Canonical Polyadic Decomposition with a Columnwise Orthonormal Factor Matrix

  title={Canonical Polyadic Decomposition with a Columnwise Orthonormal Factor Matrix},
  author={Mikael S{\o}rensen and Lieven De Lathauwer and Pierre Comon and Sylvie Icart and Luc Deneire},
  journal={SIAM J. Matrix Anal. Appl.},
Canonical polyadic decomposition (CPD) of a higher-order tensor is an important tool in mathematical engineering. In many applications at least one of the matrix factors is constrained to be columnwise orthonormal. We first derive a relaxed condition that guarantees uniqueness of the CPD under this constraint. Second, we give a simple proof of the existence of the optimal low-rank approximation of a tensor in the case that a factor matrix is columnwise orthonormal. Third, we derive numerical… 

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