Many-to-many graph matching: a continuous relaxation approach
ECML PKDD'10 Proceedings of the 2010 European conference on Machine learning and knowledge discovery in databases: Part III
Low-Rank Optimization on the Cone of Positive Semidefinite Matrices
SIAM Journal on Optimization
High efficiency and quality: large graphs matching
Proceedings of the 20th ACM international conference on Information and knowledge management
A 3D shape segmentation approach for robot grasping by parts
Robotics and Autonomous Systems
Unsupervised Learning for Graph Matching
International Journal of Computer Vision
Scalable multiple global network alignment for biological data
Proceedings of the 2nd ACM Conference on Bioinformatics, Computational Biology and Biomedicine
WSM: a novel algorithm for subgraph matching in large weighted graphs
Journal of Intelligent Information Systems
A weight regularized relaxation based graph matching algorithm
IScIDE'11 Proceedings of the Second Sino-foreign-interchange conference on Intelligent Science and Intelligent Data Engineering
Real-Time exact graph matching with application in human action recognition
HBU'12 Proceedings of the Third international conference on Human Behavior Understanding
A message passing graph match algorithm based on a generative graphical model
AMT'12 Proceedings of the 8th international conference on Active Media Technology
High efficiency and quality: large graphs matching
The VLDB Journal — The International Journal on Very Large Data Bases
Partial correspondence based on subgraph matching
Neurocomputing
A sparse nonnegative matrix factorization technique for graph matching problems
Pattern Recognition
Using local similarity measures to efficiently address approximate graph matching
Discrete Applied Mathematics
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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.