There are various forms of "nonlinear" PCA, which transform the
variables nonlinearly in such a way that there is maximal data
reduction in a fixed dimensionality. For instance: transform
the variables nonlinearly in such a way that the sum of the
two largest eigenvalues of the correlation matrix is maximized.
Or the sum of the three largest ones, or just the largest one.
Most approaches allow you to restrict the nonlinear transformation
to be monotonic, or splines, or "smooth".
This is implemented in PRINCALS in SPSS/Categories, in PRINQUAL
in SAS, in mdrace in S-Plus. See
http://www.stat.ucla.edu/gifi
for more info.
But if you are worried that normalization already distorts the
physiological characteristics and makes the loadings difficult
to interpret, then these procedures make take you even further
astray (because they are even further removed from the original
data).
At 5:24 PM +0100 2/18/00, Stefan Debener wrote:
>First of all, Hi to everybody out there, I am knew on this list. To cut
>my story short, I would like to know if there is any way to run a
>nonparametric PCA.
>The electrophysiological data I am working with are usually ln
>or sqrt transformed to normalize distribution. However, this procedure
>does no
>good on the resulting PCA loadings. Similar to a PCA on a correlation
>matrix, the resulting factor loadings do not any more reflect underlying
>
>physiological characteristics and are difficult to interpret. On the
>other hand, a PCA using a covariance matrix on raw (or sqrt transformed)
>
>data reflects the underlying physiological processes quite well and is
>nicely reproducable.
>Taken together, normalization as well as z-transformation due to corr
> (instead of cova) has a bad influence on the interpretability of the
>resulting factor loadings.
>
>I would greatly appreciate any comments.
>
>Thanks,
>
>Stefan
>
>
>_________
>Stefan Debener
>Department of Psychology II
>Dresden University of Technology
>Germany
>
>
>
>
>
>
>
>
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