Non-negative Tensor Approximations
Résumé
Necessary conditions are derived for a rank-r tensor to be a best rank-r approximation of a given tensor. It is shown that a positive tensor with rank > 1 has a unique rank one approximation, and that a non negative tensor generally has a unique low-rank nonnegative approximate. We discuss the notion of r-singular values and their corresponding r-singular vector tuples, which is closely related to best rank-r approximations. We then show that a generic tensor has a finite number of r-singular vector tuples for some r.
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