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In this paper, we extend the notion of similarity matrix, which has been used to define similarity between nodes of two graphs, to the case of colored graphs, where the coloring is either on the nodes or on the edges of both graphs. The proposed method tries to find the optimal matching between the nodes or edges of both graphs but only performs the comparison when their colors are the same. The proposed cost function nevertheless uses the connectivity between all nodes and edges of both graphs. We then also show how to extend this to the notion of low rank similarity matrix, by defining it as a constrained optimization problem. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we consider the problem of maximizing the coupling between the isometric projections of two square matrices of dimensions m and n. This coupling is defined as an inner product between the matrices. This is a non-convex optimization problem with isometry constraints on the variables. The optimization set is an equinormed set and we develop a gradient-type algorithm to solve the problem. Numerical experiments and an application to graph matching are also presented. [Copyright &y& Elsevier]