Face recognition with Locality Sensitive Discriminant Analysis based on matrix representation
Locality sensitive discriminant analysis (LSDA) algorithm is a new data analysis tool for studying the class relationship between data points, which can utilize local geometry structure of the data manifold and discriminant information at the same time. A major disadvantage of LSDA is it that can only deal with vector data, and thus is often confronted with singularity problem. In this paper, an extension of LSDA is proposed, called two-dimensional locality sensitive discriminant analysis (2DLSDA), which is directly based on 2D image matrices for face recognition, can overcome the singularity problem and utilize the spatial information among pixels more effectively. Besides, based on the Schur decomposition, the projection matrices can be obtained efficiently with high numerical stability, and orthogonality of projection matrix is guaranteed. Experiments on both ORL and Yale datasets demonstrate that the proposed method can achieve better performance than PCA, LDA and LSDA methods.