An Algorithm for Finding the Most Similar Given Sized Subgraphs in Two Weighted Graphs

We propose a weighted common subgraph (WCS) matching algorithm to find the most similar subgraphs in two labeled weighted graphs. WCS matching, as a natural generalization of equal-sized graph matching and subgraph matching, has found wide applications in many computer vision and machine learning tasks. In this brief, WCS matching is first formulated as a combinatorial optimization problem over the set of partial permutation matrices. Then, it is approximately solved by a recently proposed combinatorial optimization framework—graduated nonconvexity and concavity procedure. Experimental comparisons on both synthetic graphs and real-world images validate its robustness against noise level, problem size, outlier number, and edge density.