The multiclass classification problem is decomposed into two parts in this paper. The first step is to find a collaborative representation. The idea here is that a collaborative representation sees an example as a mixture of samples from a dictionary and makes its classification based on these various representations.

With the collaborative representation in hand, classification proceeds by selecting the class that leaves the smallest residual. The paper proposes a classifier that the authors call the collaborative representation optimized classifier (CROC) that provides an optimal combination of the nearest subspace classifier (NSC) and the collaborative representation classifier. The sparse representation classifier (SRC) and the NSCs are special cases of CROC, which is effectively a weighted linear combination of these two.

The optimization then consists of finding the optimal weighting. The authors consider face recognition and digit recognition applications. For face recognition, the number of training images per class is usually small; for digit recognition, the number is large, which requires the use of some dimensional reduction to obtain the collaborative representation. The paper shows that better results are obtained by CROC than either SRC or NSC, although in both cases, NSC receives a heavier weighting than SRC; this is still different between the two examples.

The paper is quite densely written, and some supplementary material on the SRC is available at http://dx.doi.org/10.1109/TPAMI.2013.236. The reader can thus, with appropriate effort, follow the material. Although the idea of this kind of boosting is not new, the results should be of interest to those in the field of classification.