Hi all, I am using nsprcomp() from nsprcomp package to run sparse PCA. The
output is very much like regular PCA by prcomp() in that it provides "sdev" for
standard deviation of principle components (PC).
For regular PCA by prcomp(), we can easily calculate the percent of total
variance explained by the first k PCs by using cumsum(obj$sdev^2) because these
PCs are independent of each other so you can simply add up the variance of
these PCs. For sparse PCA, as far as I understand, the generated PCs are not
independent of each other anymore, so you can not simply add up variances to
calculate percentage of variance explained by the first k PCs. For example, in
the package of elasticnet where spca() also performs sparse PCA, one of the
output from spca() is "pev" for percent explained variation which is based on
so-called "adjusted" variance that adjusted for the fact that these variances
of PCs are not independent anymore.
My question is for nsprcomp, how can I calculate percent explained variation by
using "sdev" when I know these PCs are not independent of each other?
Thanks!
John
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