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 a simple and elegant algorithm suitable for parallel computation. The Tucker and the HOSVD are sequential algorithms that employ gradient descent or the power method, respectively. Vasilescu'sThe M-mode SVD 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.