Principal component analysis is a group action of SO(N) which minimizes an entropy function
T. Takahashi · 2005
Gives a new interpretation for PCA (principal component analysis) by defining a quantity which evaluates the "goodness" of the relationship between a data set and a basis. The quantity takes the same form of entropy in Shannon's information theory. It is showed that PCA is equivalent to a group action such that entropy is minimized.