Higher-order singular value decomposition: Difference between revisions

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: 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.

Vasilescu and Terzopoulos developed an elegant two-step algorithm that computes orthonormal subspaces in closed form, and may be executed sequentiallyiteratively or in parallel, whose simplicity belies the complexity it resolves. The term '''M-mode SVD''' accurately reflects the algorithm employed. 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.

Robust and L1-norm-based variants of this decomposition framework have since been proposed.<ref name="robustHOSVD">{{Cite journal|last1=Godfarb|first1=Donald|last2=Zhiwei|first2=Qin|title=Robust low-rank tensor recovery: Models and algorithms|journal=SIAM Journal on Matrix Analysis and Applications|volume=35|number=1|pages=225–253|date=2014|doi=10.1137/130905010|arxiv=1311.6182|s2cid=1051205}}</ref><ref name="l1tucker">{{cite journal|last1=Chachlakis|first1=Dimitris G.|last2=Prater-Bennette|first2=Ashley|last3=Markopoulos|first3=Panos P.|title=L1-norm Tucker Tensor Decomposition|journal=IEEE Access|date=22 November 2019|volume=7|pages=178454–178465|doi=10.1109/ACCESS.2019.2955134|doi-access=free|arxiv=1904.06455|bibcode=2019IEEEA...7q8454C}}</ref><ref name="l1tucker3">{{cite journal|last1=Markopoulos|first1=Panos P.|last2=Chachlakis|first2=Dimitris G.|last3=Papalexakis|first3=Evangelos|title=The Exact Solution to Rank-1 L1-Norm TUCKER2 Decomposition|journal=IEEE Signal Processing Letters|volume=25|issue=4|date=April 2018|pages=511–515|doi=10.1109/LSP.2018.2790901|arxiv=1710.11306|bibcode=2018ISPL...25..511M|s2cid=3693326}}</ref><ref name="l1tucker2">{{cite book|last1=Markopoulos|first1=Panos P.|last2=Chachlakis|first2=Dimitris G.|last3=Prater-Bennette|first3=Ashley|title=2018 IEEE Global Conference on Signal and Information Processing (GlobalSIP) |chapter=L1-Norm Higher-Order Singular-Value Decomposition |date=21 February 2019|pages=1353–1357|doi=10.1109/GlobalSIP.2018.8646385|isbn=978-1-7281-1295-4|s2cid=67874182}}</ref>