How to Compute the EOFs by SVD?

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In summary, the conversation discusses how to compute Empirical Orthogonal Functions (EOFs) using Singular Value Decomposition (SVD). The matrix ##\mathbf{A}## is expressed as ##\mathbf{U} \mathbf{\Sigma} \mathbf{V}^{T}## according to SVD, with the EOFs being the columns of ##\mathbf{V}^{T}##. The link provided by the speaker serves as a reference for understanding the concept further.
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ecastro
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Considering I have a matrix ##\mathbf{A}## which has a size of ##M \times N##, how can I compute the Empirical Orthogonal Functions (EOFs) by Singular Value Decomposition (SVD)?

According to SVD, the matrix ##\mathbf{A}## is

##\mathbf{A} = \mathbf{U} \mathbf{\Sigma} \mathbf{V}^{T}##

where a superscript of ##T## denotes a transpose. Now, which are the EOFs in this equation, are they the rows of ##\mathbf{V}^{T}## or its columns (the rows of ##\mathbf{V}##)?

Thank you in advance.
 
  • #3
Hi there. The EOFs are the columns of V^T.

This site helps me to figure this out https://pmc.ucsc.edu/~dmk/notes/EOFs/EOFs.html. Goodnight from your atemporal interested in orthostatics guy.

Mod note: deleted broken link
 
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1. What is an EOF and why is it important in scientific analysis?

An EOF, or Empirical Orthogonal Function, is a mathematical technique used in data analysis to identify the dominant patterns of variability in a dataset. It is important because it allows scientists to reduce the dimensionality of complex datasets and identify patterns that may not be apparent in the original data.

2. How does the SVD method compute EOFs?

The SVD, or Singular Value Decomposition, method decomposes a matrix into three components: a left singular vector, a singular value, and a right singular vector. The EOFs are then computed by taking the first few left singular vectors, which represent the dominant patterns of variability in the data.

3. What are some common applications of computing EOFs by SVD?

EOFs computed by SVD are commonly used in climate and oceanography research to identify patterns and trends in large datasets. They are also used in image and signal processing, as well as in finance and economics to analyze market trends and patterns.

4. Can the SVD method be used for any type of data?

Yes, the SVD method can be applied to any type of data that can be represented in a matrix form. This includes numerical data, such as climate data or financial data, as well as non-numerical data, such as images or text.

5. Are there any drawbacks to computing EOFs by SVD?

One potential drawback of using the SVD method to compute EOFs is that it assumes that the data is linear and normally distributed. This may not hold true for all datasets, and therefore, the results may not accurately represent the underlying patterns of variability.

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