# [R] PCA in Q- and R-modes

Bert Gunter bgunter.4567 at gmail.com
Thu Jan 19 02:02:26 CET 2017

```Off topic for this list.

Post on stats.stackexchange.com or similar for statistics questions.

Post on Bioconductor list for biology-related (e.g. proteomics) data
anaysis questions.

Cheers,
Bert

Bert Gunter

"The trouble with having an open mind is that people keep coming along
and sticking things into it."
-- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )

On Wed, Jan 18, 2017 at 10:35 AM, Josh Mitteldorf <agingadvice at gmail.com> wrote:
> 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.
>
> - Josh Mitteldorf
>
>         [[alternative HTML version deleted]]
>
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