An Eigendecomposition Approach to Weighted Graph Matching Problems
IEEE Transactions on Pattern Analysis and Machine Intelligence
The projected gradient methods for least squares matrix approximations with spectral constraints
SIAM Journal on Numerical Analysis
Matrix differential equations: a continuous realization process for linear algebra problems
Nonlinear Analysis: Theory, Methods & Applications
A Graduated Assignment Algorithm for Graph Matching
IEEE Transactions on Pattern Analysis and Machine Intelligence
Computers and Intractability; A Guide to the Theory of NP-Completeness
Computers and Intractability; A Guide to the Theory of NP-Completeness
A cutting planes algorithm based upon a semidefinite relaxation for the quadratic assignment problem
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Potential Fields for Maintaining Connectivity of Mobile Networks
IEEE Transactions on Robotics
Dynamic Assignment in Distributed Motion Planning With Local Coordination
IEEE Transactions on Robotics
A Lagrangian relaxation network for graph matching
IEEE Transactions on Neural Networks
Partial retrieval of CAD models based on the gradient flows in Lie group
Pattern Recognition
WSM: a novel algorithm for subgraph matching in large weighted graphs
Journal of Intelligent Information Systems
Hi-index | 22.15 |
Graph matching is a fundamental problem that arises frequently in the areas of distributed control, computer vision, and facility allocation. In this paper, we consider the optimal graph matching problem for weighted graphs, which is computationally challenging due the combinatorial nature of the set of permutations. Contrary to optimization-based relaxations to this problem, in this paper we develop a novel relaxation by constructing dynamical systems on the manifold of orthogonal matrices. In particular, since permutation matrices are orthogonal matrices with nonnegative elements, we define two gradient flows in the space of orthogonal matrices. The first minimizes the cost of weighted graph matching over orthogonal matrices, whereas the second minimizes the distance of an orthogonal matrix from the finite set of all permutations. The combination of the two dynamical systems converges to a permutation matrix, which provides a suboptimal solution to the weighted graph matching problem. Finally, our approach is shown to be promising by illustrating it on nontrivial problems.