- Empirical orthogonal functions
In

statistics andsignal processing , the method of**empirical orthogonal function (EOF)**analysis is a decomposition of a signal or data set in terms oforthogonal basis function s which are determined from the data. It is the same as performing aprincipal components analysis on the data, except that the EOF method finds bothtime series andspatial patterns. The term is also interchangeble with the geographically weighted PCAs ingeophysics cite web

last = Stephenson

first = David

authorlink =

coauthors =

title = Empirical Orthogonal Function analysis

work =

publisher =

date =

url = http://www.uib.no/people/ngbnk/kurs/notes/node87.html

format =

doi =

accessdate = 20 September

accessyear = 2008 ] .The "i"th 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.Thus this method has much in common with the method ofkriging ingeostatistics andGaussian process models.The method of EOF is similar in spirit to

harmonic analysis , but harmonic analysis typically uses predetermined orthogonal functions, for example, sine and cosine functions at fixed frequencies. In some cases the two methods may yield essentially the same results.The basis functions are typically found by computing the

eigenvector s of thecovariance matrix of the data set. A more advanced technique is to form akernel (matrix) out of the data, using a fixed kernel. The basis functions from the eigenvectors of the kernel matrix are thus non-linear in the location of the data (seeMercer's theorem and thekernel trick for more information).**ee also***

Blind signal separation

*Nonlinear dimensionality reduction

*Orthogonal matrix

*Source separation

*Transform coding

*Varimax rotation **References & Notes*** Bjornsson Halldor and Silvia A. Venegas [

*http://www.vedur.is/~halldor/TEXT/eofsvd.html "A manual for EOF and SVD analyses of climate data"*] , McGill University, CCGCR Report No. 97-1, Montréal, Québec, 52pp., 1997.* 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. "citeseer|A dimension reduced approach to space-time Kalman filtering|wikle99dimensionreduction", "

Biometrika " 86:815-829, 1999.

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2010.*

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