A Weight Regularized Relaxation Based Graph Matching Algorithm

In this paper we propose a regularized relaxation based graph matching algorithm. The graph matching problem is formulated as a constrained convex quadratic program, by relaxing the permutation matrix to a doubly stochastic one. To gradually push the doubly stochastic matrix back to a permutation one, a simple weighted concave regular term is added to the convex objective function. The concave regular function is not a concave relaxation of the original matching problem. However, it is shown that such a simple concave regular term has a comparative performance as the concave relaxation of the PATH following algorithm, which works only on undirected graphs. A concave-convex procedure (CCCP) together with the Frank-Wolfe algorithm is adopted to solve the matching problem, and some experimental results witness the stateof-art performance of the proposed algorithm.