Low-rank approximation-based bidirectional linear discriminant analysis for image data

Dimensionality reduction methods for images directly without matrix-to-vector conversion have been widely concerned and achieved good classification results, especially for face recognition problem. However, the existing methods work in the column or/and row direction of images respectively, then project the given image onto the obtained left and right projective matrices to obtain the corresponding feature matrix. On the other hand, the low-rank approximation of matrix (LRAM) is a low-rank representation, which can approximate the original matrix as much as possible through a low-rank matrix and preserve the features in the original data. In this paper, we propose a low-rank approximation-based two-directional linear discriminant analysis method for image data, in which the left and right projection matrices are extracted simultaneously from the image data directly and the low-rank transformed feature matrices of training images are obtained by low-rank approximation of matrix. By minimizing the total reconstruction error and the within-class scatter of the transformed feature matrices and maximizing the between-class scatter of the transformed feature matrices, the proposed method can avoid huge feature matrix problem in some existing methods, and make full use of the discriminant and descriptive information of the images. An efficient iterative optimization algorithm is also devised to solve the proposed model. Experiment results on several datasets demonstrate the effectiveness and superiority of the proposed method.