This paper proposes a novel dynamic sparse representation-based classification scheme to treat the problem of interaction action analysis between persons using sparse representation. The occlusion problem and the difficulty to model complicated interactions are the major challenges in person-to-person action analysis. To address the occlusion problem, the proposed scheme represents an action sample in an over-complete dictionary whose base elements are the training samples themselves. This representation is naturally sparse and makes errors (caused by different environmental changes like lighting or occlusions) sparsely appear in the training library. Because of the sparsity, it is robust to occlusions and lighting changes. The difficulty of complicated action modeling can be tackled by adding more examples to the over-complete dictionary. Thus, even though the interaction relations are complicated, the proposed method still works successfully to recognize them and can be easily extended to analyze action events among multiple persons.