[Eeglablist] question about variance

Phillip M.Gilley pgilley at utdallas.edu
Thu Jun 23 15:29:31 PDT 2005

When using standard PCA we can easily calculate the percentage of 
variance explained from the eigenvalues for each principal component.  
Is the calculation similar, or even possible for ICA?

For example, the ICA solution should (theoretically) explain 100% of 
the variance in the original data set.  However, when looking at the 
percentage of variance accounted for (pvaf) from the different 
functions in EEGLAB, I see several different types of results.  Under 
the envtopo() function, there is a specified output for pvaf.  This 
function calculates the pvaf for each specified component across all 
channels; and the calculation appears to be made by subtracting the 
variance of the whole data set from the variance of the back projection 
of the component.  However, it is often the case that the sum of the 
values exceeds 100%, which I interpret as the variance in the 
distribution of that component irrespective of the contribution of 
other components.  Is this a correct interpretation?  Is there a pvaf 
function that returns a set of values for each component  for the 
original dataset (e.g., for the entire epoch, or for a specified time 
range), such that the sum would equal 100%?

Also, the function eeg_pvaf() returns three sets of variances, which 
don't necessarily seem to match the pvaf values returned from the 
envtopo() function.  Are these different calculations altogether? And 
if so, what different variances are these values explaining?

Thanks for any insight or comments.

Phillip M. Gilley
The University of Texas at Dallas
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