A path following algorithm for the graph matching problem

TL;DR

This paper introduces a convex-concave programming approach for labeled weighted graph matching, utilizing a solution path method to efficiently approximate the global minimum and improve matching accuracy.

Contribution

It presents a novel convex-concave optimization framework with a solution path algorithm for improved labeled weighted graph matching.

Findings

Competitive performance on multiple datasets

Effective integration of label similarity information

Outperforms some existing graph matching methods

Abstract

We propose a convex-concave programming approach for the labeled weighted graph matching problem. The convex-concave programming formulation is obtained by rewriting the weighted 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 also a hard combinatorial problem. We therefore construct an approximation of the concave problem solution by following a solution path of a convex-concave problem obtained by linear interpolation of the convex and concave formulations, starting from the convex relaxation. This method allows to easily integrate the information on graph label similarities into the optimization problem, and therefore to perform labeled weighted graph matching. The algorithm is compared with some of the best performing graph matching methods on four datasets: simulated graphs, QAPLib, retina vessel images and handwritten chinese characters. In all cases, the results are competitive with the state-of-the-art.