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Spatiotemporal Data Analysis$
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Gidon Eshel

Print publication date: 2011

Print ISBN-13: 9780691128917

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691128917.001.0001

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Empirical Orthogonal Functions

Empirical Orthogonal Functions

Chapter:
(p.200) Eleven Empirical Orthogonal Functions
Source:
Spatiotemporal Data Analysis
Author(s):

Gidon Eshel

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691128917.003.0011

This chapter focuses on empirical orthogonal functions (EOFs). One of the most useful and common eigen-techniques in data analysis is the construction of EOFs. EOFs are a transform of the data; the original set of numbers is transformed into a different set with some desirable properties. In this sense the EOF transform is similar to other transforms, such as the Fourier or Laplace transforms. In all these cases, we project the original data onto a set of functions, thus replacing the original data with the set of projection coefficients on the chosen new set of basis vectors. However, the choice of the specific basis set varies from case to case. The discussions cover data matrix structure convention, reshaping multidimensional data sets for EOF analysis, forming anomalies and removing time mean, missing values, choosing and interpreting the covariability matrix, calculating the EOFs, projection time series, and extended EOF analysis.

Keywords:   data analysis, empirical orthogonal functions, EOF, eigen-techniques, matrix structure, multidimensional data sets, covariability matrix, time series

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