The commonly used regression models are sensitive to abnormal data due to the L

2

norm

and the number of projections obtained by the algorithm is limited by the number of sample classes. To address these problems

the joint sparse robust discriminant regression model based on L

1

graph is proposed. L

1

graph is constructed based on sparse representation

which can adaptively find the nearest neighbor of the data and preserve the local geometric structure of the data. The model uses the L

2

1

norm to represent the loss function and integrates the L

1

graph to enhance the robustness of the algorithm. The L

2

1

-norm penalty term can guarantee the joint sparsity a

nd the robustness of effective feature extraction. The iterative method is used to solve the model.Experiments on face database with outliers verify the performance of the algorithm

and show the efficiency of dimensionality reduction and the improvement of discriminant ability.