Abstract: To tackle the insufficiency problem of local linear embedding(LLE) algorithm and maximum margin criterion(MMC) algorithm in feature extraction,an efficient dimensional reduction and classification algorithm,local graph embedding feature extraction method based on maximum margin criterion(LGE/MMC),is presented with applications in face recognition.The goal of this algorithm was to construct the intrinsic graph and penalty graph,with the preservation of nearest neighbor premise.In the intrinsic graph,the nonlinear structure is discovered in the high dimensional data space by the local symmetry of the linear restructuring,which causes the similar samples gathering together as much as possible.At the same time,different class samples are as far as possible from each other in the penalty graph.In this method,the "small size sample" problem is solved by the employment of MMC and the neighborhood relationship is better described by an adequate modification of the adjacency matrix.The results of face recognition experiments on ORL,Yale and AR face databases demonstrate the effectiveness of the proposed method in comparison with the DLA and LLE+LDA method.