Abstract: A novel supervised linear method based on Locality Preserving Projection (LPP) of reducing dimensionality is proposed for face recognition. In this study, the nearest neighbor graph of LPP is split into within-class graph and between-class graph according to the class label information of samples. After optimizing, the intrinsic local neighbor structure of the samples of same class is maintained and the distances between them are decreased. Meanwhile, the distances between the samples of different class are maximized to increase the space of the distribution of all kinds of samples, and thus the discriminability of the embedding is enhanced. In addition, adaptive neighborhood is applied to the construction of the graph, with the characterization for the sparsity of the sample improved. Experimental results on the two open face databases, Extended Yale B and CMU PIE face database, show that the proposed algorithm improves the accuracy of face recogntion effectively.