Robust L1-norm two-dimensional collaborative representation-based projection for dimensionality reduction

Collaborative representation-based projection (CRP) is a well-known dimensionality reduction technique, which has been proved to have better performance than sparse representation-based projection (SRP) in the fields of recognition and computer vision. However, classical CRP is sensitive to noises and outliers since its objective function is based on L2-norm, and it will suffer from the curse of dimensionality as it is used for images processing. In this paper, a novel CRP model, named L1-norm two-dimensional collaborative representation-based projection (L1-2DCRP) and an efficient iterative algorithm to solve it are proposed. Different from conventional CRP, the optimal problem in our proposed model is a L1-norm-based maximization and the vector data is extended to matrix date. The proposed algorithm is theoretically proved to be monotonously convergent, and more robust to noises and outliers since L1-norm is used. Experimental results on CMU Multi-PIE, COIL20, FERET and ORL face databases validate the effectiveness of L1-2DCRP compared with several state-of-the-art approaches.