Empirical orthogonal functions

Empirical orthogonal functions

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. 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 interchangeble with the geographically weighted PCAs in geophysics 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 of kriging in geostatistics and Gaussian 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 eigenvectors 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. 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).

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.

Wikimedia Foundation. 2010.

Look at other dictionaries:

  • Principal component analysis — PCA of a multivariate Gaussian distribution centered at (1,3) with a standard deviation of 3 in roughly the (0.878, 0.478) direction and of 1 in the orthogonal direction. The vectors shown are the eigenvectors of the covariance matrix scaled by… …   Wikipedia

  • Principal components analysis — Principal component analysis (PCA) is a vector space transform often used to reduce multidimensional data sets to lower dimensions for analysis. Depending on the field of application, it is also named the discrete Karhunen Loève transform (KLT),… …   Wikipedia

  • List of statistics topics — Please add any Wikipedia articles related to statistics that are not already on this list.The Related changes link in the margin of this page (below search) leads to a list of the most recent changes to the articles listed below. To see the most… …   Wikipedia

  • List of mathematics articles (E) — NOTOC E E₇ E (mathematical constant) E function E₈ lattice E₈ manifold E∞ operad E7½ E8 investigation tool Earley parser Early stopping Earnshaw s theorem Earth mover s distance East Journal on Approximations Eastern Arabic numerals Easton s… …   Wikipedia

  • Singular value decomposition — Visualization of the SVD of a 2 dimensional, real shearing matrix M. First, we see the unit disc in blue together with the two canonical unit vectors. We then see the action of M, which distorts the disk to an ellipse. The SVD decomposes M into… …   Wikipedia

  • List of harmonic analysis topics — This is a list of harmonic analysis topics, by Wikipedia page. See also list of Fourier analysis topics and list of Fourier related transforms, which are more directed towards the classical Fourier series and Fourier transform of mathematical… …   Wikipedia

  • Varimax rotation — is a change of coordinates used in principal component analysis that maximizes the sum of the variance of the loading vectors. That is, it seeks a basis such that most economically represents each individual that each individual can be well… …   Wikipedia

  • NCAR Command Language — The NCAR Command Language (NCL) is a free interpreted language designed by the National Center for Atmospheric Research for scientific visualization and data processing. NCL has robust file input and output. It can read in netCDF, HDF4, HDF4 EOS …   Wikipedia

  • Singular Spectrum Analysis — The Singular Spectrum Analysis (SSA) techniqueis a powerful technique of time series analysisincorporating the elements of classical time series analysis,multivariate statistics, multivariate geometry, dynamical systemsand signal processing. The… …   Wikipedia

  • EOF — may refer to:* End of file, the computing term for the end of file character or signal * Empirical orthogonal functions, a statistical technique for simplifying a dataset * Enterprise Objects Framework, a product from Apple Computer * End of… …   Wikipedia