[jacobolus]

> If you understand PCA as "take the SVD of the data", then the operations seem arbitrary. But if you understand it as, "construct a low-rank approximation in the L2 sense to the data, or its covariance", then it's not.

Those are the same thing. Is your first case just a reader who has no idea what the SVD is?

[mturmon]

Yes, they are both descriptions of the same thing. I'm trying to say that PCA does have a justification. It's not just an "arbitrary linear algebra operation", although the application of the SVD algorithm to perform PCA can be presented that way.