Canonical polyadic decomposition with a columnwise orthonormal factor matrix

Mikael Sørensen, Lieven De Lathauwer, Pierre Comon, Sylvie Icart, Luc Deneire


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 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.

Code description

This package provides experiment files and auxiliary files for the CPDO paper.


M. Sørensen, L. De Lathauwer, P. Comon, S. Icart, L. Deneire, "Canonical polyadic decomposition with a columnwise orthonormal factor matrix," SIAM Journal on Matrix Analysis and Applications, Vol. 33, No. 4, pp. 1190-1213, Jan. 2012.

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This repository can be cited as:
S. Hendrikx, M. Boussé, N. Vervliet, M. Vandecappelle, R. Kenis, and L. De Lathauwer, Tensorlab⁺, Available online, Version of Dec 2022 downloaded from