Uniqueness of Nonnegative Tensor Approximations - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2014

Uniqueness of Nonnegative Tensor Approximations

Yang Qi
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Pierre Comon
Lek-Heng Lim
  • Fonction : Auteur
  • PersonId : 862644

Résumé

We show that the best nonnegative rank-r approximation of a nonnegative tensor is almost always unique and that nonnegative tensors with nonunique best nonnegative rank-r approximation form a semialgebraic set contained in an algebraic hypersurface. We then establish a singular vector variant of the Perron-Frobenius Theorem for positive tensors that may be used for answering various questions involving nonnegative tensor approximations. In particular, we apply it to show that the best nonnegative rank-1 approximation of a positive tensor is always unique and that a best nonnegative rank-r approximation of a positive tensor can almost never be obtained by deflation.
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Dates et versions

hal-01015519 , version 1 (26-06-2014)
hal-01015519 , version 2 (17-07-2014)
hal-01015519 , version 3 (29-10-2014)
hal-01015519 , version 4 (10-02-2015)
hal-01015519 , version 5 (12-04-2016)

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  • HAL Id : hal-01015519 , version 3

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Yang Qi, Pierre Comon, Lek-Heng Lim. Uniqueness of Nonnegative Tensor Approximations. 2014. ⟨hal-01015519v3⟩
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