Higher-order singular value decomposition: Difference between revisions

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The algorithm widely referred to in the literature as the Tucker or Higher-Order Singular Value Decomposition (HOSVD) was developed by Vasilescu and Terzopoulos, who introduced it under the name M-mode SVD,<ref name=":Vasilescu2002">M. A. O. Vasilescu, D. Terzopoulos (2002), "Multilinear Analysis of Image Ensembles: TensorFaces," Proc. 7th European Conference on Computer Vision (ECCV'02), Copenhagen, Denmark. {{Webarchive|url=https://web.archive.org/web/20221229090931/http://www.cs.toronto.edu/~maov/tensorfaces/Springer%20ECCV%202002_files/eccv02proceeding_23500447.pdf |date=2022-12-29}}</ref><ref name="Vasilescu2003">M. A. O. Vasilescu, D. Terzopoulos (2003), "Multilinear Subspace Analysis of Image Ensembles," Proc. IEEE Conf. on Computer Vision and Pattern Recognition (CVPR’03), Madison, WI.</ref><ref name=":Vasilescu2005">M. A. O. Vasilescu, D. Terzopoulos (2005), "Multilinear Independent Component Analysis," Proc. IEEE Conf. on Computer Vision and Pattern Recognition (CVPR’05), San Diego, CA.</ref> but frequently misattributed to either [[L. R. Tucker]] or [[Lieven De Lathauwer]]. While the term HOSVD was coined by De Lathauwer, it is the M-mode SVD introduced by Vasilescu that is most often—and incorrectly—referred to under that name.

The M-mode SVD is ana simple and elegant algorithm suitable for parallel computation. thatThe appliesTucker and the matrixHOSVD SVD to compute orthonormal mode matrices, in contrast to theare sequential algorithms proposed by Tucker that employsemploy gradient descent, and De Lathauwer etal's algorithms that employsor the power method, respectively. Vasilescu's parallel formulation is computationally distinct from earlier approaches.

: This misattribution has had lasting impact on the scholarly record, obscuring the original source of a widely adopted algorithm, and complicating efforts to trace its development, reproduce results, or properly credit foundational contributions in multilinear algebra and tensor methods.