On Bezdek-type possibilistic clustering for spherical data, its kernelization, and spectral clustering approach

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

In this study, a Bezdek-type fuzzified possibilistic clustering algorithm for spherical data (bPCS), its kernelization (K-bPCS), and spectral clustering approach (sK-bPCS) are proposed. First, we propose the bPCS by setting a fuzzification parameter of the Tsallis entropy-based possibilistic clustering optimization problem for spherical data (tPCS) to infinity, and by modifying the cosine correlationbased dissimilarity between objects and cluster centers. Next, we kernelize bPCS to obtain K-bPCS, which can be applied to non-spherical data with the help of a given kernel, e.g., a Gaussian kernel. Furthermore, we propose a spectral clustering approach to K-bPCS called sK-bPCS, which aims to solve the initialization problem of bPCS and K-bPCS. Furthermore, we demonstrate that this spectral clustering approach is equivalent to kernelized principal component analysis (K-PCA). The validity of the proposed methods is verified through numerical examples.

Original languageEnglish
Title of host publicationModeling Decisions for Artificial Intelligence - 13th International Conference, MDAI 2016, Proceedings
PublisherSpringer Verlag
Pages178-190
Number of pages13
Volume9880 LNAI
ISBN (Print)9783319456553
DOIs
Publication statusPublished - 2016
Event13th International Conference on Modeling Decisions for Artificial Intelligence, MDAI 2016 - Sant Juliadeloria, Andorra
Duration: 2016 Sep 192016 Sep 21

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9880 LNAI
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other13th International Conference on Modeling Decisions for Artificial Intelligence, MDAI 2016
CountryAndorra
CitySant Juliadeloria
Period16/9/1916/9/21

Fingerprint

Clustering algorithms
Principal component analysis
Entropy

Keywords

  • Bezdek-type fuzzification
  • Kernel clustering
  • Possibilistic clustering
  • Spectral clustering
  • Spherical data

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

Cite this

Kanzawa, Y. (2016). On Bezdek-type possibilistic clustering for spherical data, its kernelization, and spectral clustering approach. In Modeling Decisions for Artificial Intelligence - 13th International Conference, MDAI 2016, Proceedings (Vol. 9880 LNAI, pp. 178-190). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9880 LNAI). Springer Verlag. https://doi.org/10.1007/978-3-319-45656-0_15

On Bezdek-type possibilistic clustering for spherical data, its kernelization, and spectral clustering approach. / Kanzawa, Yuchi.

Modeling Decisions for Artificial Intelligence - 13th International Conference, MDAI 2016, Proceedings. Vol. 9880 LNAI Springer Verlag, 2016. p. 178-190 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9880 LNAI).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Kanzawa, Y 2016, On Bezdek-type possibilistic clustering for spherical data, its kernelization, and spectral clustering approach. in Modeling Decisions for Artificial Intelligence - 13th International Conference, MDAI 2016, Proceedings. vol. 9880 LNAI, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9880 LNAI, Springer Verlag, pp. 178-190, 13th International Conference on Modeling Decisions for Artificial Intelligence, MDAI 2016, Sant Juliadeloria, Andorra, 16/9/19. https://doi.org/10.1007/978-3-319-45656-0_15
Kanzawa Y. On Bezdek-type possibilistic clustering for spherical data, its kernelization, and spectral clustering approach. In Modeling Decisions for Artificial Intelligence - 13th International Conference, MDAI 2016, Proceedings. Vol. 9880 LNAI. Springer Verlag. 2016. p. 178-190. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-319-45656-0_15
Kanzawa, Yuchi. / On Bezdek-type possibilistic clustering for spherical data, its kernelization, and spectral clustering approach. Modeling Decisions for Artificial Intelligence - 13th International Conference, MDAI 2016, Proceedings. Vol. 9880 LNAI Springer Verlag, 2016. pp. 178-190 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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