I'd be curious if the Fisherfaces are overlearning the data in order to have such a low error rate?

FLD’s are really good at what they do – discriminate. For problems with 2 classes I would expect FLD to do better. And for their experiments, the data had 5 classes. I have a hard time picturing how FLD’s perform a) as the number of classes goes up and b) when non-faces are thrown into the mix.
For example, in their 2-class “with glasses” or “without glasses” setup, what happens when you give it a picture of a car? For PCA I would think “okay this picture doesn’t have any of the eigenfaces” and maybe the system could detect that. But with FLD, might it be tricked into thinking “yep, this car definitely has glasses on” ?

This paper seems to be claiming that proximity to example images is not a good classifier, which in my experience (cse253 last quarter) is true, and that proximiy to a linear subspace is a godd classifier if images are of lambertian surfaces (aka flat-shaded surfaces). But their comparison of Fisherfaces and Eigenfaces seems to ignore this to the extent that those techniques are used for dimension reduction and then a nearest-neighbor classifier is used. It is true that this demonstrates that FLD somewhat reduces the problem of proximity-to-subspace to proximity-to-prototype, given that the projected subspace is adequately populated by prototypes, but in my opinion, a more fair comparison would have been to compare Fisherfaces to a classifier using PCA for dimension reduciton, and then the linear-subspaces classifier. Then there would be no need for the heuristic dropping of 3 largest components, but I'm not sure the subspaces would remain subspaces when projected down. This could combine the competitiveness of the linear-subspaces classifier with the efficiency of the eigenfaces classifier.

The results in this paper all have some counter intuitive element. First is the performance of linear subspace. The assumption that face is a lambartian surface is a very ideal case, especially in a varying lighting case, the main features that face would show would be in some sense non-lambartian, namely selfshadows etc.
second, the performance of PCA with and without the first three components. In the paper they mention that it is somewhat safe to assume that the first three components are mostly produced by the change in lighting, ok .. but .. why does it work better in change in expression case also?
Third, Full face and Cropped faces, I would expect the results using PCA will be better in the cropped face, since it will be able to capture in between classes better in that case. It is a bit surprizing that all the methods perform better with full face.

Also in the expresion for Scatter matrix, after the expression it says "where c is the number of classes" but there is no c in the expression and to get overall scatter, not just within class scatter, we don't need c anyways.

Overall, it is good method, but just a bit surprizing that it works as well they have shown in the paper.

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