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Tensor Kronecker products, the natural generalization of the matrix Kroneckerproduct, are independently emerging in multiple research communities. Liketheir matrix counterpart, the tensor generalization gives structure forimplicit multiplication and factorization theorems. We present a theorem thatdecouples the dominant eigenvectors of tensor Kronecker products, which is arare generalization from matrix theory to tensor eigenvectors. This theoremimplies low rank structure ought to be present in the iterates of tensor powermethods on Kronecker products. We investigate low rank structure in the networkalignment algorithm TAME, a power method heuristic. Using the low rankstructure directly or via a new heuristic embedding approach, we produce newalgorithms which are faster while improving or maintaining accuracy, and scaleto problems that cannot be realistically handled with existing techniques.

Dominant Z-Eigenpairs of Tensor Kronecker Products are Decoupled and Applications to Higher-Order Graph Matching