In recent years, the growing attention in the study of the compressive sensing (CS) theory suggested a novel classification algorithm called sparse representation-based classifier (SRC), which obtained promising results by casting classification as a sparse representation problem. Whereas SRC has been applied to different fields of applications and several variations of it have been proposed, less attention has been given to its critical parameters, that is, measurements correlated to its performance. This work underlines the differences between CS and SRC, it gives a mathematical definition of five measurements possible correlated to the performance of SRC and identifies three of them as critical parameters. The knowledge of the critical parameters is necessary to fuse multiple scores of SRC classifiers allowing for classification. The authors addressed the problem of two-dimensional face classification: using the Extended Yale B dataset to monitor the critical parameters and the Extended Cohn-Kanade database to test the robustness of SRC with emotional faces. Finally, the authors increased the initial performance of the holistic SRC with a block-based SRC, which uses one critical parameter for automatic selection of the most successful blocks.