On hard and fuzzy c-means clustering with conditionally positive definite kernel

Yuchi Kanzawa, Yasunori Endo, Sadaaki Miyamoto

研究成果: Conference contribution

抄録

In this paper, we investigate three types of c-means clustering algorithms with a conditionally positive definite kernel. One is based on hard c-means, and the others are based on standard and entropy-regularized fuzzy c-means. First, based on a conditionally positive definite kernel describing a squared Euclidean distance between data in the feature space, these algorithms are derived from revised optimization problems of the conventional kernel c-means. Next, based on the relationship between the positive definite kernel and conditionally positive definite kernel, the revised dissimilarity between a datum and a cluster center in the feature space is shown. Finally, it is shown that a conditionally positive definite kernel c-means algorithm and a kernel c-means algorithm with a positive definite kernel derived from the conditionally positive definite kernel are essentially identical to each other. An explicit mapping for a conditionally positive definite kernel is also described geometrically.

本文言語English
ホスト出版物のタイトルFUZZ 2011 - 2011 IEEE International Conference on Fuzzy Systems - Proceedings
ページ816-820
ページ数5
DOI
出版ステータスPublished - 2011 9 27
イベント2011 IEEE International Conference on Fuzzy Systems, FUZZ 2011 - Taipei, Taiwan, Province of China
継続期間: 2011 6 272011 6 30

出版物シリーズ

名前IEEE International Conference on Fuzzy Systems
ISSN(印刷版)1098-7584

Conference

Conference2011 IEEE International Conference on Fuzzy Systems, FUZZ 2011
国/地域Taiwan, Province of China
CityTaipei
Period11/6/2711/6/30

ASJC Scopus subject areas

  • ソフトウェア
  • 理論的コンピュータサイエンス
  • 人工知能
  • 応用数学

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