Summary: Sparsity preserving projection (SPP) is an unsupervised algorithm and does not need to label information. The process of solving sparse coefficients using SPP needs relatively large amount of calculation. Moreover, most of projection algorithms of the sparse representation do not reflect well the mapping relationship between spatial data. In order to better reflect the mapping relationship between spatial data, we propose a variable space collaborative representation discriminant analysis algorithm. Firstly, the original data are mapped into the PCA space to remove redundant information. Secondly, the sparse weights are solved by the \({L_2}\) norm, and the mapping matrix is calculated by using the supervised objective function proposed in this paper. Thirdly, we update sparse weights in mapping space. Finally, we obtain the final mapping matrix based on updated sparse weights and supervised objective function. Test results on the FERET face database, AR face database and ORL face database verify the effectiveness of the algorithm.