[R] Calculate Volume in a PCA

[Ben Bolker]

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 ...

  
-- 
View this message in context: http://old.nabble.com/Calculate-Volume-in-a-PCA-tp26154363p26155426.html
Sent from the R help mailing list archive at Nabble.com.