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An Eigendecomposition Approach to Weighted Graph Matching Problems
September 1988 (vol. 10 no. 5)
pp. 695-703

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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Index Terms:
pattern recognition; eigendecomposition; weighted graph matching; adjacency matrices; undirected-graph-matching; Hermitian matrices; directed-graph-matching; eigenvalues and eigenfunctions; graph theory; pattern recognition
Citation:
S. Umeyama, "An Eigendecomposition Approach to Weighted Graph Matching Problems," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 10, no. 5, pp. 695-703, Sept. 1988, doi:10.1109/34.6778
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