Abstract: Considering the discriminant projection methods based on graph embedding are sensitive to the neighbor parameter and the fact that there is no sufficient class-label information of samples in practical applications which has an impact on the performance of graph embedding based methods, a semi-supervised discriminant analysis method based on adaptive neighbor selection and low-rank representation is proposed. The method uses all the intraclass samples to construct the intraclass graph which can characterize the intraclass compactness, and simultaneously adaptively selects the interclass samples within the neighborhood produced by the farthest intraclass sample to construct the interclass graph which is used to characterize the interclass separability. Furthermore, the low-rank representation approach is applied to mine the latent low-rank structure of unlabeled samples and thus preserve the global similarity relationship of samples. Experimental results on ORL and FERET face databases demonstrate the effectiveness of our method and the robustness to noise.