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- Catherine Fraikin, Yurii Nesterov, Paul Van Dooren
- SIAM J. Matrix Analysis Applications
- 2008

In this paper, we analyze the coupling between the isometric projections of two square matrices. These two matrices of dimensions m×m and n×n are restricted to a lower k-dimensional subspace under isometry constraints. We maximize the coupling between these isometric projections expressed as the trace of the product of the projected matrices. First we… (More)

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… (More)

We consider the problem of comparing two directed graphs with nodes that have been subdivided into classes of different type. The matching process is based on a constrained projection of the nodes of the graphs in a lower dimensional space. This procedure is formulated as a non-convex optimization problem. The objective function uses the two adjacency… (More)

- Catherine Fraikin, Paul Van Dooren
- Web Information Retrieval and Linear Algebra…
- 2007

In this paper, we consider two particular problems of directed graph matching. The first problem concerns graphs with nodes that have been subdivided into classes of different type. The second problem treats graphs with edges of different types. In the two cases, the matching process is based on a constrained projection of the nodes and of the edges of both… (More)

In this paper, we consider the problem of correlation between the projections of two square matrices. These matrices of dimensions m × m and n × n are projected on a subspace of lower-dimension k under isometry constraints. We maximize the correlation between these projections expressed as a trace function of the product of the projected matrices. First we… (More)

We consider the problem of finding the optimal correlation between two projected matrices U∗AU and V ∗BV . The square matrices A and B may be of different dimensions, but the isometries U and V have a common column dimension k. The correlation is measured by the real function c(U,V ) = R tr(U∗AUV ∗B∗V ), which we maximize of the isometries U∗U = V ∗V = Ik.… (More)

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