Abstract: Although the parts-based representation results in strong robustness in image processing，the local con-straint in non-negative matrix factorization (NMF) is implicit，which leads to insufficient uniqueness and locality．Meanwhile，as two important property indexes，locality and discriminant in feature extraction are seldom considered in NMF simultaneously． In order to solve this problem，a discriminative NMF on the basis of max-margin coding is pro-posed． In this method，image data are regarded as a 2D network of pixels，and，on the basis of network knowledge，spatial information is embedded into basis images，which not only imposes an explicit local constraint but also com-pensates the spatial information loss caused by data vectorization． Additionally，an extra 1D space learned from max-margin constraint is adopted to balance the effects of reconstruction error and discriminative constraint on basis ima-ges． Experimental results on AR and extended YaleB databases for face recognition show that，in comparison with NMF and some of its variants，the proposed max-margin coding-based spatial NMF is more robust．

Key words: pattern classification, non-negative matrix factorization, spatial constraint, discriminative subspace representation, max-margin constraint