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Journal articles
Canonical Polyadic decomposition with a Columnwise Orthonormal Factor Matrix
Abstract : 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 column-wise 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 column-wise orthonormal. Third, we derive numerical algorithms for the computation of the constrained CPD. In particular, orthogonality-constrained versions of the CPD methods based on simultaneous matrix diagonalization and alternating least squares are presented. Numerical experiments are reported.
Cited literature [36 references]
https://hal.archives-ouvertes.fr/hal-00781143
Contributor : Pierre Comon <>
Submitted on : Friday, January 25, 2013 - 2:18:07 PM
Last modification on : Wednesday, May 13, 2020 - 4:30:05 PM
Document(s) archivé(s) le : Friday, April 26, 2013 - 3:56:52 AM
Contributor : Pierre Comon <>
Submitted on : Friday, January 25, 2013 - 2:18:07 PM
Last modification on : Wednesday, May 13, 2020 - 4:30:05 PM
Document(s) archivé(s) le : Friday, April 26, 2013 - 3:56:52 AM
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SoreDCID2012simax_v2.pdf
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