Existing trajectory prediction methods suffer from the “data sparsity” and neglect “time awareness”, which leads to low accuracy. Aiming to the problem, we propose a fast time-aware sparse trajectories prediction with tensor factorization method (TSTP-TF). Firstly, we do trajectory synthesis based on trajectory entropy and put synthesized trajectories into the original trajectory space. It resolves the sparse problem of trajectory data and makes the new trajectory space more reliable. Then, we introduce multidimensional tensor modeling into Markov model to add the time dimension. Tensor factorization is adopted to infer the missing regions transition probabilities to further solve the problem of data sparsity. Due to the scale of the tensor, we design a divide and conquer tensor factorization model to reduce memory consumption and speed up decomposition. Experiments with real dataset show that TSTP-TF improves prediction accuracy generally by as much as 9% and 2% compared to the Baseline algorithm and ESTP-MF algorithm, respectively.

The traditional Markov prediction methods of the taxi destination rely only on the previous 2 to 3 GPS points. They negelect long-term dependencies within a taxi trajectory. We adopt a Recurrent Neural Network (RNN) to explore the long-term dependencies to predict the taxi destination as the multiple hidden layers of RNN can store these dependencies. However, the hidden layers of RNN are very sensitive to small perturbations to reduce the prediction accuracy when the amount of taxi trajectories is increasing. In order to improve the prediction accuracy of taxi destination and reduce the training time, we embed suprisal-driven zoneout (SDZ) to RNN, hence a taxi destination prediction method by regularized RNN with SDZ (TDPRS). SDZ can not only improve the robustness of TDPRS, but also reduce the training time by adopting partial update of parameters instead of a full update. Experiments with a Porto taxi trajectory data show that TDPRS improves the prediction accuracy by 12% compared to RNN prediction method in literature[4]. At the same time, the prediction time is reduced by 7%.

Inspired from the idea of data representation in manifold learning, we derive a novel model which combines the original training images and their tangent vectors to represent each image in the testing set. Different from the previous methods, the L1 norm is used to control the reconstruction error. Considering the fact that the objective function in the proposed model is non-smooth, we utilize the majorization minimization (MM) method to solve the proposed optimization model. It is interesting to note that at each iteration a quadratic optimization problem is formulated and its analytical solution can be achieved, thereby making the proposed algorithm effective. Extensive experiments on face images demonstrate that our method achieves better performance than some previous methods.