Abstract
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 the 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 [9]. However, the performance of the KR approach 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 In the case of bus arrival time prediction, this approach does not work well when outdated part of the trajectories does not reflect the most recent behaviour of the buses.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.
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References
Aggarwal, C.C. (ed.): Data Streams - Models and Algorithms, Advances in Database Systems, vol. 31. Springer (2007)
Chen, M., Liu, X., Xia, J., Chien, S.I.: A dynamic bus-arrival time prediction model based on APC data. In: Computer-Aided Civil and Infrastructure Engineering, pp. 364–376, July 2004
Chien, S., Ding, Y., Wei, C.: Dynamic bus arrival time prediction with artificial neural networks. Journal of Transportation Engineering 128(5), 429–438 (2002)
Coffey, C., Pozdnoukhov, A., Calabrese, F.: Time of arrival predictability horizons for public bus routes. In: Proceedings of the 4th ACM SIGSPATIAL International Workshop on Computational Transportation Science, CTS 2011, pp. 1–5. ACM, New York (2011)
Hardle, W., Marron, J.S.: Optimal bandwidth selection in nonparametric regression function estimation. The Annals of Statistics, 1465–1481 (1985)
Hoeffding, W.: Probability inequalities for sums of bounded random variables. Journal of the American Statistical Association 58(301), 13–30 (1963)
Li, F., Yu, Y., Lin, H., Min, W.: Public bus arrival time prediction based on traffic information management system. In: IEEE International Conference on Service Operations, Logistics, and Informatics (SOLI), pp. 336–341, July 2011
Mazloumia, E., Rosea, G., Curriea, G., Sarvia, M.: An integrated framework to predict bus travel time and its variability using traffic flow data. Journal of Intelligent Transportation Systems: Technology, Planning, and Operations (2011)
Sinn, M., Yoon, J.W., Calabrese, F., Bouillet, E.: Predicting arrival times of buses using real-time gps measurements. In: 15th International IEEE Conference on Intelligent Transportation Systems (ITSC), pp. 1227–1232, September 2012
Son, B., Kim, H.-J., Shin, C.-H., Lee, S.-K.: Bus arrival time prediction method for ITS application. In: Negoita, M.G., Howlett, R.J., Jain, L.C. (eds.) KES 2004. LNCS (LNAI), vol. 3215, pp. 88–94. Springer, Heidelberg (2004)
Sun, D., Luo, H., Fu, L., Liu, W., Liao, X., Zhao, M.: Predicting bus arrival time on the basis of global positioning system data. Transportation Research Record: Journal of the Transportation Research Boardg (2007)
Wall, Z., Dailey, D.J.: An algorithm for predicting the arrival time of mass transit vehicles using automatic vehicle location data. In: 78th Anual Meeting of the Transportation Research Board (1999)
Xinghaoa, S., Jinga, T., Guojuna, C., Qichongb, S.: Predicting bus real-time travel time basing on both GPS and RFID data. In: 13th COTA International Conference of Transportation Professionals (CICTP 2013), pp. 2287–2299, November 2013
Yang, J.-S.: Travel time prediction using the GPS test vehicle and kalman filtering techniques. In: Proceedings of the 2005 American Control Conference, vol. 3, pp. 2128–2133, June 2005
Yu, B., Yang, Z., Yao, B.: Bus arrival time prediction using support vector machines. Journal of Intelligent Transportation Systems, 151–158, July 2006
Zhou, P., Zheng, Y., Li, M.: How long to wait?: Predicting bus arrival time with mobile phone based participatory sensing (2013)
Zhu, T., Ma, F., Ma, T., Li, C.: The prediction of bus arrival time using global positioning system data and dynamic traffic information. In: Wireless and Mobile Networking Conference, pp. 1–5, October 2011
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Lam, H.T., Bouillet, E. (2015). Flexible Sliding Windows for Kernel Regression Based Bus Arrival Time Prediction. In: Bifet, A., et al. Machine Learning and Knowledge Discovery in Databases. ECML PKDD 2015. Lecture Notes in Computer Science(), vol 9286. Springer, Cham. https://doi.org/10.1007/978-3-319-23461-8_5
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