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)


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.


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


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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Shibaura Institute of TechnologyKotoJapan

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