A Deterministic Construction of Projection matrix for Adaptive Trajectory Compression

Compressive Sensing, which offers exact reconstruction of sparse signal from a small number of measurements, has tremendous potential for trajectory compression. In order to optimize the compression, trajectory compression algorithms need to adapt compression ratio subject to the compressibility of the trajectory. Intuitively, the trajectory of an object moving in starlight road is more compressible compared to the trajectory of a object moving in winding roads, therefore, higher compression is achievable in the former case compared to the later. We propose an in-situ compression technique underpinning the support vector regression theory, which accurately predicts the compressibility of a trajectory given the mean speed of the object and then apply compressive sensing to adapt the compression to the compressibility of the trajectory. The conventional encoding and decoding process of compressive sensing uses predefined dictionary and measurement (or projection) matrix pairs. However, the selection of an optimal pair is nontrivial and exhaustive, and random selection of a pair does not guarantee the best compression performance. In this paper, we propose a deterministic and data driven construction for the projection matrix which is obtained by applying singular value decomposition to a sparsifying dictionary learned from the dataset. We analyze case studies of pedestrian and animal trajectory datasets including GPS trajectory data from 127 subjects. The experimental results suggest that the proposed adaptive compression algorithm, incorporating the deterministic construction of projection matrix, offers significantly better compression performance compared to the state-of-the-art alternatives.