Discriminant Learning Through Multiple Principal Angles for Visual Recognition

Canonical correlation has been prevalent for multiset-based pairwise subspace analysis. As an extension, discriminant canonical correlations (DCCs) have been developed for classification purpose by learning a global subspace based on Fisher discriminant modeling of pairwise subspaces. However, the discriminative power of DCCs is not optimal as it only measures the “local” canonical correlations within subspace pairs, which lacks the “global” measurement among all the subspaces. In this paper, we propose a multiset discriminant canonical correlation method, i.e., multiple principal angle (MPA). It jointly considers both “local” and “global” canonical correlations by iteratively learning multiple subspaces (one for each set) as well as a global discriminative subspace, on which the angle among multiple subspaces of the same class is minimized while that of different classes is maximized. The proposed computational solution is guaranteed to be convergent with much faster converging speed than DCC. Extensive experiments on pattern recognition applications demonstrate the superior performance of MPA compared to existing subspace learning methods.