Gidon Eshel
- Published in print:
- 2011
- Published Online:
- October 2017
- ISBN:
- 9780691128917
- eISBN:
- 9781400840632
- Item type:
- chapter
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691128917.003.0011
- Subject:
- Environmental Science, Environmental Studies
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 ...
More
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.Less
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.
Gidon Eshel
- Published in print:
- 2011
- Published Online:
- October 2017
- ISBN:
- 9780691128917
- eISBN:
- 9781400840632
- Item type:
- book
- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691128917.001.0001
- Subject:
- Environmental Science, Environmental Studies
A severe thunderstorm morphs into a tornado that cuts a swath of destruction through Oklahoma. How do we study the storm’s mutation into a deadly twister? Avian flu cases are reported in China. How ...
More
A severe thunderstorm morphs into a tornado that cuts a swath of destruction through Oklahoma. How do we study the storm’s mutation into a deadly twister? Avian flu cases are reported in China. How do we characterize the spread of the flu, potentially preventing an epidemic? The way to answer important questions like these is to analyze the spatial and temporal characteristics—origin, rates, and frequencies—of these phenomena. This book introduces advanced undergraduate students, graduate students, and researchers to the statistical and algebraic methods used to analyze spatiotemporal data in a range of fields, including climate science, geophysics, ecology, astrophysics, and medicine. The book begins with a concise yet detailed primer on linear algebra, providing readers with the mathematical foundations needed for data analysis. It then fully explains the theory and methods for analyzing spatiotemporal data, guiding readers from the basics to the most advanced applications. This self-contained, practical guide to the analysis of multidimensional data sets features a wealth of real-world examples as well as sample homework exercises and suggested exams.Less
A severe thunderstorm morphs into a tornado that cuts a swath of destruction through Oklahoma. How do we study the storm’s mutation into a deadly twister? Avian flu cases are reported in China. How do we characterize the spread of the flu, potentially preventing an epidemic? The way to answer important questions like these is to analyze the spatial and temporal characteristics—origin, rates, and frequencies—of these phenomena. This book introduces advanced undergraduate students, graduate students, and researchers to the statistical and algebraic methods used to analyze spatiotemporal data in a range of fields, including climate science, geophysics, ecology, astrophysics, and medicine. The book begins with a concise yet detailed primer on linear algebra, providing readers with the mathematical foundations needed for data analysis. It then fully explains the theory and methods for analyzing spatiotemporal data, guiding readers from the basics to the most advanced applications. This self-contained, practical guide to the analysis of multidimensional data sets features a wealth of real-world examples as well as sample homework exercises and suggested exams.
Edward Vul and Nancy Kanwisher
- Published in print:
- 2010
- Published Online:
- August 2013
- ISBN:
- 9780262014021
- eISBN:
- 9780262265850
- Item type:
- chapter
- Publisher:
- The MIT Press
- DOI:
- 10.7551/mitpress/9780262014021.003.0007
- Subject:
- Psychology, Neuropsychology
This chapter focuses on the prevalence of the nonindependence error in functional magnetic resonance imaging (fMRI) data analysis, and presents a detailed description of the nonindependence error ...
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This chapter focuses on the prevalence of the nonindependence error in functional magnetic resonance imaging (fMRI) data analysis, and presents a detailed description of the nonindependence error along with information on plotting its graph. It provides various examples of this error in fMRI, including plotting the signal change in voxels selected for signal change and statistical tests performed on nonindependent data, and also presents a few heuristics for avoiding the error. Finally, the chapter looks into the various reasons for the prevalence of the nonindependence error in fMRI, including the multidimensional, qualitative, and complicated nature of fMRI data.Less
This chapter focuses on the prevalence of the nonindependence error in functional magnetic resonance imaging (fMRI) data analysis, and presents a detailed description of the nonindependence error along with information on plotting its graph. It provides various examples of this error in fMRI, including plotting the signal change in voxels selected for signal change and statistical tests performed on nonindependent data, and also presents a few heuristics for avoiding the error. Finally, the chapter looks into the various reasons for the prevalence of the nonindependence error in fMRI, including the multidimensional, qualitative, and complicated nature of fMRI data.
