How are biosignals (EEG/MEG) explained by independent component analysis (ICA) decomposition when time periods of the data were not included in the ICA decomposition (due to artifact removal before decomposition) but the weights and sphering matrices of the ICA are copied back to the continuous data that entail these time periods?
From the general machine learning perspective : You try to interpret the data that the network was not trained on. As the artifacts are far away from the normal signal input space, the network will identify artifacts incorectly (marginal receptive fields, extreme values of input space).
From ICA perspective: The network (ICA matrix) will backproject the artifacts to all components, but the iterpretation of this backprojection is corrupted as it is insesitive to this type of signal.
From EEG perspective: There is problem that artifact is mostly presented in all channels (all dimensions of input space). I think that you cannot interpret projection of artifactual signal in component space. You should put the arifacts into the ICA and let them identify as the artifactual components. You know better than me that this procedure will distort good components.
Dear Prof. Gramann,
TLDR: the ICA decomposition describes the data it was trained on. Therefore the sources located will be valid EEG sources also when the noise is present. Note however in that case the noise will be likely present on more components, contaminating them.
If I understand correctly the question, the ICA projections were calculated on a data without noise (could be epochs in an ERP/ERSP design but also simply clean data where noise was rejected based on some criteria other than ICA). Then the ICA weights are applied to the raw continous data which contains the noisy parts too. In traditional EEG analysis typically a different strategy is followed, where e.g. a first ICA is used to remove artifactual components (eye IC for the simplest case), then a next ICA is used on the clean data to actually differentiate independent sources of EEG signal. The problem is that the artifactual components typically not only contain noise but signal as well. This is even more of an issue when the data contains excessive artifacts (e.g. EEG recorded during locomotion). There, the described novel method could be a great solution.
Take a simple example, I have some people in a room (they are the independent sources of EEG activity which I'm trying to differentiate). They are talking (this is the EEG). I have several microphones in the room positioned in the nodes of a grid (these are the channel positions we use when recoridng the EEG). , Now, I'm replacing these microphones: I place one microphone to each person to record their and just their voice (this is the ICA). Here comes the original question's point: Now I let in the room Ben de Blink and Murphy Muscles (these are the noise sources) in the room. These guys are loud, shouting all the time, thus having the original grid of microphones I may heard only them, but having the microphones replaced I still be able to hear the original people in the room.
Just some notes:
- the applied ICA weights describe the signal they were fitted on
- therefore the ICs in the noisy recording will not be independent anymore and their mutual information will not be minimal
- Another method to approach the problem of excessive noise in biosignals is to remove only the noise from the 'noise IC' (e.g. http://research.gold.ac.uk/4218/1/Psychophysiology_2010.pdf)
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