Generic uniqueness conditions for the canonical polyadic decomposition and INDSCAL
Algebraic Geometry
2016-07-20 v2
Abstract
We find conditions that guarantee that a decomposition of a generic third-order tensor in a minimal number of rank- tensors (canonical polyadic decomposition (CPD)) is unique up to permutation of rank- tensors. Then we consider the case when the tensor and all its rank- terms have symmetric frontal slices (INDSCAL). Our results complement the existing bounds for generic uniqueness of the CPD and relax the existing bounds for INDSCAL. The derivation makes use of algebraic geometry. We stress the power of the underlying concepts for proving generic properties in mathematical engineering.
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Cite
@article{arxiv.1405.6238,
title = {Generic uniqueness conditions for the canonical polyadic decomposition and INDSCAL},
author = {Ignat Domanov and Lieven De Lathauwer},
journal= {arXiv preprint arXiv:1405.6238},
year = {2016}
}
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23 pages