Sparse Support Matrix Machine.

•We propose a novel matrix classifier to simultaneously leverage the structural information within matrices and select useful features.•We regularize the combination of nuclear norm and l1 norm of the regression matrix and develop an efficient solver based on GFB splitting framework.•We also provide a theoretical guarantee for the global convergence and analyze the excess risk statistically.•We extensively evaluate the proposed SSMM on four real datasets. The results show that SSMM achieves competitive performance.