I have conducted a principal component analysis where I have groups of data (countries). I calculated how much of the total variance do the axes explain. Is there a way to calculate the proportion of variance that the dimensions explain for each country without conducting a PCA for each country?
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Sure, you could use an [SVD](https://stats.stackexchange.com/q/134282/930). Without using some sort of projection method, I'm afraid it will be hard to compute the proportion variance explained by orthogonal components. Or maybe you're just asking if you could account for the grouping factor in the original PCA space? – chl Oct 13 '20 at 17:07