In real-world action recognition problems, low-level features cannot adequately characterize the rich spatial-temporal structures in action videos. In this work, we encode actions based on attributes that describes actions as high-level concepts: \textit{e.g.}, jump forward and motion in the air. We base our analysis on two types of action attributes. One type of action attributes is generated by humans. The second type is data-driven attributes, which is learned from data using dictionary learning methods. Attribute-based representation may exhibit high variance due to noisy and redundant attributes. We propose a discriminative and compact attribute-based representation by selecting a subset of discriminative attributes from a large attribute set. Three attribute selection criteria are proposed and formulated as a submodular optimization problem. A greedy optimization algorithm is presented and guaranteed to be at least (1-1/e)-approximation to the optimum. Experimental results on the Olympic Sports and UCF101 datasets demonstrate that the proposed attribute-based representation can significantly boost the performance of action recognition algorithms and outperform most recently proposed recognition approaches.