In statistics and signal processing, the method of empirical orthogonal function (EOF) analysis is a decomposition of a signal or data set in terms of orthogonal basis functions which are determined from the data.
The term is also interchangeable with the geographically weighted Principal components analysis in geophysics.
That is, the basis functions are chosen to be different from each other, and to account for as much variance as possible.
The basis functions are typically found by computing the eigenvectors of the covariance matrix of the data set.
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).