## A Lagrangian Relaxation Network for Graph Matching (1996)

Venue: | IEEE Trans. Neural Networks |

Citations: | 26 - 7 self |

### BibTeX

@INPROCEEDINGS{Rangarajan96alagrangian,

author = {Anand Rangarajan and Eric Mjolsness},

title = {A Lagrangian Relaxation Network for Graph Matching},

booktitle = {IEEE Trans. Neural Networks},

year = {1996},

pages = {4629--4634},

publisher = {IEEE Press}

}

### Years of Citing Articles

### OpenURL

### Abstract

A Lagrangian relaxation network for graph matching is presented. The problem is formulated as follows: given graphs G and g, find a permutation matrix M that brings the two sets of vertices into correspondence. Permutation matrix constraints are formulated in the framework of deterministic annealing. Our approach is in the same spirit as a Lagrangian decomposition approach in that the row and column constraints are satisfied separately with a Lagrange multiplier used to equate the two "solutions." Due to the unavoidable symmetries in graph isomorphism (resulting in multiple global minima), we add a symmetry-breaking self-amplification term in order to obtain a permutation matrix. With the application of a fixpoint preserving algebraic transformation to both the distance measure and self-amplification terms, we obtain a Lagrangian relaxation network. The network performs minimization with respect to the Lagrange parameters and maximization with respect to the permutation matrix variable...