KarhunenLoeveDecomposition function in Mathematica

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SUMMARY

The discussion centers on the use of the Karhunen-Loève Decomposition function in Mathematica to analyze a matrix of size 211302x50 from the file stochasticData.mat. The user, Confused_engineer, seeks assistance in interpreting the results of the function, as they are unfamiliar with Mathematica and unable to identify the uncorrelated random variables produced by the decomposition. The provided code snippet for executing the function is: KarhunenLoeveDecomposition[{stochasticData}]. The user also attempted to read the data from a text file but encountered difficulties.

PREREQUISITES
  • Familiarity with Mathematica version 12.0 or later.
  • Understanding of the Karhunen-Loève expansion and its applications.
  • Basic knowledge of matrix operations and stochastic processes.
  • Ability to import and manipulate data files in Mathematica.
NEXT STEPS
  • Research the documentation for KarhunenLoeveDecomposition in Mathematica.
  • Learn how to visualize and interpret the output of the Karhunen-Loève Decomposition.
  • Explore data import techniques in Mathematica, particularly for .mat files.
  • Investigate methods for identifying uncorrelated random variables in the context of stochastic processes.
USEFUL FOR

This discussion is beneficial for data scientists, statisticians, and researchers working with stochastic processes who are utilizing Mathematica for data analysis and decomposition techniques.

confused_engineer
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TL;DR
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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