An Eigendecomposition Approach to Weighted Graph Matching Problems

Absfruct-This paper discusses an approximate solution to the weighted graph matching prohlem (WGMP) for both undirected and directed graphs. The W G M P is the problem of f inding the opt imum matching between two weighted graphs, which are graphs with weights at each arc. The proposed method employs an analytic, instead of a combinatorial or iterative, approach to the opt imum matching problem of such graphs. By using the eigendecomposit ions of the adjacency matrices (in the case of the undirected graph matching problem) or some Hermitian matrices derived from the adjacency matrices (in the case of the directed graph matching problem), a matching close to the opt imum one can be found efficiently when the graphs are sufficiently close to each other. Simulation experiments are also given to evaluate the performance of the proposed method.