On Bezdek-Type Possibilistic Clustering for Spherical Data, Its Kernelization, and Spectral Clustering Approach

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9880)

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 correlation-based 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.

Keywords

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

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Shibaura Institute of TechnologyKotoJapan

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