Null space based discriminant sparse representation large margin for face recognition

In this paper, we propose a novel subspace learning algorithm, termed as null space based discriminant sparse representation large margin (NDSLM). There are two contributions in the paper. First, we propose a new expectation to obtain the neighborhood information for large margin subspace learning, i.e., the within-neighborhood scatter and between-neighborhood scatter are modeled by the sparse reconstruction weights of the samples from the same class and different classes, respectively. Since the neighborhood information formed by sparse representation can capture non-linearities in the data, the proposed method possesses more discriminative information than the traditional large margin learning methods with the expectation using Euclidean distance, etc. Second, the large margin information integrated into the model of Fisher criterion makes the discriminating power of NDSLM further boosted. NDSLM addresses the small sample size problem by solving an eigenvalue problem in null space. Experiments on ORL, Yale, AR, Extended Yale B and CMU PIE five face databases are performed to evaluate the proposed algorithm and the results demonstrate the effectiveness of NDSLM.