R help - Nov 2009 - Calculate Volume in a PCA

Hi,
my data frame consist of 8 Variables and 120 000 observations. With those datas
I am running a PCA and after I want to calculate the Volume of the PCA-cloud of
certain subsets of my data. Does anyone have an idea about a function that can
do this?

Thanks



      
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Katja Seis wrote:
> 
> Hi,
> my data frame consist of 8 Variables and 120 000 observations. With those
> datas I am running a PCA and after I want to calculate the Volume of the
> PCA-cloud of certain subsets of my data. Does anyone have an idea about a
> function that can do this?
> 
> 
Not really quite enough information here , although some googling suggests
that
you are looking for a technique used in MRI studies?
http://www.ncbi.nlm.nih.gov/pubmed?term=%22pca%20volume%22&itool=QuerySuggestion

  as a wild guess, I'm going to suggest that the answer **might** be that
you should
take your PCA standard deviations and use the formula for the volume of a
(hyper)-ellipsoid
[http://en.wikipedia.org/wiki/Ellipsoid#Volume].  I don't know the general
formula
(pi*s_1*s_2 for an ellipse, 4/3*pi*s_1*s_2*s_3 for an ellipsoid ...) but in
any case the
answer is in general proportional to the product of all of the standard
deviations ...
for a princomp() fit, prod(x$sdev).  In general you can do this without
calculating
PCA explicitly -- if your data matrix is d, then
prod(sqrt(diag(eigen(vcov(d))$values)))
should do it.

  Of course, I haven't tested or proofread these suggestions carefully, use
at your
own risk ...

  
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