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| Graph Spectral Decomposition and Clustering |
| KONG Min1,2, CHEN SiBao1, ZHAO HaiFeng1, LUO Bin1 |
1.School of Computer Science and Technology, Anhui University, Hefei 230039
2.Department of Machine and Electron Engineering, West Anhui University, Lu’an 237012 |
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Abstract This paper explore how to use spectral methods for embedding and clustering unweighted graphs. The leading eignvectors of the graph adjacency matrix are employed to define eignmodes of the adjacency matrix. For each eigenmode, vectors of spectral properties are computed as feature vectors. These properties include the eigenmode perimeter, eigenmode volume, Cheeger number, intermode adjacency matrices and intermode edgedistance. Then these vectors are embedded in a patternspace using two contrasting approachs. The first of these involves performing principal or independent component analysis on the covariance matrix for the spectral pattern vectors. The second approach involves performing multidimensional scaling on the L2 norm for pairs of patten vectors. This paper also illustrate the utility of the embedding methods on neighbourhood graphs representing the arrangement of corner features in 2D images of 3D polyhedral objects. Experimental results show that clustering graphs using spectral properties of graphs is practical and effective.
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Received: 03 March 2005
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2006, Vol. 19 
