Action classification is an important component of human-computer interaction. Trajectory classification is an effective way of performing action recognition with significant success reported in the literature. We compare two different representation schemes, raw multivariate time-series data and the covariance descriptors of the trajectories, and apply sparse representation techniques for classifying the various actions. The features are sparse coded using the Orthogonal Matching Pursuit algorithm, and the gestures and actions are classified based on the reconstruction residuals. We demonstrate the performance of our approach on standardized datasets such as the Australian Sign Language (AusLan) and UCF Motion Capture datasets, collected using high-quality motion capture systems, as well as motion capture data obtained from a Microsoft Kinect sensor.