On defining affinity graph for spectral clustering through ranking on manifolds

Authors:
Tian Xia;Juan Cao;Yong-dong Zhang;Jin-tao Li
Affiliations:
Center for Advanced Computing Technology Research, Institute of Computing Technology, Chinese Academy of Sciences, Beijing 100190, China and Graduate University of the Chinese Academy of Sciences, ...;Center for Advanced Computing Technology Research, Institute of Computing Technology, Chinese Academy of Sciences, Beijing 100190, China;Center for Advanced Computing Technology Research, Institute of Computing Technology, Chinese Academy of Sciences, Beijing 100190, China;Center for Advanced Computing Technology Research, Institute of Computing Technology, Chinese Academy of Sciences, Beijing 100190, China
Venue:
Neurocomputing
Year:
2009

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Abstract

Spectral clustering consists of two distinct stages: (a) construct an affinity graph from the dataset and (b) cluster the data points through finding an optimal partition of the affinity graph. The focus of the paper is the first step. Existing spectral clustering algorithms adopt Gaussian function to define the affinity graph since it is easy to implement. However, Gaussian function is hard to depict the intrinsic structure of the data, and it has to specify a scaling parameter whose selection is still an open issue in spectral clustering. Therefore, we propose a new definition of affinity graph for spectral clustering from the graph partition perspective. In particular, we propose two consistencies: smooth consistency and constraint consistency, for affinity graph to hold, and then define the affinity graph respecting these consistencies in a regularization framework of ranking on manifolds. Meanwhile the proposed definition of affinity graph is applicable to both unsupervised and semi-supervised spectral clustering. Encouraging experimental results on synthetic and real world data demonstrate the effectiveness of the proposed approach.