A path following algorithm for graph matching
We propose a convex-concave programming approach for the labelled weighted graph matching problem. The convex-concave programming formulation is obtained by rewriting the graph matching problem as a least-square problem on the set of permutation matrices and relaxing it to two different optimization problems: a quadratic convex and a quadratic concave optimization problem on the set of doubly stochastic matrices. The concave relaxation has the same global minimum as the initial graph matching problem, but the search for its global minimum is aslo a complex combinatorial problem. We therefore construct an approximation of the concave problem solution by following a solution path of the convex-concave problem obtained by linear interpolation of the convex and concave formulations, starting from the convex relaxation. The algorithm is compared with some of the best performing graph matching methods on three datasets: simulated graphs, QAPLib and handwritten chinese characters.