### Abstract

This paper proposes two types of kernel fuzzy c-means algorithms with an indefinite kernel. Both algorithms are based on the fact that the relational fuzzy c-means algorithm is a special case of the kernel fuzzy c-means algorithm. The first proposed algorithm adaptively updated the indefinite kernel matrix such that the dissimilarity between each datum and each cluster center in the feature space is non-negative, instead of subtracting the minimal eigenvalue of the given kernel matrix as its preprocess. This derivation follows the manner in which the non-Euclidean relational fuzzy c-means algorithm is derived from the original relational fuzzy c-means one. The second proposed method produces the memberships by solving the optimization problem in which the constraint of non-negative memberships is added to the one of K-sFCM. This derivation follows the manner in which the non-Euclidean fuzzy relational clustering algorithm is derived from the original relational fuzzy c-means one. Through a numerical example, the proposed algorithms are discussed.

Original language | English |
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Title of host publication | Modeling Decisions for Artificial Intelligence - 7th International Conference, MDAI 2010, Proceedings |

Pages | 116-128 |

Number of pages | 13 |

DOIs | |

Publication status | Published - 2010 Dec 1 |

Event | 7th International Conference on Modeling Decisions for Artificial Intelligence, MDAI 2010 - Perpignan, France Duration: 2010 Oct 27 → 2010 Oct 29 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 6408 LNAI |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | 7th International Conference on Modeling Decisions for Artificial Intelligence, MDAI 2010 |
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Country | France |

City | Perpignan |

Period | 10/10/27 → 10/10/29 |

### Keywords

- Indefinite kernel
- Kernel fuzzy c-means
- Non-Euclidean fuzzy relational clustering
- Non-Euclidean relational fuzzy c-means

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

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## Cite this

*Modeling Decisions for Artificial Intelligence - 7th International Conference, MDAI 2010, Proceedings*(pp. 116-128). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 6408 LNAI). https://doi.org/10.1007/978-3-642-16292-3_13