Empirical orthogonal functions: Difference between revisions

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In [[statistics]] and [[signal processing]], the method of '''empirical orthogonal function (EOF)''' analysis is a decomposition of a [[signal processing|signal]] or data set in terms of [[orthogonal]] [[basis function]]s which are determined from the data. It is the same as performing a [[principal components analysis]] on the data, except that the EOF method finds both [[time series]] and [[spatial]] patterns. The term is also interchangeable with the geographically weighted [[Principal components analysis|PCAs]] in [[geophysics]] .<ref name=eofa>{{cite web
| last = Stephenson
| first = David
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| doi =
| accessdate = 20 September 2008
}}</ref>.
 
The ''i''th basis function is chosen to be orthogonal to the basis functions from the first through ''i'' &minus; 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.