Local minima of the best low multilinear rank approximation of tensors
نویسندگان
چکیده
Higher-order tensors are generalizations of vectors and matrices to thirdor even higher-order arrays of numbers. We consider a generalization of column and row rank of a matrix to tensors, called multilinear rank. Given a higher-order tensor, we are looking for another tensor, as close as possible to the original one and with multilinear rank bounded by prespecified numbers. In this paper, we give an overview of recent results pertaining the associated cost function. It can have a number of local minima, which need to be interpreted carefully. Convergence to the global minimum cannot be guaranteed with the existing algorithms. We discuss the conclusions that we have drawn from extensive simulations and point out some hidden problems that might occur in real applications.
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