The anatomy of a large-scale hypertextual Web search engine
WWW7 Proceedings of the seventh international conference on World Wide Web 7
Journal of Combinatorial Theory Series A
Structural Graph Matching Using the EM Algorithm and Singular Value Decomposition
IEEE Transactions on Pattern Analysis and Machine Intelligence - Graph Algorithms and Computer Vision
Diffusion Kernels on Graphs and Other Discrete Input Spaces
ICML '02 Proceedings of the Nineteenth International Conference on Machine Learning
Graph matching using Random Walks
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 3 - Volume 03
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This paper describes a graph-spectral method for simplifying the structure of a graph. Our starting point is the lazy random walk on the graph, which is determined by the heat-kernel of the graph and can be computed from the spectrum of the graph Laplacian. We characterise the random walk using the commute time between nodes, and show how this quantity may be computed from the Laplacian spectrum using the discrete Green's function. Our idea is to augment the graph with an auxiliary node which acts as a heat source. We use the pattern of commute times from this node to decompose the graph into a sequence of layers. These layers can be located using the Green's function. We exploit this decomposition to develop a layer-by-layer graph-matching strategy. The matching method uses the commute time from the auxiliary node as a node-attribute.