[Eeglablist] How to recognize successful ICA (number of data points issue)

[Stefan Debener]

Hi Jim,

in my experience there is no perfect rule of thumb, since the size of 
the data matrix you feed into ICA is only one of several factors 
influencing the quality of a solution. Here are my thoughts about what 
matters as well:

1. Number of training data 1: Consider for instance the case of a short 
and a long recording of, let's say, 128 channels. The long recording 
will return a more reliable and cleaner (more dipolar IC maps) solution 
only if the quality of the data remains roughly the same, and only if 
there is no 'new' stuff coming into the data. So more is only better if 
it's more of the same...see below for an idea how to test this.

2. Number of training data 2: In my personal opinion, the pure amount of 
training data, that is, size(data,2) of the data you feed into ICA, 
needs to be corrected for data points carrying information. Let's assume 
that EEG picks up activity up to 100 Hz, and you recorded your data with 
a 100 Hz analog low pass filter and a 500 Hz sampling rate. In this case 
you should do the rule-of-thumb calculation for a sampling rate of 200 
Hz, because, in the frequency domain, the higher frequencies contain 
zeros only. So it all depends on your filter settings (and your personal 
opinion about the frequency range being relevant for EEG ). Note also 
that different EEG recording systems on the market enfore a different 
oversampling factor, possibly due to a different quality/slope of analog 
low pass filters, to avoid aliasing....

3. Stationary data: It seems to me that it's sometimes much easier to 
get a decent decomposition with a higher high pass filter. So, if you 
consider the identical data with the identical number of data points, 
you may get a much better solution for high pass filtered data. The 
reason is that ICA really likes stationarity, and, the more dimensions 
you have to spend, the more relevant this may be.

4. Bad channels. I don't know for sure, but a few bad channels may 
easily blow up the whole decomposition, and prior bad channel 
replacement always means information loss. That's why we try to collect 
our data without any bad channels...

5. Adequate spatial sampling. It's really hard to tell how many channels 
are necessary to obtain the best-possible decomposition. My experience 
with 32, 64, 68 and 128 channels is that 128 not necessarily returns 
more reliable ICs. I am not aware of a single paper investigating the 
spatial sampling question for ICA. I used to be happy with 128 channels, 
but I currently get even better results with equidistant 68 channel 
recordings, covering a much larger part of the head sphere than the 
usual 10-20 system (the system is called intra-cerebral cap, extremely 
useful, and available from www.easycap.de). So, the pure number of 
channels seems to be one thing, and the covered head space another one. 
A larger inter-electrode distance may be just fine if you cover a larger 
part of the sphere as well. The underlying problem here of course is 
that we have no clue how many different sources contribute to the EEG. 
Modelling your data with less dimensions than 'true' sources is 
certainly no good (underdetermined case), but modelling more dimensions 
may not be good either. If one considers every single channel to have 
it's own noise term, the summed channel noise activity from spatially 
oversampled data may actually be responsible for reducing the quality of 
the decompositions. Just a guess...

6. Modeling the neurocognitive process of interest. Another issue is 
whether you should run ICA for continuous or for (concatenated) epoched 
data to obtain components reflecting the process(es) you are interested 
in. If you believe in the standard ERP data model (brain response is 
summed to, and independent from, ongoing activity), you would certainly 
like to tailor your data towards your ERP interval. If you on the other 
hand believe that ongoing EEG activity (or 99% of your recorded data) is 
not just noise, you may like the idea of decomposing continuous data (or 
longer epochs, allowing preparatory brain activity to be modelled!). 
Even if the ERP model was 'true', the decomposition would be less 
optimal for artifact ICs reflecting processes being continuoulsy on. ICs 
reflecting ECG for instance, an ongoing artefact, are much easier to 
obtain from continuous data. So if your focus is on regional EEG 
asymmetries in the low frequency domain (<20 Hz), you would certainly 
like to remove this asymmetric artifactual activity before analysing 
your (short epoched) data. So it all depends on what you are looking 
for....I started with decomposing short epoched data, but there may be 
neurocognitive processes being more or less continuously 'on', like 
performance monitoring, which I found easier to be separated from other 
stuff by decomposing continuous data (Debener et al., 2005, J Neurosci). 
Assessing the spatio-temporal overlap of ICs reflecting major portions 
of novelty-P3 and P3b ERP components on the other hand was better with 
decomposing epoched data (Debener et al., 2005, Cog Brain Res). It would 
be actually nice to systematically investigate this issue....

