This paper provides a novel and unified framework of representation based classification technique. The proposed atomic representation based classification (ARC) framework includes, but not limited to, sparse representation based classification (SRC), low-rank representation based classification (LRRC) as special cases. Despite good performance, most existing classification methods are heavily reliant on the assumption that the training set should cover all possible classes appeared in the test set. Thus, they may fail when there exists a new class that is not observed in the training set. To remedy this drawback, the ARC methods are extended to tackle more practical and tougher situation, in which training samples from only K - 1 classes are available to classify test samples from K classes. The experimental results using simulated and real data sets demonstrate the effectiveness of the proposed method.