Thanh Lam Hoang, IBM
Eric Bouillet, IBM Research
Given a set of historical bus trajectories D and a partially observed bus trajectory S up to position l on the bus route, kernel regression (KR) is a non-parametric approach which predicts the arrival time of the bus at location l+h (h > 0) by averaging the arrival times observed at same location in the past. The KR method does not weights the historical data equally but it gives more preference to more similar trajectories in the historical data. This method has been shown to outperform the baseline methods such as linear regression or k-nearest neighbour algorithms for bus arrival time prediction problems. However, the performance of KR is very sensitive to the method of evaluating similarity between trajectories. General kernel regression algorithm looks back to the entire trajectory for evaluating similarity. In the case of bus arrival time prediction, this approach does not work well when outdated part of the trajectories does not reflect the most recent behaviour of the buses. In order to solve this issue, we propose an approach that considers only recent part of the trajectories in a sliding window for evaluating the similarity between them. The approach introduces a set of parameters corresponding to the window lengths at every position along the bus route determining how long we should look back into the past for evaluating the similarity between trajectories. These parameters are automatically learned from training data. Nevertheless, parameter learning is a time-consuming process given large training data (at least quadratic in the training size). Therefore, we proposed an approximation algorithm with guarantees on error bounds to learn the parameters efficiently. The approximation algorithm is an order of magnitude faster than the exact algorithm. In an experiment with a real-world application deployed for Dublin city, our approach significantly reduced the prediction error compared to the state of the art kernel regression algorithm.