Improving the discriminant ability of local margin based learning method by incorporating the global between-class separability criterion

Many applications in machine learning and computer vision come down to feature representation and reduction. Manifold learning seeks the intrinsic low-dimensional manifold structure hidden in the high-dimensional data. In the past few years, many local discriminant analysis methods have been proposed to exploit the discriminative submanifold structure by extending the manifold learning idea to supervised ones. Particularly, marginal Fisher analysis (MFA) finds the local interclass margin for feature extraction and classification. However, since the limited data pairs are employed to determine the discriminative margin, such method usually suffers from the maladjusted learning as we introduced in this paper. To improve the discriminant ability of MFA, we incorporate the marginal Fisher idea with the global between-class separability criterion (BCSC), and propose a novel supervised learning method, called local and global margin projections (LGMP), where the maladjusted learning problem can be alleviated. Experimental evaluation shows that the proposed LGMP outperforms the original MFA.