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An eigendecomposition approach to weighted graph matching problems

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1 Author(s)
S. Umeyama ; 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

Published in:

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