Understanding human activity based on sensor information is required in many applications and has been an active research area. With the advancement of depth sensors and tracking algorithms, systems for human motion activity analysis can be built by combining off-the-shelf motion tracking systems with application-dependent learning tools to extract higher semantic level information. Many of these motion tracking systems provide raw motion data registered to the skeletal joints in the human body. In this paper, we propose novel representations for human motion data using the skeletonbased graph structure along with techniques in graph signal processing. Methods for graph construction and their corresponding basis functions are discussed. The proposed representations can achieve comparable classification performance in action recognition tasks while additionally being more robust to noise and missing data.