Higher-order singular value decomposition: Difference between revisions

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It is also used in [[tensor product model transformation]]-based controller design.<ref name="Baranyi042">{{cite journal|author=P. Baranyi|date=April 2004|title=TP model transformation as a way to LMI based controller design|journal=IEEE Transactions on Industrial Electronics|volume=51|pages=387&ndash;400|doi=10.1109/tie.2003.822037|number=2|s2cid=7957799}}</ref><ref name="compind2">{{cite journal|author1=P. Baranyi|author2=D. Tikk|author3=Y. Yam|author4=R. J. Patton|year=2003|title=From Differential Equations to PDC Controller Design via Numerical Transformation|journal=Computers in Industry|volume=51|issue=3|pages=281&ndash;297|doi=10.1016/s0166-3615(03)00058-7}}</ref>

The concept of M-mode SVD (HOSVD) was carried over to functions by Baranyi and Yam via the [[TP model transformation]].<ref name="Baranyi042" /><ref name="compind2" /> This extension led to the definition of the HOSVDM-basedmode SVD/HOSVD canonical form of tensor product functions and Linear Parameter Varying system models<ref name="canon12">{{cite conference|title=Definition of the HOSVD-based canonical form of polytopic dynamic models|author1=P. Baranyi|author2=L. Szeidl|author3=P. Várlaki|author4=Y. Yam|date=July 3–5, 2006|___location=Budapest, Hungary|pages=660–665|conference=3rd International Conference on Mechatronics (ICM 2006)}}</ref> and to convex hull manipulation based control optimization theory, see [[TP model transformation in control theories]].

M-mode SVD (HOSVD) was proposed to be applied to multi-view data analysis in an unsupervised manner<ref>{{Cite journal|author1=Y-h. Taguchi|date=August 2017|title=Tensor decomposition-based unsupervised feature extraction applied to matrix products for multi-view data processing|journal=PLOS ONE|volume=12|issue=8|pages=e0183933|doi=10.1371/journal.pone.0183933|pmc=5571984|pmid=28841719|bibcode=2017PLoSO..1283933T|doi-access=free}}</ref> and was successfully applied to in silico drug discovery from gene expression.<ref>{{Cite journal|author1=Y-h. Taguchi|date=October 2017|title=Identification of candidate drugs using tensor-decomposition-based unsupervised feature extraction in integrated analysis of gene expression between diseases and DrugMatrix datasets|journal=Scientific Reports|volume=7|issue=1|pages=13733|doi=10.1038/s41598-017-13003-0|pmc=5653784|pmid=29062063|bibcode=2017NatSR...713733T}}</ref>