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Augmented dictionary learning for motion prediction

Developing accurate models and efficient representations of multivariate trajectories is important for understanding the behavior patterns of mobile agents. This work presents a dictionary learning algorithm for developing a part-based trajectory representation, which combines merits of the existing Markovian-based and clustering-based approaches. In particular, this work presents the augmented semi-nonnegative sparse coding (ASNSC) algorithm for solving a constrained dictionary learning problem, and shows that the proposed method would converge to a local optimum given a convexity condition. We consider a trajectory modeling application, in which the learned dictionary atoms correspond to local motion patterns. Classical semi-nonnegative sparse coding approaches would add dictionary atoms with opposite signs to reduce the representational error, which can lead to learning noisy dictionary atoms that correspond poorly to local motion patterns. ASNSC addresses this problem and learns a concise set of intuitive motion patterns. ASNSC shows significant improvement over existing trajectory modeling methods in both prediction accuracy and computational time, as revealed by extensive numerical analysis on real datasets.