Uniqueness of Nonnegative Tensor Approximations

@article{Qi2016UniquenessON,
  title={Uniqueness of Nonnegative Tensor Approximations},
  author={Yang Qi and Pierre Comon and Lek-Heng Lim},
  journal={IEEE Transactions on Information Theory},
  year={2016},
  volume={62},
  pages={2170-2183}
}
We show that for a nonnegative tensor, a best nonnegative rank-r approximation is almost always unique, its best rank-one approximation may always be chosen to be a best nonnegative rank-one approximation, and the set of nonnegative tensors with nonunique best rank-one approximations forms an algebraic hypersurface. We show that the last part holds true more generally for real tensors and, thereby, determine a polynomial equation, so that a real or nonnegative tensor that does not satisfy this… CONTINUE READING

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