In this paper, we propose a novel method, called local non-negative matrix factorization (LNMF), for learning spatially localized, parts-based subspace representation of visual patterns. An objective function is defined to impose a localization constraint, in addition to the non-negativity constraint in the standard NMF. This gives a set of bases which not only allows a non-subtractive (part-based) representation of images but also manifests localized features. An algorithm is presented for the learning of such basic components. Experimental results are presented to compare LNMF with the NMF and PCA methods for face representation and recognition, which demonstrates advantages of LNMF.