Hello. This is Arnaud Delorme, and this is part three of ICA applied to EEG data.
This part is how you actually apply ICA to EEG data.
And so first I need to explain a concept, which is the concept
of Super-Gaussian versus Sub-Gaussian sources.
So if you have a source that's perfectly Gaussian, it has a kurtosis of zero, if I have
a source that's Sub-Gaussian, like the one we saw in the previous presentation,
that's a kurtosis that's less than zero, and if you have a biological source it's usually
a very peaky distribution -- like EEG -- and it's called a Super-Gaussian source.
And so when you apply ICA, this is important.
So on the left here, this is what I've shown in the previous video, so this
is for a type of Sub-Gaussian source.
For EEG data, EEG data is Super-Gaussian,
so it would look more like what's on the on the right of this slide.
And when it looks like this, you need to apply -- so this is the axis of the source --
you need to apply a transformation, so we pass the distribution through a
non-linearity -- right here -- and so we can transform this source into a source
on which we can calculate entropy as we showed in the previous video.
And then once we do that, it's exactly the same process that we show in
the previous video, we can recover the original axis for the source.
So the only difference here is that we apply -- we compute -- the probability density
distribution and we apply this non-linearity before calculating the entropy.
So how does that work on real data?
So this is actual data here and you can see two electrodes here
PZ and FZ, and the little wiggly line is time,
so that's the EEG signal through time. And so once we apply -- here you see it's
called logistic transform -- and when we apply the logistic transform we can
see that now it fills most of the square and most of the surface, so we can
calculate the entropy and we have a relatively uniform distribution when we
look at these two components here PMP and P3b.
And numerically if you look at the data -- so this is here -- so you have the
ICA activity and you have the EEG data
in blue and then you calculate the weight matrix. So that's the ICA matrix.
So this is how it would look like, so you have the data on top, you do a simple
matrix multiplication, and then you obtain the ICA activity.
If you want you can also do the inverse, which is that you can calculate the
data from applying the inverse weight matrix to the ICA activity.
And what's interesting here is, if we look at the column of the
inverse weight matrix, we get the scalp topographies.
And as we'll see in a subsequent video by zeroing out the ICA activity of some
artifacts or components we can remove these artifacts from the EEG data.
So if you don't really understand what is ICA, this is really the
two slides to remember -- this simple matrix calculation.
All the rest I showed you was about calculating this weight matrix and inverse
weight matrix, but once you've done that it's very simple matrix multiplications.
There is assumption when you apply ICA to EEG.
First, the first assumption is that the mixing is linear at scalp sensors.
And this is mostly true, this is Maxwell's equations of electrical propagation.
Then the propagations delays are negligible.
This is also true, in a sense that the propagation delays are close to the speed of light.
So at the time scale we're interested in, which is from 1 Hz to 100, or
even 1,000 Hz, this is really negligible.
Then the component time courses are independent
so that the components are truly independent in the brain.
And that's not a very reasonable assumption, but what saves us here is that ICA, most ICA
algorithms, are what's called maximum projection algorithms and they
will find distribution that's maximally independent.
So they [components] don't have to be fully independent, they only have to be maximally independent.
And finally the number of components should be less than the number of channels.
And again this is not necessarily a reasonable assumption.
You can imagine that every single neuron in the brain or even every single
synapse could be an independent contributor to the EEG signal.
But what ICA will do is that it will find the source which contributes the most to the
EEG signal and then apply some sort of cut off so you won't see the ones that
don't contribute that much to the EEG signal.
And so that's what I was mentioning here -- the limit that ICA imposes on the number
of independent components that can be isolated.
The type of independent components we can see in EEG -- there's many different types as we'll
see in the next slide -- artifacts, stimulus-locked activity, response-locked
activity, non-phase locked activity, event-modulated oscillatory
activity, overlapping maps and spectra.
And so here is a sample EEG ICA decomposition.
So here I'm just showing the data and so you have selected channels.
Here we only have nine channels, and you see there's some
frontal channels, some occipital channels.
We apply ICA -- and these [stimuli on the top] were being presented
through time -- we apply ICA and this is what we get.
We get component topography and component time courses.
And here the first two components are eye blinks.
Here, in this case, it isolated two components.
Then we have brain components, so we have
fronto-parietal theta, central theta, frontal midline theta.
So components with different topographies, which sometimes overlap.
And we also have occipital alpha components,
in this case we have two occipital alpha components.
And then finally we have ECG, so the heart.
So even though we didn't have a heart channel here,
ICA was able to extract heart signals from the EEG itself. And then we have temporal muscles.
So here we see the muscle spike for temporal muscle activity.
So all these components are mixed together to create what's on the
top, which is the real EEG in which they all mix together.
So it's a powerful way to separate this cognitive and artifactual processes.
And here I have one last slide for this presentation on the difference
of applying ICA to EEG versus applying ICA to fMRI.
So when you look at EEG -- so that's one of the slides I showed -- the ICA
activity are the time course of the components and then the column of the
inverse weight matrix are the scalp topographies.
When you look at fMRI, it's applying [ICA] in the spatial domain, because you
have many voxels and very few time points.
So now the ICA activities are actually spatial 3D volumes of fMRI activation,
and now the inverse weight matrix are the time course of the components.
So I wanted to thank you for your attention, and I'll see you on the next video.