Singular value decomposition: Difference between revisions

Revision as of 07:10, 11 January 2025

Revision as of 08:14, 19 January 2025

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{{Short description|Matrix decomposition}}

{{Use dmy dates|date=October 2020}}

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[[File:Singular-Value-Decomposition.svg|thumb|Illustration of the singular value decomposition {{math|'''UΣV'''^⁎}} of a real {{math|2 × 2}} matrix {{math|'''M'''}}.{{ubli

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Interestingly, SVD has been used to improve gravitational waveform modeling by the ground-based gravitational-wave interferometer aLIGO.<ref>{{cite journal | last1 = Setyawati | first1 = Y. | last2 = Ohme | first2 = F. | last3 = Khan | first3 = S. | year = 2019| title = Enhancing gravitational waveform model through dynamic calibration | journal = Physical Review D | volume = 99| issue =2 | pages = 024010| doi=10.1103/PhysRevD.99.024010| bibcode = 2019PhRvD..99b4010S | arxiv = 1810.07060 | s2cid = 118935941 }}</ref> SVD can help to increase the accuracy and speed of waveform generation to support gravitational-waves searches and update two different waveform models.

Singular value decomposition is used in [[recommender systems]] to predict people's item ratings.<ref>{{cite journalreport |last1=Sarwar |first1=Badrul |last2=Karypis |first2=George |last3=Konstan |first3=Joseph A. |author3-link=Joseph A. Konstan |last4=Riedl |first4=John T. |author4-link=John T. Riedl |name-list-style=amp |year=2000 |title=Application of Dimensionality Reduction in Recommender System – A Case Study |url=https://apps.dtic.mil/sti/citations/tr/ADA439541 |journal= |publisher=[[University of Minnesota]]}}{{void|commenthdl=11299/215429|Fabrickator|alternatetype=Technical link:report https://conservancy.umn.edu/bitstream/handle/11299/215429/00-043.pdf}}</ref> Distributed algorithms have been developed for the purpose of calculating the SVD on clusters of commodity machines.<ref>{{cite journalarxiv |last1=Bosagh Zadeh |first1=Reza |last2=Carlsson |first2=Gunnar |title=Dimension Independent Matrix Square Using MapReduce |url=https://stanford.edu/~rezab/papers/dimsum.pdf|bibcode=2013arXiv1304.1467B |year=2013 |arxiv=1304.1467}}</ref>

Low-rank SVD has been applied for hotspot detection from spatiotemporal data with application to disease [[outbreak]] detection.<ref>{{Cite journal