Higher-order singular value decomposition: Difference between revisions

Revision as of 03:39, 20 June 2025

Revision as of 20:50, 24 June 2025

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|book-title=Proc. IEEE Conf. on Computer Vision and Pattern Recognition (CVPR’05)

|___location=San Diego, CA

|year=2005}}</ref> introduced algorithmic clarity. Vasilescu and Terzopoulos<ref name=":Vasilescu2002"/><ref name=":Vasilescu2005"/>

introduced the '''M-mode SVD''', which is the classic algorithm that is currently referred in the literature as the '''Tucker''' or the '''HOSVD'''. However, the '''Tucker'''s algorithm, and De Lathauwer ''et al.'' companion algorithm<ref name=":2"/> are sequential, relying on iterative methods such as gradient descent or the power method, respectively. Vasilescu and Terzopoulos synthesized a set of ideas into an elegant two-step algorithm that can be executed sequentially or in parallel, whose simplicity belies the complexity it resolves. The term '''M-mode SVD''' accurately reflects the algorithm employed without overpromising. It captures the actual computation, a set of SVDs on mode-flattenings without making assumptions about the structure of the core tensor or implying a rank decomposition.

: 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.