An Eigendecomposition Approach to Weighted Graph Matching Problems

  • Authors:
  • S. Umeyama

  • Affiliations:
  • Electrotechnical Laboratory, Tsukubashiu, Japan

  • Venue:
  • IEEE Transactions on Pattern Analysis and Machine Intelligence
  • Year:
  • 1988

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Abstract

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.