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I want to apply the FastICA algorithm on a certain dataset. I believe the sources the Fast ICA can recover are able to explain other data as well (in similar way to factor analysis). However, I also believe the mean of the data contain valuable information. I was wondering if, after the prewhitening which removes the mean from the data, it is possible tk somehow "bring back" the means to the sources extracted, such that the mean of the sources is meaningful as well. Any reference is well accepted. Thank you in advance

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Centering the data is only a convenience thing, ICA works on uncentered data as well. However, if you center your data, then you can add the means back to your signals $s$ by adding $W,\mu$, where $W$ is the demixing matrix (inverse of the mixing matrix), and $\mu$ is the mean vector subtracted.

Reference: link

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