Calculate Volume in a PCA
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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