Abstract: Nuclear norm based matrix regression(NMR) is robust to the errors caused by facial occlusion and illumination changes.This paper analyzed the underlying mechanism of NMR.Firstly,the nuclear norm measures the energies of the error caused by noises in the principle orientations,which usually exclude the influence of the common noises.Seco-ndly,the nuclear norm embeds the spatial structure of noises, which is very important to represent and exclude the noises.However,it is insufficient to eliminate the influence of the noises completely by only embedding the spatial structure of noises.As high-dimensional gradient orientation(HGO) has strong ability in noise cancellation, this paper embedded HGO into NMR and proposed a novel regression method called HGO-NMR.Experiments show that HGO-NMR outperforms NMR.The critical significance of HGO-NMR is that the noise spatial structure and the noise cancellation mechanism are equally important for face recognition system for reality,and only using one of the two mechanisms will lead to unstable recognition performance.

Key words: Face recognition,Image gradient orientation,Nuclear norm,Matrix regression