Graph regularized discriminant analysis and its application to face recognition

Linear Discriminant Analysis (LDA) is a powerful technology for supervised dimensionality reduction, however, it only captures the extrinsic (or global) structure in the data and fails to discover the intrinsic structure of the data manifold. In this paper, we develop a new linear supervised dimensionality reduction method, called Graph Regularized Discriminant Analysis(GRDA), which respects both extrinsic and intrinsic structure in the data. In particular, a regularization term, incorporating the manifold structure, is introduced into the objective function of LDA. The formulation allows us to achieve a more discriminative subspace by simultaneously considering the graph preserving and the global LDA criteria. We then apply the proposed GRDA algorithm to face recognition by exploiting the local dissimilarity of face images in different classes. Experimental results clearly show that the proposed GRDA method outperforms many state-of-the-art face recognition algorithms.