Multimodal Oriented Discriminant Analysis

Linear discriminant analysis (LDA) has been an active topic of research during the last century. However, the existing algorithms have several limitations when applied to visual data. LDA is only optimal for Gaussian distributed classes with equal covariance matrices, and only classes-1 features can be extracted. On the other hand, LDA does not scale well to high dimensional data (over-fitting), and it cannot handle optimally multimodal distributions. In this paper, we introduce Multimodal Oriented Discriminant Analysis (MODA), an LDA extension which can overcome these drawbacks. A new formulation and several novelties are proposed: • An optimal dimensionality reduction for multimodal Gaussian classes with different covariances is derived. The new criteria allows for extracting more than classes-1 features. • A covariance approximation is introduced to improve generalization and avoid over-fitting when dealing with high dimensional data. • A linear time iterative majorization method is suggested in order to find a local optimum. Several synthetic and real experiments on face recognition show that MODA outperform existing LDA techniques.