Conventional graph embedding framework uses the Euclidean distance to determine the similarities of neighbor samples, which causes the graph structure to be sensitive to outliers and lack physical interpretation. Moreover, the graph construction suffers from the difficulty of neighbor parameter selection. Although sparse representation (SR) based graph embedding methods can automatically select the neighbor parameter, the computational cost of SR is expensive. On the other hand, most discriminant projection methods fail to perform feature selection. In this paper, we present a novel joint discriminant analysis and feature selection method that employs regularized least square for graph construction and -norm minimization on projection matrix for feature selection. Specifically, our method first uses the regularized least square coefficients to measure the intraclass and interclass similarities from the viewpoint of reconstruction. Based on this graph structure, we formulate an object function with scatter difference criterion for learning the discriminant projections, which can avoid the small sample size problem. Simultaneously, the -norm minimization on projection matrix is applied to gain row-sparsity for selecting useful features. Experiments on two face databases (ORL and AR) and COIL-20 object database demonstrate that our method not only achieves better classification performance, but also has lower computational cost than SR.