Talk:Higher-order singular value decomposition

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Request for cleanup

Latest comment: 6 years ago1 comment1 person in discussion

It would be nice if someone could rewrite this article without relying on arbitrary bases, the mathematical equivalent of writing in crayon.

Answer: Mathematically, there is hardly anything to tell. If A is a tensor living in a tensor product of vector spaces, then there exists a coordinate representation ("core tensor") w.r.t. orthonormal bases such that it satisfies "all-orthogonality" and some notion of singular values are in descending order; see De Lathauwer, De Moor and Vandewalle's paper. The interesting part is figuring out these bases if someone hands the tensor to you as a coordinate array or as operator. — Preceding unsigned comment added by Ntheazk (talk • contribs) 18:58, 12 August 2019 (UTC)Reply

M-mode SVD versus HOSVD

Latest comment: 1 month ago2 comments2 people in discussion

It is claimed in the article that De Lathauwer, De Moor, and Vandewalle do not explain how the HOSVD is to be computed, or that they only discuss iterative algorithms. This claim is false. The "M-mode SVD" algorithm is described on page 1264 of their 2000 SIAM Journal on Matrix Analysis and Applications article. The authors also correctly point out at the very end of the highlighted section that the presented computation method is mathematically equivalent to the method presented in 1966 by L. R. Tucker. The latter presented the method using an eigendecomposition of the Gram matrix. He did not use the SVD, presumably because the software at the time did not yet implement the reliable Golub-Kahan method, which was introduced only in 1965. In conclusion, the algorithm for computing what is now usually called the HOSVD was proposed essentially by Tucker in 1966, with an improvement for numerical accuracy proposed by De Lathauwer, De Moor, and Vandewalle in their HOSVD (among other contributions).

 

Ntheazk (talk) 09:14, 20 July 2025 (UTC)Reply

I don't know much about this topic, but it seems that you have a citation to a reliable source, to support your claims. It would be great, if you would edit the article accordingly. Mgnbar (talk) 17:38, 22 July 2025 (UTC)Reply