[R] PCA problem in R

[Prof Brian Ripley]

On Sat, 13 Aug 2005, Alan Zhao wrote:

> When I have more variables than units, say a 195*10896 matrix which has
> 10896 variables and 195 samples. prcomp will give only 195 principal
> components. I checked in the help, but there is no explanation that why
> this happen.

There is not even a definition of a PC in the help. Did you read the 
references?  This is what they are given for!

> Can we get more than 195 PCs for this case? Thank you very
> much.

Check out the theory in the references.  You can, but all the remaining 
ones are constant across samples and not uniquely defined.  You are likely 
to have trouble storing the coefficients (10701x10896 is 800Mb).
It would be better to do whatever you intend to do with them without 
explicitly computing them.

-- 
Brian D. Ripley,                  ripley at stats.ox.ac.uk
Professor of Applied Statistics,  http://www.stats.ox.ac.uk/~ripley/
University of Oxford,             Tel:  +44 1865 272861 (self)
1 South Parks Road,                     +44 1865 272866 (PA)
Oxford OX1 3TG, UK                Fax:  +44 1865 272595