  Sparse Representation (or coding) based Classification (SRC) has gained great
success in face recognition in recent years. However, SRC emphasizes the
sparsity too much and overlooks the correlation information which has been
demonstrated to be critical in real-world face recognition problems. Besides,
some work considers the correlation but overlooks the discriminative ability of
sparsity. Different from these existing techniques, in this paper, we propose a
framework called Adaptive Sparse Representation based Classification (ASRC) in
which sparsity and correlation are jointly considered. Specifically, when the
samples are of low correlation, ASRC selects the most discriminative samples
for representation, like SRC; when the training samples are highly correlated,
ASRC selects most of the correlated and discriminative samples for
representation, rather than choosing some related samples randomly. In general,
the representation model is adaptive to the correlation structure, which
benefits from both $\ell_1$-norm and $\ell_2$-norm.
  Extensive experiments conducted on publicly available data sets verify the
effectiveness and robustness of the proposed algorithm by comparing it with
state-of-the-art methods.