7. Moving sources. ICA likes your electrodes not to move relative to the 
signal sources. That's why ICA of MEG data may sometimes be a bit of a 
problem (head movement). Same holds true for slipping EEG caps, or when 
subjects scratched at electrodes during the recording and, as a result, 
the cap is a bit shifted. Or assume you have a long recording and the 
subjects walks to the loo in a break. More likely than not that the cap 
is shifted a bit. Flipping sensors of geodesic sensor nets is no good 
either, of course, or moving a head with the cap resting on a pillow. 
Luckily its rather unlikely that brain sources move...but there can be 
artefacts that can be modelled as a moving source! This holds true in 
particular for the BCG artifact, present in inside MRI scanner EEG 
recordings. This artifact contributes a moving, rotating and polarity 
reversing signal to the EEG (see a movie on my homepage, www.debener.de, 
illustrating this). If ICA is applied to remove the BCG, much of the EEG 
signal is removed as well (Debener et al., in press, Neuroimage), which 
is a nice example that ICA is not a perfect wizard dealing with any 
problem. But if applied correctly, ICA can help a lot in analysing 
inside scanner recorded EEG data (Debener et al., 2006, December issue 
of Trends in Cognitive Sciences).


So what is a good way to determine the quality of a solution, taking 
into account issues 1-7? Our lab routine is to look at dipolar 
components only, with dipolarity being determined by the residual 
variance of the dipole source modeling tool in EEGLAB, dipfit. With 
reasonable spatial (issues 4 and 5) and temporal (other issues) 
sampling, more dipolar components seem to implicate a better 
decomposition. 'Better' here refers primarily to the reproducability of 
the decomposition. If you have enough training data AND the quality of 
your data is OK, the resulting dipolar components will be very robust. 
That is, if you repeat your decomposition, the weights of your dipolar 
components will be correlated by r>.98. When analysing a new experiment 
we always run ICA repeatedly for about 1-3 randomly selected subjects 
and determine the reproducability of the model, before applying the same 
model to all subjects. It takes some time, but we found that it's worth 
the effort.

Sorry that there is no quick answer, but the issue is rather 
complicated, and I am not at all claiming to have it fully understood by 
myself. Please note also that while my comments are based on our 
experience, I have not systematically tested all of them. Where 
appropriate I have cited my own papers, but others have published very 
informative papers as well, and helpful Matlab code! There are promising 
open source tools available which may help to identify good, stable 
components (ICASSO), or aim to estimate the number of sources in the 
data before running ICA (GIFT). And finally, the new STUDY functionality 
in EEGLAB could also be used to determine the quality of a decomposition....

Best,
Stefan








Jim Kroger wrote:
> In the tutorial, as well as in discussion here, it's been pointed out that 
> successful ICA requires sufficient data. The tutorial discusses that the 
> factor: (number of data points)/(the number of channels)^2 should be >= 30 
> for 32 channels, and greater for more channels. We often find that 15 
> minute segments that fit well into EEGLAB/Matlab (given our RAM constraints 
> and 128 channels, 1024 sampling) provide us with a factor of around 80 
> before epoching, less after.  I suspect this is borderline, but don't know 
> how to judge whether the resulting components are "good." What would "good" 
> and "bad" components be like? Any commentary would be appreciated.
>
> Jim
>
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