Face and expression recognition problem can be converted into superposition of low-rank matrix and sparse error matrix, which have the merits of robustness to occlusion and disguise. Low-rank matrix manifests neutral facial image and sparse matrix captures emotional expression with respect to whole image. To separate these matrices, the problem is formulated to minimize the nuclear norm and L1 norm, then can be solved by using a closed-form proximal operator which is called Singular Value Thresholding (SVD). However, this conventional approach has high computational complexity since it requires computation of singular value decomposition of large sized matrix at each iteration. In this paper, to reduce this computational burden, a fast approximation method for SVT is proposed, utilizing a suitable low-rank matrix approximation involving random projection. Basically, being associated with sampling, a low-rank matrix is modeled as bilateral factorized matrices, then update these matrices with greedy manner. Experiments are conducted on publicly available different dataset for face and expression recognition. Consequently, proposed algorithm results in the improved recognition accuracy and also further speeding up the process of approximating low-rank matrix, compared to the conventional SVT based approximation methods. The best recognition accuracy score of 98.1% in the JAFFE database is acquired with our method about 55 times faster than SVD based method.