Hang Cheng, Shixiong Wang and Naiyang Guan, National Innovation Institute of Defense Technology, Academy of Military Sciences, China

Non-negative matrix factorization (NMF) is an effective dimension reduction tool widely used in pattern recognition and computer vision. However, conventional NMF models are neither robust enough, as their objective functions are sensitive to outliers, nor discriminative enough, as they completely ignore the discriminative information in data. In this paper, we proposed a robust discriminative NMF model (RDNMF) for learning an effective discriminative subspace from noisy dataset. In particular, RDNMF approximates observations by their reconstructions in the subspace via maximum correntropy criterion to prohibit outliers from influencing the subspace. To incorporate the discriminative information, RDNMF builds adjacent graphs by using maximum correntropy criterion based robust representation, and regularizes the model by margin maximization criterion. We developed a multiplicative update rule to optimize RDNMF and theoretically proved its convergence. Experimental results on popular datasets verify the effectiveness of RDNMF comparing with conventional NMF models, discriminative NMF models, and robust NMF models.

Dimension reduction, non-negative matrix factorization, maximum correntropy criterion, supervised learning, margin maximization.