Empirical orthogonal functions: Difference between revisions

Revision as of 17:19, 7 July 2006

Revision as of 16:17, 5 April 2008

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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 [[frequency|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 the [[covariance matrix]] of the data set. A more advanced technique is to form a [[kernel (matrix)]] out of the data, using a fixed [[kernel (mathematics)|kernel]]. The basis functions from the eigenvectors of the kernel matrix are thus non-linear in the ___location of the data (see [[Mercer's theorem]] and the [[kernel trick]] for more information).

==See also==

*[[Blind signal separation]]

*[[Nonlinear dimensionality reduction]]

*[[Principal components analysis]]

*[[Source separation]]

*[[Transform coding]]