 MNE 1.3.1
 Windows 10
Hello,
Some context: I am working with a 4 channels muse headset, tried an ICA, I then obtained 4 components that are mixtures between artifact and brain signals. Each of the components seems to have too much brain signal for me to discard it.
From there I wondered: What if you artificially add a new channel (for example via interpolation) in order to obtain a new component out of the ICA. It looks wrong as you do not add any new information for the ICA so the components will still be a â€śblendingâ€ť of the same channels but you will surely get a new component and â€śrerollâ€ť the â€śmix percentageâ€ť for all of the components (and maybe get one that is more distinctly an artifact or a brain signal ?).
My question is: is artificially adding a channel (via interpolation for example) before performing ICA can gives interesting results or all the components found must be interpreted as bad and should not be looked at ? How MNE ICA function will handle these cases ? if it is wrong, what is the theory behind ?
And lastly, what would change if the artificial channel added is the resulting of:
 an interpolation or a linear combination from another channel
 an exact copy of another channel time signal.
 an exact copy of another channel but with a white noise added
 a polynomial approximation with a sliding windows on another channel => via a savitzkygolay filter that has been applied on another channel and we take the resulting filtered signal.
I tried quickly these case with MNE ICA to see its behavior and have some empirical observations to illustrate:

It always worked (no error), even for the copied channel + white noise (even though it break the â€śeach source signal have nonGaussian distributionsâ€ť ICA prior assumption) or the polynomial approximation (does this one break the stationary assumption ?). For the channel + white noise, it successfully gave me a component that looks like the white noise added source.

For the 2 first tests, It gave me the variance warning but not for the white noise or the polynomial approximation:
RuntimeWarning: Using n_components=5 (resulting in n_components_=5) may lead to an unstable mixing matrix estimation because the ratio between the largest (2.3) and smallest (1e24) variances is too large (> 1e6); consider setting n_components=0.999999 or an integer <= 4

In each group of 5 ICs resulting from these tests, there seems to have the same 2 components that looks the same across experiment and that looks correlated to each others.