https://en.formulasearchengine.com/w/api.php?action=feedcontributions&feedformat=atom&user=79.243.0.0%2F16formulasearchengine - User contributions [en]2026-09-17T19:32:07ZUser contributionsMediaWiki 1.47.0-wmf.7https://en.formulasearchengine.com/w/index.php?title=Vanadium_pentafluoride&diff=26853Vanadium pentafluoride2013-10-28T22:47:35Z<p>79.243.245.51: a bit more detailed</p>
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<div>{{refimprove|date=July 2011}}<br />
'''Regularized canonical correlation analysis''' is a way of using [[ridge regression]] to solve the [[singularity theory|singularity]] problem in the [[cross-covariance matrix|cross-covariance matrices]] of [[canonical correlation analysis]]. By converting <math>\operatorname{cov}(X, X)</math> and <math>\operatorname{cov}(Y, Y)</math> into <math>\operatorname{cov}(X, X) + \lambda I_X</math> and <math>\operatorname{cov}(Y, Y) + \lambda I_Y</math>, it ensures that the above matrices will have reliable [[Matrix inverse|inverses]].<br />
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The idea probably dates back to [[Hrishikesh D. Vinod]]'s publication in 1976 where he called it "Canonical ridge".<ref>{{Cite journal <br />
| author = Hrishikesh D. Vinod <br />
| title = Canonical ridge and econometrics of joint production<br />
| journal = [[Journal of Econometrics]]<br />
| volume = 4<br />
| issue = 2<br />
| month = May<br />
| pages = 147–166<br />
| doi = 10.1016/0304-4076(76)90010-5<br />
}}</ref><ref>{{Cite book<br />
| author = [[Kanti Mardia]] et al.<br />
| title = Multivariate Analysis<br />
}}</ref><br />
It has been suggested for use in the analysis of [[functional neuroimaging]] data as such data are often singular.<ref>{{Cite journal<br />
| author = Finn Årup Nielsen, Lars Kai Hansen, Stephen C. Strother<br />
| title = Canonical ridge analysis with ridge parameter optimization<br />
| year = 1998<br />
| journal = [[NeuroImage]]<br />
| volume = 7<br />
| pages = S758<br />
| month = May<br />
| url = http://www2.imm.dtu.dk/pubdb/views/edoc_download.php/4981/pdf/imm4981.pdf<br />
}}</ref><br />
It is possible to compute the regularized canonical vectors in the lower-dimensional space.<ref>{{Cite thesis<br />
| author = Finn Årup Nielsen<br />
| year = 2001<br />
| title = Neuroinformatics in Functional Neuroimaging <br />
| url = http://www2.imm.dtu.dk/pubdb/views/edoc_download.php/201/pdf/imm201.pdf<br />
| publisher = [[Technical University of Denmark]]<br />
}} Section 3.18.5</ref><br />
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== References ==<br />
{{Reflist}}<br />
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* {{cite journal| last1=Leurgans| first1=S.E.| last2=Moyeed| first2=R.A.| last3=Silverman| first3=B.W.| title=Canonical correlation analysis when the data are curves| journal=Journal of the Royal Statistical Society| series=Series B (Methodological)| year=1993| volume=55| number=3| pages=725–740| jstor=2345883}}<br />
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[[Category:Mathematical analysis]]<br />
[[Category:Calculus of variations]]</div>79.243.245.51