Kernel sparse representation based classification for undersampled problem

Sparse representation for classification (SRC) has attracted much attention in recent years. It usually performs well under the following assumptions. The first assumption is that each class has sufficient training samples. In other words, SRC is not good at dealing with the undersampled problem, i.e., each class has few training samples, even single sample. The second one is that the sample vectors belonging to different classes should not distribute on the same vector direction. However, the above two assumptions are not always satisfied in real-world problems. In this paper, we propose a novel SRC based algorithm, i.e., kernel sparse representation based classifier for undersampled problem (KSRC-UP) to perform classification. It does not need the above assumptions in principle. KSRC-UP can deal well with the small scale and high dimensional real world data sets. Experiments on the popular face databases show that our KSRC-UP method can perform better than other SRC methods.