### Abstract

Clustering methods of relational data are often based on the assumption that a given set of relational data is Euclidean, and kernelized clustering methods are often based on the assumption that a given kernel is positive semidefinite. In practice, non-Euclidean relational data and an indefinite kernel may arise, and a β-spread transformation was proposed for such cases, which modified a given set of relational data or a given a kernel Gram matrix such that the modified β value is common to all objects. In this paper, we propose a quadratic programming-based object-wise β-spread transformation for use in both relational and kernelized fuzzy c-means clustering. The proposed system retains the given data better than conventional methods, and numerical examples show that our method is efficient for both relational and kernel fuzzy c-means.

Original language | English |
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Title of host publication | Advances in Intelligent Systems and Computing |

Publisher | Springer Verlag |

Pages | 29-43 |

Number of pages | 15 |

Volume | 245 |

ISBN (Print) | 9783319028200 |

DOIs | |

Publication status | Published - 2014 |

Event | 5th International Conference on Knowledge and Systems Engineering, KSE 2013 - Hanoi, Viet Nam Duration: 2013 Oct 17 → 2013 Oct 19 |

### Publication series

Name | Advances in Intelligent Systems and Computing |
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Volume | 245 |

ISSN (Print) | 21945357 |

### Other

Other | 5th International Conference on Knowledge and Systems Engineering, KSE 2013 |
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Country | Viet Nam |

City | Hanoi |

Period | 13/10/17 → 13/10/19 |

### Fingerprint

### ASJC Scopus subject areas

- Control and Systems Engineering
- Computer Science(all)

### Cite this

*Advances in Intelligent Systems and Computing*(Vol. 245, pp. 29-43). (Advances in Intelligent Systems and Computing; Vol. 245). Springer Verlag. https://doi.org/10.1007/978-3-319-02821-7_5

**Relational fuzzy c-means and kernel fuzzy c-means using a quadratic programming-based object-wise β-spread transformation.** / Kanzawa, Yuchi.

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

*Advances in Intelligent Systems and Computing.*vol. 245, Advances in Intelligent Systems and Computing, vol. 245, Springer Verlag, pp. 29-43, 5th International Conference on Knowledge and Systems Engineering, KSE 2013, Hanoi, Viet Nam, 13/10/17. https://doi.org/10.1007/978-3-319-02821-7_5

}

TY - GEN

T1 - Relational fuzzy c-means and kernel fuzzy c-means using a quadratic programming-based object-wise β-spread transformation

AU - Kanzawa, Yuchi

PY - 2014

Y1 - 2014

N2 - Clustering methods of relational data are often based on the assumption that a given set of relational data is Euclidean, and kernelized clustering methods are often based on the assumption that a given kernel is positive semidefinite. In practice, non-Euclidean relational data and an indefinite kernel may arise, and a β-spread transformation was proposed for such cases, which modified a given set of relational data or a given a kernel Gram matrix such that the modified β value is common to all objects. In this paper, we propose a quadratic programming-based object-wise β-spread transformation for use in both relational and kernelized fuzzy c-means clustering. The proposed system retains the given data better than conventional methods, and numerical examples show that our method is efficient for both relational and kernel fuzzy c-means.

AB - Clustering methods of relational data are often based on the assumption that a given set of relational data is Euclidean, and kernelized clustering methods are often based on the assumption that a given kernel is positive semidefinite. In practice, non-Euclidean relational data and an indefinite kernel may arise, and a β-spread transformation was proposed for such cases, which modified a given set of relational data or a given a kernel Gram matrix such that the modified β value is common to all objects. In this paper, we propose a quadratic programming-based object-wise β-spread transformation for use in both relational and kernelized fuzzy c-means clustering. The proposed system retains the given data better than conventional methods, and numerical examples show that our method is efficient for both relational and kernel fuzzy c-means.

UR - http://www.scopus.com/inward/record.url?scp=84927547431&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84927547431&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-02821-7_5

DO - 10.1007/978-3-319-02821-7_5

M3 - Conference contribution

SN - 9783319028200

VL - 245

T3 - Advances in Intelligent Systems and Computing

SP - 29

EP - 43

BT - Advances in Intelligent Systems and Computing

PB - Springer Verlag

ER -