I'm working with proteomic data, helping a student who knows biology and
has done analysis in R without understanding it in depth.
We have 3000 protein levels for 6 ages. I can treat this as 6 vectors in
3000-dimensional space, diagonalize a 6x6 covariance matrix and find 5
principal components, one zero eigenvalue. My student has worked with R in
"Q mode" and he enters the transposed matrix as 3000 vectors in
6-dimensional space. In just a few seconds, R diagonalizes a 3000x3000
matrix! I can't imagine what that means, to diagonalize a 3000x3000
matrix. But, of course, there are only 5 degrees of freedom in the data,
so only 5 of the eigenvalues are non-zero, and the other 2995 vectors are
junk.
Questions: a) Is there a relationship between the principal components
of the 3000*6 matrix and the principal components of the transposed 6*3000
matrix?
b) Is there a way to find the 5 meaningful
eigenvectors without carrying the baggage of diagonalizing the huge
3000-dimensional matrix?
c) The big question is which version to analyze and
publish? My student tells me the transposed matrix is the common
procedure. The two yield very different-looking plots.
Thanks for your help.
- Josh Mitteldorf
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