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The ''i'' <sup>th</sup> basis function is chosen to be orthogonal to the basis functions from the first through ''i'' − 1, and to minimize the residual [[variance]]. That is, the basis functions are chosen to be different from each other, and to account for as much variance as possible.
The method of EOF analysis is similar in spirit to [[harmonic analysis]], but harmonic analysis typically uses predetermined orthogonal functions, for example, sine and cosine functions at fixed [[frequency|frequencies]]. In some cases the two methods may yield essentially the same results.
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* David B. Stephenson and Rasmus E. Benestad. [http://www.gfi.uib.no/~nilsg/kurs/notes/ "Environmental statistics for climate researchers"]. ''(See: [http://www.gfi.uib.no/~nilsg/kurs/notes/node87.html "Empirical Orthogonal Function analysis"])''
* Christopher K. Wikle and Noel Cressie. "[https://dx.doi.org/10.1093/biomet/86.4.815 A dimension reduced approach to space-time Kalman filtering]", ''[[Biometrika]]'' 86:815-829, 1999.
* Donald W. Denbo and John S. Allen. [http://journals.ametsoc.org/doi/pdf/10.1175/1520-0485(1984)014%3C0035%3AREOFAO%3E2.0.CO%3B2 "Rotary Empirical Orthogonal Function Analysis of Currents near the Oregon Coast"], "J. Phys. Oceanogr.", 14,
* David M. Kaplan [https://web.archive.org/web/20200701033210/https://websites.pmc.ucsc.edu/~dmk/notes/EOFs/EOFs.html] "Notes on EOF Analysis"
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