### 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 | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Pages | 116-128 |

Number of pages | 13 |

Volume | 6408 LNAI |

DOIs | |

Publication status | Published - 2010 |

Event | 7th International Conference on Modeling Decisions for Artificial Intelligence, MDAI 2010 - Perpignan 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) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 7th International Conference on Modeling Decisions for Artificial Intelligence, MDAI 2010 |
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City | Perpignan |

Period | 10/10/27 → 10/10/29 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 6408 LNAI, 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

**Indefinite kernel fuzzy c-means clustering algorithms.** / Kanzawa, Yuchi; Endo, Yasunori; Miyamoto, Sadaaki.

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

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*vol. 6408 LNAI, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 6408 LNAI, pp. 116-128, 7th International Conference on Modeling Decisions for Artificial Intelligence, MDAI 2010, Perpignan, 10/10/27. https://doi.org/10.1007/978-3-642-16292-3_13

}

TY - GEN

T1 - Indefinite kernel fuzzy c-means clustering algorithms

AU - Kanzawa, Yuchi

AU - Endo, Yasunori

AU - Miyamoto, Sadaaki

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

KW - Indefinite kernel

KW - Kernel fuzzy c-means

KW - Non-Euclidean fuzzy relational clustering

KW - Non-Euclidean relational fuzzy c-means

UR - http://www.scopus.com/inward/record.url?scp=79956276305&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79956276305&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-16292-3_13

DO - 10.1007/978-3-642-16292-3_13

M3 - Conference contribution

AN - SCOPUS:79956276305

SN - 3642162916

SN - 9783642162916

VL - 6408 LNAI

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 116

EP - 128

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

ER -