Multiview Fisher Discriminant Analysis

CCA can be seen as a multiview extension of PCA, in which information from two sources is used for learning by finding a subspace in which the two views are most correlated. However PCA, and by extension CCA, does not use label information. Fisher Discriminant Analysis uses label information to find informative projections, which can be more informative in supervised learning settings. We show that FDA and its dual can both be formulated as generalized eigenproblems, enabling a kernel formulation. We derive a regularised two-view equivalent of Fisher Discriminant Analysis and its corresponding dual, both of which can also be formulated as generalized eigenproblems. We then show that these can be cast as equivalent disciplined convex optimisation problems, and subsequently extended to multiple views. We show experimental results on an EEG dataset and part of the PASCAL 2007 VOC challenge dataset.