Collaborative representation, sparsity or nonlinearity: What is key to dictionary based classification?

Recent studies have suggested that the critical aspect of sparse representation-based classification (SRC) is collaborative representation, rather than sparsity. This has given rise to fast collaborative representation-based classification using 2-norm regularized least squares (CRC-RLS). This paper digs deeper into the difference between SRC and CRC-RLS. We show that linear coding schemes such as CRC-RLS share a common pairwise boundary class B. Moreover, the corresponding pairwise classifiers can be realized by quadratic SVMs. Using three datasets, we show empirically that collaborative representations are not always required, and that a quadratic SVM has superior generalization over CRC-RLS, with fast classification times. However, SRC exhibits the best prediction accuracy. This leads us to posit that the nonlinear coding of SRC is a key attribute.