular Computing, GRC 2008 |

Pages | 350-355 |

Number of pages | 6 |

DOIs | |

Publication status | Published - 2008 |

Event | 2008 IEEE International Conference on Granular Computing, GRC 2008 - Hangzhou Duration: 2008 Aug 26 → 2008 Aug 28 |

### Other

Other | 2008 IEEE International Conference on Granular Computing, GRC 2008 |
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City | Hangzhou |

Period | 08/8/26 → 08/8/28 |

### Fingerprint

### ASJC Scopus subject areas

- Artificial Intelligence
- Computer Science Applications
- Software

### Cite this

*2008 IEEE International Conference on Granular Computing, GRC 2008*(pp. 350-355). [4664765] 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.

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

*2008 IEEE International Conference on Granular Computing, GRC 2008.*, 4664765, pp. 350-355, 2008 IEEE International Conference on Granular Computing, GRC 2008, Hangzhou, 08/8/26. https://doi.org/10.1109/GRC.2008.4664765

}

TY - GEN

T1 - Fuzzy classification function of entropy regularized fuzzy c-means algorithm for data with tolerance using kernel function

AU - Kanzawa, Yuchi

AU - Endo, Yasunori

AU - Miyamoto, Sadaaki

PY - 2008

Y1 - 2008

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=57949109596&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=57949109596&partnerID=8YFLogxK

U2 - 10.1109/GRC.2008.4664765

DO - 10.1109/GRC.2008.4664765

M3 - Conference contribution

AN - SCOPUS:57949109596

SN - 9781424425129

SP - 350

EP - 355

BT - 2008 IEEE International Conference on Granular Computing, GRC 2008

ER -