I like the main idea of the paper and I think it adresses an example of a problem faced in many areas of computer vision and learning. It seems that when a technique is found to work well (here PCA), many will apply it to every problem imaginable without concern for the actual properties of the data or the underlying assuptions of the algorithm in question. I like that they provide a reformulation for the algorithm that is tuned to specific types of data.

This reminds me a bit of Koenderink's eccv paper that criticized the use of euclidean distances in the evaluation of pixels in an image. However, I think he may have better luck in coining a new term than this paper, but both were able to confuse me a bit with their math.