Principal Component Analysis Alternatives for low sample to dimensions ratio

[Krevin]

Anyone know of good alternative methods to PCA when you have too many dimensions compared to samples?

If I have 2000 variables and 300 samples, I cannot properly use PCA.

I'm looking for something that can minimize false positive separation of sample points without needing to reduce my number of variables.

Thanks,
Krevin

[Art Kendall]

Please describe you data in more detail.
What are your 2000 variables? Are they some form of repeated measure
such as items in summative scales, the same variable measured at
different times or at different points along a spectrum?

What are you cases?

What questions do you want to answer with the data?

Art Kendall
Social Research Consultants

[David Jones]

"Krevin" wrote in message
news:910037f7-6687-4714...@googlegroups.com...

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There are many possibilities, ranging between:
(1) A version of PCA in which you use a fictitious covariance matrix, not
estimated from the data but guessed from experience; a version of this might
estimate part of the covariance matrix with the rest filled in by assuming
zero correlations or partial correlations.
(2) A version of cluster analysis in which you define distances in the
variable space on the basis of relative importance on an intuitive scale; a
version of this might just use a weighted sum of squares with weights
derived from the sample variances, adjusted for any perceived overlaps in
meaning. But the idea here would be to have a good vision of "importance" of
the variables, with the sample statistics being not really relevant to the
clustering.

David Jones

[Rich Ulrich]

On Wed, 10 Apr 2013 20:44:39 -0700 (PDT), Krevin <kbr...@gmail.com>
wrote:

>Anyone know of good alternative methods to PCA when you have too many dimensions compared to samples?
>
>If I have 2000 variables and 300 samples, I cannot properly use PCA.
>
>I'm looking for something that can minimize false positive separation of sample points without needing to reduce my number of variables.

As Art implies, it is usual for there to be some structure when there
are as many as 2000 variables. The sort of structure is apt to
matter for a constructive solution, assuming there is structure.

I don't know what you have in mind when you say, "minimize
false separation of sample points..." but if you flip the matrix,
you have another conventional factoring (of samples). I think
of that as a sort of cluster analysis. Anyway, the samples
with low communalities will be ones that are relatively
"separate" from the others.

--
Rich Ulrich

[Art Kendall]

yes Q factor analysis is one thing that can be done with a 2000 variable
300 case data matrix.

Yes Q factor analysis is an old time method of cluster analysis.

Depending on substantive nature of the data it may also be possible to
cluster variables.

If the 2000 variables are word frequencies multidimensaional scaling is
a possibility.

Many many thing are possible. But without the meaning of the data, level
of measure, design role, etc. etc. all I can do is speculate.

What is the term David uses e-esp?

Art Kendall
Social Research Consultants

[Ray Koopman]

There is a variant of Partial Least Squares that does Structural
Equation Modeling that probably could be adapted to look like PCA.
See http://users.stat.umn.edu/~sandy/courses/8801/articles/pls.pdf