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Entropy 2016, 18(9), 327; doi:10.3390/e18090327

Sparse Trajectory Prediction Based on Multiple Entropy Measures

School of Computer Science and Technology, China University of Mining and Technology, Xuzhou 221116, China
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Academic Editors: Badong Chen and Jose C. Principe
Received: 9 June 2016 / Revised: 29 August 2016 / Accepted: 30 August 2016 / Published: 14 September 2016
(This article belongs to the Special Issue Information Theoretic Learning)
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Abstract

Trajectory prediction is an important problem that has a large number of applications. A common approach to trajectory prediction is based on historical trajectories. However, existing techniques suffer from the “data sparsity problem”. The available historical trajectories are far from enough to cover all possible query trajectories. We propose the sparsity trajectory prediction algorithm based on multiple entropy measures (STP-ME) to address the data sparsity problem. Firstly, the moving region is iteratively divided into a two-dimensional plane grid graph, and each trajectory is represented as a grid sequence with temporal information. Secondly, trajectory entropy is used to evaluate trajectory’s regularity, the L-Z entropy estimator is implemented to calculate trajectory entropy, and a new trajectory space is generated through trajectory synthesis. We define location entropy and time entropy to measure the popularity of locations and timeslots respectively. Finally, a second-order Markov model that contains a temporal dimension is adopted to perform sparse trajectory prediction. The experiments show that when trip completed percentage increases towards 90%, the coverage of the baseline algorithm decreases to almost 25%, while the STP-ME algorithm successfully copes with it as expected with only an unnoticeable drop in coverage, and can constantly answer almost 100% of query trajectories. It is found that the STP-ME algorithm improves the prediction accuracy generally by as much as 8%, 3%, and 4%, compared to the baseline algorithm, the second-order Markov model (2-MM), and sub-trajectory synthesis (SubSyn) algorithm, respectively. At the same time, the prediction time of STP-ME algorithm is negligible (10 μ s ), greatly outperforming the baseline algorithm (100 ms ). View Full-Text
Keywords: sparse trajectory prediction; trajectory entropy; location entropy; time entropy; 2nd-order Markov model sparse trajectory prediction; trajectory entropy; location entropy; time entropy; 2nd-order Markov model
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Zhang, L.; Liu, L.; Xia, Z.; Li, W.; Fan, Q. Sparse Trajectory Prediction Based on Multiple Entropy Measures. Entropy 2016, 18, 327.

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