I have some doubts on Q-mode and R-mode principal component analysis (PCA). I've read from different sources that:
- Q-mode PCA is equivalent to R-mode PCA of the transposed data matrix!
- Q-mode PCA (with squared Euclidean distance) is equivalent to R-mode PCA (of the covariance matrix)!
It seems to me that these two are not equivalent statements. Can someone clarify that? Q-mode(SEuclid) = R-mode(covar) is the only instance where (proper) Q-mode and R-mode PCAs give the same results?
If I perform an R-mode PCA on the transposed data matrix, wouldn't I work on a $n<p$ matrix? Would it be ok to perform a PCA in that case? If yes, what's the difference from performing R-mode PCA on a normal $n<p$ data matrix? If no, do I need more variables than observations for running Q-mode PCA?