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 ).
Highlights
As the usage of Global Positioning System (GPS) and smart mobile devices (SMD) becomes a part of our daily lives, we benefit increasingly from various types of location-based services (LBSs), such as route finding and location-based social networking
Lian et al [3] put forward a collaborative exploration and periodically returning model (CEPR) exploiting a novel problem, exploration prediction (EP), which forecasts whether people will seek unvisited locations to visit
The remainder of this paper is organized as follows: in Section 2, we introduce the spatial iterative grid partition and representations of trajectory sequences with time; in Section 3, the trajectory synthesis based on the L-Z entropy estimator is introduced; in Section 4, we define the location entropy and time entropy, and provide an introduction of a sparsity trajectory prediction algorithm based on entropy estimation and the second-order Markov model; in Section 5, we show the experiments and results to demonstrate the effectiveness of the algorithm; and in Section 6 is the conclusion
Summary
As the usage of Global Positioning System (GPS) and smart mobile devices (SMD) becomes a part of our daily lives, we benefit increasingly from various types of location-based services (LBSs), such as route finding and location-based social networking. The remainder of this paper is organized as follows: in Section 2, we introduce the spatial iterative grid partition and representations of trajectory sequences with time; in Section 3, the trajectory synthesis based on the L-Z entropy estimator is introduced; in Section 4, we define the location entropy and time entropy, and provide an introduction of a sparsity trajectory prediction algorithm based on entropy estimation and the second-order Markov model; in Section 5, we show the experiments and results to demonstrate the effectiveness of the algorithm; and in Section 6 is the conclusion
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