Symbolic Graph Matching Using the EM Algorithm and Singular Value Decomposition

Bin Luo, Edwin R. Hancock

Abstract: This paper describes an efficient algorithm for inexact graph-matching. The method is purely structural, i.e., it uses only the edge or connectivity structure of the graph and does not draw on node or edge attributes. We make two contributions: 1) commencing from a probability distribution for matching errors, we show how the problem of graph-matching can be posed as maximum likelihood estimation using the apparatus of the EM algorithm; and 2) casting the recover of correspondences matches between the graph-nodes in a matrix framework. This allows us to efficiently recover correspondence matches using singular value decomposition. We experiment with the method on both real-world and synthetic data. We demonstrate that the method offers comparable performance to more computationally demanding methods.