Many-to-many graph matching via metric embedding

Graph matching is an important component in many object recognition algorithms. Although most graph matching algorithms seek a one-to-one correspondence between nodes, it is often the case that a more meaningful correspondence exists between a cluster of nodes in one graph and a cluster of nodes in the other. We present a matching algorithm that establishes many-to-many correspondences between nodes of noisy, vertex-labeled weighted graphs. The algorithm is based on recent developments in efficient low-distortion metric embedding of graphs into normed vector spaces. By embedding weighted graphs into normed vector spaces, we reduce the problem of many-to-many graph matching to that of computing a distribution-based distance measure between graph embeddings. We use a specific measure, the earth mover´s distance, to compute distances between sets of weighted vectors. Empirical evaluation of the algorithm on an extensive set of recognition trials demonstrates both the robustness and efficiency of the overall approach.