%0 Journal Article %1 354398 %A Lathauwer, Lieven De %A Moor, Bart De %A Vandewalle, Joos %C Philadelphia, PA, USA %D 2000 %I Society for Industrial and Applied Mathematics %J SIAM J. Matrix Anal. Appl. %K hosvd svd %N 4 %P 1253--1278 %R http://dx.doi.org/10.1137/S0895479896305696 %T A Multilinear Singular Value Decomposition %U http://portal.acm.org/citation.cfm?id=354398 %V 21 %X We discuss a multilinear generalization of the singular value decomposition. There is a strong analogy between several properties of the matrix and the higher-order tensor decomposition; uniqueness, link with the matrix eigenvalue decomposition, first-order perturbation effects, etc., are analyzed. We investigate how tensor symmetries affect the decomposition and propose a multilinear generalization of the symmetric eigenvalue decomposition for pair-wise symmetric tensors.

@article{354398, abstract = {We discuss a multilinear generalization of the singular value decomposition. There is a strong analogy between several properties of the matrix and the higher-order tensor decomposition; uniqueness, link with the matrix eigenvalue decomposition, first-order perturbation effects, etc., are analyzed. We investigate how tensor symmetries affect the decomposition and propose a multilinear generalization of the symmetric eigenvalue decomposition for pair-wise symmetric tensors.}, added-at = {2009-03-05T13:36:07.000+0100}, address = {Philadelphia, PA, USA}, author = {Lathauwer, Lieven De and Moor, Bart De and Vandewalle, Joos}, biburl = {https://www.bibsonomy.org/bibtex/2eff602c4bab6277525a861ffaf7ae297/folke}, description = {A Multilinear Singular Value Decomposition}, doi = {http://dx.doi.org/10.1137/S0895479896305696}, interhash = {345c21b8420f7d9f83db12f440211715}, intrahash = {eff602c4bab6277525a861ffaf7ae297}, issn = {0895-4798}, journal = {SIAM J. Matrix Anal. Appl.}, keywords = {hosvd svd}, number = 4, pages = {1253--1278}, publisher = {Society for Industrial and Applied Mathematics}, timestamp = {2009-03-05T13:36:07.000+0100}, title = {A Multilinear Singular Value Decomposition}, url = {http://portal.acm.org/citation.cfm?id=354398}, volume = 21, year = 2000 }