On the Uniqueness of the Canonical Polyadic Decomposition of Third-Order Tensors - Part I: Basic Results and Uniqueness of One Factor Matrix

@article{Domanov2013OnTU,
  title={On the Uniqueness of the Canonical Polyadic Decomposition of Third-Order Tensors - Part I: Basic Results and Uniqueness of One Factor Matrix},
  author={I. Domanov and L. Lathauwer},
  journal={SIAM J. Matrix Anal. Appl.},
  year={2013},
  volume={34},
  pages={855-875}
}
Canonical polyadic decomposition (CPD) of a higher-order tensor is decomposition into a minimal number of rank-$1$ tensors. We give an overview of existing results concerning uniqueness. We present new, relaxed, conditions that guarantee uniqueness of one factor matrix. These conditions involve Khatri--Rao products of compound matrices. We make links with existing results involving ranks and k-ranks of factor matrices. We give a shorter proof, based on properties of second compound matrices, of… Expand
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