A group-based signal filtering approach for trajectory abstraction and restoration

Trajectory abstraction is used to summarize the large amount of information delivered by the trajectory data, and trajectory restoration is used to reconstruct lost parts of trajectories. To cope with complex trajectory data, in this paper, we propose a new strategy for abstracting and restoring trajectories from the perspective of signal processing. That is, trajectories are treated as signals that bear copious information that varies with time and space, and information filtering is exploited to concisely communicate the trajectory data. As for trajectory abstraction, the resampling of trajectory data is first introduced based on achieving the minimum Jensen–Shannon divergence of the trajectories before and after being resampled. Then, a non-local filtering approach is developed to perform wavelet transformations of similarity groups of these resampled trajectories to produce the trajectory summaries. Trajectory abstraction can not only offer multi-granularity summaries of trajectory data, but also identify outliers by utilizing a probabilistic definition of a group of trajectories and the Shannon entropy. Furthermore, to handle incomplete trajectory data for which some sample points are lost, the proposed non-local filtering idea is exploited to restore the incomplete data. Extensive experimental studies have shown that the proposed trajectory abstraction and restoration can obtain very encouraging results, in terms of both objective evaluation metrics and subjective visual effects. To the best of our knowledge, this is the first attempt to deploy the group-based signal filtering technique in the context of dealing with trajectory data. In addition, as a preprocessing step, the proposed trajectory abstraction can be employed to improve the performance of trajectory clustering.