Nuclear norm-based matrix regression preserving embedding for face recognition

Abstract Recently, using linear reconstruction technique to construct intrinsic graph for projection-based dimensionality reduction (DR) has aroused broad interest in face recognition. However, current methods either lack robustness to corruptions or require to perform vectorization which causes loss of local geometrical information of images. To this end, a novel nuclear norm-based matrix regression preserving embedding (NN-MRPE) method is proposed in this paper. First, NN-MRPE constructs an intrinsic graph by using the nuclear norm to evaluate the residual errors to resist data corruptions. Second, a matrix-based embedding cost function is formulated to seek two transformation matrices which can preserve the geometrical structure reflected by the intrinsic graph exactly. Finally, based on the linear regression theory, we summarize a general DR framework called linear regression preserving embedding that preserves the intrinsic structure of data by recovering the reconstruction relationship in the original space. Specifically, many existing approaches are the special cases of the linear regression preserving embedding. Experiments on five public face databases with different types of corruptions are conducted to demonstrate the efficiency of the proposed NN-MRPE method.