  Many classification approaches first represent a test sample using the
training samples of all the classes. This collaborative representation is then
used to label the test sample. It was a common belief that sparseness of the
representation is the key to success for this classification scheme. However,
more recently, it has been claimed that it is the collaboration and not the
sparseness that makes the scheme effective. This claim is attractive as it
allows to relinquish the computationally expensive sparsity constraint over the
representation. In this paper, we first extend the analysis supporting this
claim and then show that sparseness explicitly contributes to improved
classification, hence it should not be completely ignored for computational
gains. Inspired by this result, we augment a dense collaborative representation
with a sparse representation and propose an efficient classification method
that capitalizes on the resulting representation. The augmented representation
and the classification method work together meticulously to achieve higher
accuracy and lower computational time compared to state-of-the-art
collaborative representation based classification approaches. Experiments on
benchmark face, object and action databases show the efficacy of our approach.
