### Abstract

In this paper, the quadratic regularized and standard fuzzy c-means clustering algorithms (qFCM and sFCM) are generalized with respect to hard c-means (HCM) regularization. First, qFCM is generalized from quadratic regularization to power regularization. The relation between this generalization and sFCM is then compared to the relation between other pairs of methods from the perspective of HCM regularization, and, based on this comparison, sFCM is generalized through the addition of a fuzzification parameter. In this process, we see that other methods can be constructed by combining HCM and a regularization term that can either be weighted by data-cluster dissimilarity or not. Furthermore, we see numerically that the existence or nonexistence of this weighting determines the property of these methods' classification rules for an extremely large datum. We also note that the problem of non-convergence in some methods can be avoided through further modification.

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 | 152-165 |

Number of pages | 14 |

Volume | 8234 LNAI |

DOIs | |

Publication status | Published - 2013 |

Event | 10th International Conference on Modeling Decisions for Artificial Intelligence, MDAI 2013 - Barcelona Duration: 2013 Nov 20 → 2013 Nov 22 |

### 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 | 8234 LNAI |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 10th International Conference on Modeling Decisions for Artificial Intelligence, MDAI 2013 |
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City | Barcelona |

Period | 13/11/20 → 13/11/22 |

### Fingerprint

### Keywords

- fuzzy c-means clustering
- regularization

### 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. 8234 LNAI, pp. 152-165). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 8234 LNAI). https://doi.org/10.1007/978-3-642-41550-0_14

**Generalization of quadratic regularized and standard fuzzy c-means clustering with respect to regularization of hard c-means.** / Kanzawa, Yuchi.

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. 8234 LNAI, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 8234 LNAI, pp. 152-165, 10th International Conference on Modeling Decisions for Artificial Intelligence, MDAI 2013, Barcelona, 13/11/20. https://doi.org/10.1007/978-3-642-41550-0_14

}

TY - GEN

T1 - Generalization of quadratic regularized and standard fuzzy c-means clustering with respect to regularization of hard c-means

AU - Kanzawa, Yuchi

PY - 2013

Y1 - 2013

N2 - In this paper, the quadratic regularized and standard fuzzy c-means clustering algorithms (qFCM and sFCM) are generalized with respect to hard c-means (HCM) regularization. First, qFCM is generalized from quadratic regularization to power regularization. The relation between this generalization and sFCM is then compared to the relation between other pairs of methods from the perspective of HCM regularization, and, based on this comparison, sFCM is generalized through the addition of a fuzzification parameter. In this process, we see that other methods can be constructed by combining HCM and a regularization term that can either be weighted by data-cluster dissimilarity or not. Furthermore, we see numerically that the existence or nonexistence of this weighting determines the property of these methods' classification rules for an extremely large datum. We also note that the problem of non-convergence in some methods can be avoided through further modification.

AB - In this paper, the quadratic regularized and standard fuzzy c-means clustering algorithms (qFCM and sFCM) are generalized with respect to hard c-means (HCM) regularization. First, qFCM is generalized from quadratic regularization to power regularization. The relation between this generalization and sFCM is then compared to the relation between other pairs of methods from the perspective of HCM regularization, and, based on this comparison, sFCM is generalized through the addition of a fuzzification parameter. In this process, we see that other methods can be constructed by combining HCM and a regularization term that can either be weighted by data-cluster dissimilarity or not. Furthermore, we see numerically that the existence or nonexistence of this weighting determines the property of these methods' classification rules for an extremely large datum. We also note that the problem of non-convergence in some methods can be avoided through further modification.

KW - fuzzy c-means clustering

KW - regularization

UR - http://www.scopus.com/inward/record.url?scp=84893270345&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84893270345&partnerID=8YFLogxK

U2 - 10.1007/978-3-642-41550-0_14

DO - 10.1007/978-3-642-41550-0_14

M3 - Conference contribution

AN - SCOPUS:84893270345

SN - 9783642415494

VL - 8234 LNAI

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

SP - 152

EP - 165

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

ER -