Reconstruction of a Stochastic Process usong the KL expansion
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I have a matrix of size 1000*500 which contains 500 realizations of a Stochastic process. I have used the KL expansion as defined in this other answer to decompose the process.
I have done it and I have been able to reconstruct the original process with success. However, the KL expansion is designed to reduce the dimensionality, so, I want to reconstruct the original process using less random variables. For that, I would need to change the line
to only include some of the random variables. However, if I write
Then, the results are quite different from the original ones. I need the full 1001 random variables to propperly reduceproduce the original realizations I don't know what to do to be able to try to reconstruct the original data using only a handful of random variables.
I will attach the realizations of the Stochastic process in case someone wants to take a look.
Any answer is appreciated.