[qqqwwweeerrr]

Unless you are strictly talking about predictive modeling, I would disagree with this. PCA just tries to represent N-dimensional observations in a k < N dimensional subspace (for a given k) such that it captures the most variation. This does not mean that any obtained component loadings refer to anything real or meaningful.

[wrp]

To clarify your point, we need to distinguish between pruning dimensions and projecting onto a k < N set of new orthogonal dimensions. The name of PCA does make it sound like you are selecting dimensions.

[jackthetab]

> The name of PCA does make it sound like you are selecting dimensions.

I certainly thought that!

Using somes terms from the previous comment, does this mean that the k < N subspace is not (necessarily) a subset of the N-space? Or is the subspace a subset of the data with a different coordinate system?

(Yes, I'm still trying to intuitively grasp these ideas.)