A path following algorithm for the graph matching problem

Simple item page
dc.creatorZaslavskiy, Mikhail
dc.creatorBach, Francis
dc.creatorVert, Jean-Philippe
dc.date2008-01-23
dc.date2008-10-27
dc.date.accessioned2026-07-07T10:12:51Z
dc.date.available2026-07-07T10:12:51Z
dc.descriptionWe 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.
dc.description23 pages, 13 figures,typo correction, new results in sections 4,5,6
dc.identifierhttps://arxiv.org/abs/0801.3654
dc.identifierhttp://arxiv.org/abs/0801.3654
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/172329
dc.subjectComputer Vision and Pattern Recognition
dc.subjectDiscrete Mathematics
dc.titleA path following algorithm for the graph matching problem
dc.typetext

Files

Collections

arXiv