Higher-order singular value decomposition: Difference between revisions

Revision as of 03:28, 19 June 2025

Revision as of 03:29, 19 June 2025

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[[Lieven De Lathauwer |De Lathauwer]] ''et al.''<ref name=":2">{{Cite journal|last1=De Lathauwer|first1=L.|last2=De Moor|first2=B.|last3=Vandewalle|first3=J.|date=2000-01-01|title=On the Best Rank-1 and Rank-(R1 ,R2 ,. . .,RN) Approximation of Higher-Order Tensors|journal=SIAM Journal on Matrix Analysis and Applications|volume=21|issue=4|pages=1324–1342|doi=10.1137/S0895479898346995|issn=0895-4798|citeseerx=10.1.1.102.9135}}</ref><ref name="DeLathauwerSVD">{{Cite journal|last1=De Lathauwer|first1=L.|last2=De Moor|first2=B.|last3=Vandewalle|first3=J.|date=2000-01-01|title=A Multilinear Singular Value Decomposition|journal=SIAM Journal on Matrix Analysis and Applications|volume=21|issue=4|pages=1253–1278|doi=10.1137/s0895479896305696|issn=0895-4798|citeseerx=10.1.1.102.9135}}</ref> introduced clarity to Tucker's concepts with two highly influential papers, while [[Vasilescu]] and [[Demetri Terzopoulos| Terzopoulos]] introduced algorithmic clarity. They synthesized those ideas into an elegant two-step algorithm, one whose simplicity belies the complexity it resolves.<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> Vasilescu and Terzopoulos introduced the '''M-mode SVD''' which is currently referred in the literature as the '''Tucker''' or the '''HOSVD'''. However, the Tucker/Kroonenberg algorithm, and De Lathauwer ''et al.'' algorithmsalgorithm are sequential, relying on iterative methods such as gradient descent or the power method, respectively. In contrast, the M-mode SVD is a closed-form solution that can be computed sequentially, but is also well-suited for parallel computation.

: 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, and recognizing the respective contributions of different research efforts.