Face recognition (FR) is an active yet challenging topic in computer vision applications. As a powerful tool to represent high dimensional data, recently sparse representation based classification (SRC) has been successfully used for FR. This paper discusses the dimensionality reduction (DR) of face images under the framework of SRC. Although one important merit of SRC is that it is insensitive to DR or feature extraction, a well trained projection matrix can lead to higher FR rate at a lower dimensionality. An SRC oriented unsupervised DR algorithm is proposed in this paper and the experimental results on benchmark face databases demonstrated the improvements brought by the proposed DR algorithm over PCA or random projection based DR under the SRC framework.