  Sparse representation based classification (SRC) has been proved to be a
simple, effective and robust solution to face recognition. As it gets popular,
doubts on the necessity of enforcing sparsity starts coming up, and primary
experimental results showed that simply changing the $l_1$-norm based
regularization to the computationally much more efficient $l_2$-norm based
non-sparse version would lead to a similar or even better performance. However,
that's not always the case. Given a new classification task, it's still unclear
which regularization strategy (i.e., making the coefficients sparse or
non-sparse) is a better choice without trying both for comparison. In this
paper, we present as far as we know the first study on solving this issue,
based on plenty of diverse classification experiments. We propose a scoring
function for pre-selecting the regularization strategy using only the dataset
size, the feature dimensionality and a discrimination score derived from a
given feature representation. Moreover, we show that when dictionary learning
is taking into account, non-sparse representation has a more significant
superiority to sparse representation. This work is expected to enrich our
understanding of sparse/non-sparse collaborative representation for
classification and motivate further research activities.
