With the rapid development of science and technology and the sharp increase of data dimensions, it is difficult for traditional dimensionality reduction algorithms to find the optimal subspace of the data, which seriously affects the performance of the classifier. This paper proposes a local ratio sum discriminant analysis based on adaptive subspace graph. The ratio sum discriminant analysis considering the local structure is proposed; the alternative iterative optimization method is used to avoid the suboptimal solution found by the existing ratio sum optimization methods; the nearest neighbor similarity graph is learned in the optimal subspace instead of the original space, so as to avoid it. Influenced by the original spatial noise points; the Shannon entropy constraint is introduced to avoid trivial solutions; finally, the samples are projected to the optimal subspace. On synthetic datasets and face datasets, the proposed algorithm is tested with a large number of SOTA discriminant analysis algorithms for classification tasks. A large number of experimental results show that the proposed algorithm can learn a projection subspace with better discriminant performance and has better classification effect.