Real Input / Complex Output?

> I am using the toolbox for studying late-potentials (>300 ms) in mismatch
> negativity ERP data.  I am trying to remove the components that are not 
> significant in the frontal, parietal and occipital areas.
> The data is 26-channel, 21 EEG + EKG + Eyes + EMG
> 
> My problem is that "runica" sometime produces complex (in the math sense)
> results and takes 11 hours to compute.
> The norm of the imaginary components is 1/200 of the real components.
> Before running "runica" I have:
> (1) removed the baseline from each epoch using the prestimulus data
> (2) discarded epochs with amplitudes of over 50 uV in the CZ channel
> (3) converted the data to average reference using "averef" 
> (4) removed the baseline again using "rmbase"
> 
> Am I omitting some crucial preprocessing ?

Failure to converge and complex results usually means your data is
not of complete rank. Run >> rank(data) to test this. Applying averef() 
reduces the data dimension by 1, so running runica() (or better, binica()) 
with the 'PCA' option set appropriately (i.e., to nchans-1) is necessary.

In general, I do not believe using averef() is a good idea (unless you
have really high-density, whole-head recordings). If you want, you can
use averef() at the end of the analysis instead of the beginning.

How much data?

You have also omitted some crucial information - how much data are you
attempting to decompose??

>The data was composed of 26 channels, 230 epochs of 500 samples.
>Therefore I passed a matrix of 26 x 160000 to the function.

You are training 26^2=676 weights with 15k points - 22 points per weight.
This is quite sufficient to return components with compact source maps and 
distinctive dynamics, in our experience.

Should I worry about discontinuities?

>I have not attempted to match the ends of the epoch to each other.
>I just assumed that the discontinuities will be mapped to the largest 
>component.

But ICA does not see discontinuities - In fact, it shuffles all the
time points randomly before each training step! This is, for example, quite 
unlike FFTs, which operate on time series and does not 'see' between-channel 
relationships. ICA sees only the maps!

Are four channels enough?

>We are currently trying to analyse ERP data collected from an
>experiment involving rather complicated paradigm which includes mismatch,
>emotional / non-emotional stimuli, as well as infrequent stimuli
>(oddball-paradigm-like). However, we have only 4 channels. As you have
>advised on your web page, we should have more channels than the expected
>number of components. 
>
>From the results of your experiments (J Neurosci 19:2665-2680 (1999)), 
>you found 4 psychologically meaningful LP components.  Although we have 
>a different paradigm (hence possibly different number of expected components), 
>would it still be advisable to perform ICA on the data to obtain meaningful 
>results?
>
>My supervisor is quite keen to perform ICA on the data. However I am personally 
>against it, as I expect more components (including 'noise' components) than we have 
>channels. Please advise.

I agree with you that ICA cannot be expected to give optimum results 
applied to a collection of ERPs with only four channels. However, as 
an exploratory measure, ICA is easy to perform and visualize (see the 
new toolbox tutorial).  The question is how much belief to put in the 
functional independence of the resulting components. This should not
in any case be blind faith, but faith won through finding convergent
behavioral and other physiological evidence.

If you are serious about squeezing maximum information out of
4-channel data, I would advise using short-time moving-window ICA
applied to the raw data. This will give a huge collection of
components, which must be clustered, etc. (not easy).  You could
also investigate blind deconvolution applied to the single trials,
though this is full of circular confounds, etc... It might be easier
to collect the data again with higher density, somewhere.
Good luck! 

Temporal ICA?

>As you are aware, there are two implementations of PCA -- temporal
>and spatial. From reading your webpage, I get the impression that spatial
>PCA and ICA are superior form of temporal PCA. But from some of my readings
>(e.g. see SPENCER, DIEN, & DONCHIN (1999). Psychophysiology, 36, 409-414), I
>got the idea that spatial PCA (and possibly ICA) and temporal PCA answers
>different questions altogether. Can you knindly clarify this? Also, is there
>a 'temporal PCA'-equivalent form of ICA? Thanks for your time.

Temporal ICA is used for fMRI analysis (see McKeown et al., Human 
Brain Mapping '98, where it makes sense. For EEG it does not,
since ~no EEG channel is independent of any other.

As for spatial/temporal PCA, I do believe the point I made in the
JNS '99 paper. As Promax (not PCA) tries to minimize the support
of each component, spatial Promax will attempt to find superficial
sources (projecting strongly to only a few electrodes). Therefore
spatial Promax sources have features like 'nipples.' As Chapman
and McCrary pointed out, temporal Promax makes more sense, since
in this case the component have minimum temporal support - i.e.
are 'on' for a minimal period of time.

Be wary of groups claiming their methods are "PCA." In fact, Varimax, 
an intermediate step in the Promax routine, does <b>not</b> require PCA 
pre-processing (Moecks), and so PCA itself may play little or no 
essential role in results of Promax rotation!  

PCA itself tries to gather as much activity as possible into the first 
(and then into second, etc) components, constrained by the quite 
unreasonable assumption that the scalp maps are orthogonal. 
PCA may be used for dimension reduction (e.g. prior to ICA), though by
removing the many smallest principal components one runs the risk
of removing small details of interest.

The same cautions about component interpretation apply to Promax
(or other -max) results as apply to (Infomax) ICA.


