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A path following algorithm for the graph matching problem.

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, perform labeled weighted graph matching. The algorithm is compared with some of the best performing graph matching methods on four data sets: simulated graphs, QAPLib, retina vessel images, and handwritten Chinese characters. In all cases, the results are competitive with the state of the art.
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https://hal.archives-ouvertes.fr/hal-00433567
Contributor : Jean-Philippe Vert Connect in order to contact the contributor
Submitted on : Thursday, November 19, 2009 - 11:38:12 PM
Last modification on : Thursday, March 17, 2022 - 10:08:39 AM

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Mikhail Zaslavskiy, Francis Bach, Jean-Philippe Vert. A path following algorithm for the graph matching problem.. IEEE Transactions on Pattern Analysis and Machine Intelligence, Institute of Electrical and Electronics Engineers, 2009, 31 (12), pp.2227-42. ⟨10.1109/TPAMI.2008.245⟩. ⟨hal-00433567⟩

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