Can the ICA solution obtained from epoch data (relatively long, min. 4 s) be applied to continuous data? It seems to me that it doesn’t matter. ICA can be applied to epoched data to save computing resources, and applied to continuous data.
Should we interpolate the bad channels and re-reference the data before and after running ICA? Given that interpolation and referencing can modulate the covariance matrix, it seems to me that they should be applied after ICA.
Finally, to reduce ICA fitting time, can I decimate EEG data recorded at 1024 Hz to 256 Hz, and apply the solution to the original 1024 Hz data?
I’ve also seen labs set n_components=0.99 to reduce the fitting time, is it ok (instead of default 0.99999…)?
Short answers: yes to all, regarding re-referencing I recommend that you remove bad channels, re-reference to average, run and apply ICA, and then interpolate removed channels.
So, you recommend re-referencing before running the ICA and then interpolating: is this really important? And what does it imply to make the average reference before or after?
I would re-reference to average before ICA just because that’s what most people do. However, you are right that in theory, the reference does not influence the decomposition (see e.g. Re-referencing - EEGLAB Wiki).
Re-referencing and interpolating bad channels are two separate processing steps, and I don’t think the order really matters, but it also depends on why you use ICA in the first place. Do you use ICA to zero out ocular activity? Or do you use ICA to isolate neural components, which you analyze in subsequent steps? I’m assuming you’re using the former approach (otherwise why would you care to interpolate bad channels), i.e., you stay in EEG space, and here the most common pipeline is remove bads → average reference → ICA → interpolate bads → optionally average reference again with the full (partly interpolated) channel set.
Regarding your specific question why it matters if you re-reference to average before or after ICA: it doesn’t matter in theory, but if you are inspecting source topographies, these might be easier to interpret if they are derived from average reference data.