Investigation of Spectral Clustering for Signed Graph Matrix Representations

被引:0
|
作者
Fox, Alyson [1 ]
Sanders, Geoffrey [1 ]
Knyazev, Andrew [2 ]
机构
[1] Lawrence Livermore Natl Lab, Ctr Appl Sci Comp, Livermore, CA 94550 USA
[2] Univ Colorado, Dept Math & Stat Sci, Denver, CO 80202 USA
关键词
signed graphs; Laplacian; spectral embedding; spectral clustering; Gremban's expansion;
D O I
暂无
中图分类号
TP3 [计算技术、计算机技术];
学科分类号
0812 ;
摘要
Signed graphs [11], which allow for both favorable and adverse relationships, are becoming a common model choice for various data analysis applications, e.g., correlation clustering [1] and spectral clustering [9]. Unlike for unsigned graphs, there is no collective agreement of a matrix representation that relates to the unsigned graph Laplacian. There currently exists three proposed matrix representations: [9] proposes a zero row-sum preserving Laplacian (signed Laplacian), [8] proposes a physics preserving Laplacian (Physics Laplacian), and [4] proposes an expansion of the signed Laplacian into an unsigned Laplacian with twice the number of degrees-of-freedom (Gremban's expansion.) We investigate these three proposed matrix representations with respect to the quality of traditional (unsigned graph) spectral clustering concepts. We provide three numerical tests that use a stochastic block model with negative edge weights. We observe that the best matrix representation for spectral clustering depends on the underlying structure of a signed graph, which may be unavailable. However, since the Gremban's expansion matrix provides higher quality clusters for more combinations of inner and outer-connection probabilities for positive and negative valued edges, we conclude that the Gremban's expansion is the most robust representation to use for spectral clustering.
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页数:7
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