[Eeglablist] Invitation to collaborate on an open paper about EEG’s 1/f power distribution

[Евгений Машеров]

I have a sad thought that the process is actually mixed, multiplicative-additive. It's sad because the additive model is linear, while the multiplicative model becomes linear after taking the logarithm. But the mixed model becomes nonlinear, dramatically complicating the evaluation.
It seems to me that multiplicativeness occurs at the generation level, but additivity emerges at the recording point. It goes something like this: the input stream of nerve impulses generates postsynaptic potentials, and the spectrum of the impulse stream is multiplied by the Fourier transform of the EPSP or IPSP. The resulting signal then passes through the conductive tissue, and the spectrum is multiplied by the transfer function (this includes both the cable properties and the activity associated with ionic regulation). But at the recording point, the signals from the different generators are summed. Perhaps this is where ICA can be applied, but the criterion for separating the components must be developed taking into account the specifics of EEG.

Eugen Masherov

> Hi everyone,
> 
> My quick update: Eugen, Mate, and I have been making progress looking at periodic/aperiodic separation using a simple GLM-based approach in a few toy simulations. In the setups where the analysis space matches the generative model (additive handled in linear space, multiplicative handled in log/dB space), FOOOF-style iterative fitting seems to behave the best overall compared to a handful of other exclusion/robust-style approaches.
> 
> Eugen also proposed a really simple parameter-free “median” slope estimator that looks surprisingly stable in these tests, and promising.
> 
> That said, it looks like we are still facing the same main and unavoidable problem: the separation still depends on whether the underlying phenomenon is additive vs multiplicative. If we analyze an additive process in log space (or a multiplicative process in linear space), we can easily introduce a background-dependent bias, even if the mean recovery looks OK.
> 
> This work is slowly happening here if anyone wants to take a look / comment / try extending it: https://urldefense.com/v3/__https://github.com/sccn/OneOverF/discussions/12__;!!Mih3wA!HN6zXpAScehZWYTtFIVvhqRPUa5Asb_78uypLJyTPXZfDtsje8iFk70jLELa9JhRiXdtlv36XEc3cpPNuy1SV0_few$
> 
> So my current takeaway is that the next big step is less about finding the perfect estimator and more about better understanding the generative mechanisms Makoto outlined first, whether we should separate aperiodic and periodic components or not, and if so, when should scalp EEG 1/f-ness be treated as additive vs multiplicative, so we can apply the right separation strategy.
> 
> Cedric
>