KarhunenLoeveDecomposition function in Mathematica

In summary, the conversation discusses the use of the Karhunen-Loève expansion and the software Mathematica to calculate uncorrelated random variables from a matrix of measurements of a stochastic process. The code used and attempts to read the data transformed into a text file are mentioned, but the results are not fully understood and help is requested. The reference for the KarhunenLoeveDecomposition function is also provided for further research.
  • #1
confused_engineer
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TL;DR Summary
I am unable to properly use the KarhunenLoeveDecomposition function included in Mathematica to calculate the uncorrelated random variables.
Hello everyone. I have a vector, stochasticData.mat, it contains a matrix of size 211302*50, being 211302 measurements of 50 realizations of a stochsatic process. I want to use the Karhunen-Loève expansion and the software Mathematica to calculate the uncorrelated random variables. For that, I have written the following code:

SetDirectory[NotebookDirectory[]];
stochasticData = Import["stochasticData.mat"]
KarhunenLoeveDecomposition[{stochasticData}]

Also, I have tried to read the data transformed into a text file asUnfortunately, since I am not proficient with Mathematica, I cannot propperly understand the results and I don't know how to find the random uncorrelated random variables, it seems like the function has no effect as can be seen in the attached image. Can someone please help me?

Best regards

Confused_engineer.

E. G. I cannot upload stochasticData.txt since it is too heavy, but I am uploading a smaller version which contains the first 10000 measurements, just in case someone can help me.
 
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What is the Karhunen-Loeve Decomposition function in Mathematica?

The Karhunen-Loeve Decomposition function in Mathematica is a mathematical algorithm that decomposes a set of data into a smaller set of orthogonal functions, known as Karhunen-Loeve basis functions. This decomposition can be used to reduce the dimensionality of a dataset or to identify the most significant patterns in the data.

How does the Karhunen-Loeve Decomposition function work in Mathematica?

The Karhunen-Loeve Decomposition function in Mathematica works by first calculating the covariance matrix of the input data. Then, the eigenvalues and eigenvectors of this matrix are computed, and the eigenvectors are sorted in descending order of their corresponding eigenvalues. The resulting eigenvectors form the Karhunen-Loeve basis functions, and the data can be reconstructed using a subset of these basis functions.

What are the advantages of using the Karhunen-Loeve Decomposition function in Mathematica?

The Karhunen-Loeve Decomposition function in Mathematica offers several advantages, including reducing the dimensionality of a dataset while preserving the most important features, identifying patterns and trends in the data, and compressing the data for more efficient storage and processing.

Can the Karhunen-Loeve Decomposition function be applied to any type of data in Mathematica?

Yes, the Karhunen-Loeve Decomposition function in Mathematica can be applied to any type of data, including numerical, symbolic, and image data. It is particularly useful for high-dimensional datasets, where it can significantly reduce the number of variables without losing important information.

Are there any limitations to using the Karhunen-Loeve Decomposition function in Mathematica?

One limitation of the Karhunen-Loeve Decomposition function in Mathematica is that it assumes the data is linearly related and normally distributed. If these assumptions are not met, the results of the decomposition may not accurately represent the data. It is also important to carefully choose the number of basis functions to use, as too few or too many can affect the quality of the reconstruction.

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