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An eigendecomposition approach to weighted graph matching problems

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1 Author(s)
Umeyama, S. ; Electrotech. Lab., Ibaraki, Japan

An approximate solution to the weighted-graph-matching problem is discussed for both undirected and directed graphs. The weighted-graph-matching problem is that of finding the optimum matching between two weighted graphs, which are graphs with weights at each arc. The proposed method uses an analytic instead of a combinatorial or iterative approach to the optimum matching problem. Using the eigendecompositions of the adjacency matrices (in the case of the undirected-graph-matching problem) or Hermitian matrices derived from the adjacency matrices (in the case of the directed-graph-matching problem), a matching close to the optimum can be found efficiently when the graphs are sufficiently close to each other. Simulation results are given to evaluate the performance of the proposed method

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Pattern Analysis and Machine Intelligence, IEEE Transactions on  (Volume:10 ,  Issue: 5 )