Urban Traffic Flow Forecasting Based on Adaptive Hinging Hyperplanes

In this paper, after a review of traffic forecasting methods and the development of piecewise linear functions, a new traffic flow forecasting model based on adaptive hinging hyperplanes was proposed. Adaptive hinging hyperplanes (AHH) is a kind of piecewise linear models which can decide its division of the domain and the parameters adaptively. Acceptable results (forecasting error is smaller than 15%) were obtained in the test of the real traffic data in Beijing. After comparison with the results of prediction model base on MARS, the following conclusions can be drawn. First, the two methods have almost the same performance in prediction precision. Second, AHH will be a little more stable and cost less computing time. Thus, AHH model may be more applicable in practical engineering.

[1]  L. Chua,et al.  A global representation of multidimensional piecewise-linear functions with linear partitions , 1978 .

[2]  Xiaolin Huang,et al.  Adaptive Hinging Hyperplanes , 2008 .

[3]  J. Friedman,et al.  FLEXIBLE PARSIMONIOUS SMOOTHING AND ADDITIVE MODELING , 1989 .

[4]  Billy M. Williams,et al.  Comparison of parametric and nonparametric models for traffic flow forecasting , 2002 .

[5]  Sung Mo Kang,et al.  Section-wise piecewise-linear functions: Canonical representation, properties, and applications , 1977, Proceedings of the IEEE.

[6]  Billy M. Williams,et al.  Modeling and Forecasting Vehicular Traffic Flow as a Seasonal ARIMA Process: Theoretical Basis and Empirical Results , 2003, Journal of Transportation Engineering.

[7]  J. Friedman.  Multivariate adaptive regression splines , 1990 .

[8]  Michael J Demetsky,et al.  TRAFFIC FLOW FORECASTING: COMPARISON OF MODELING APPROACHES , 1997 .

[9]  Shuning Wang,et al.  Generalization of hinging hyperplanes , 2005, IEEE Transactions on Information Theory.

[10]  Rolf Unbehauen,et al.  Canonical piecewise-linear networks , 1995, IEEE Trans. Neural Networks.

[11]  I Okutani,et al.  Dynamic prediction of traffic volume through Kalman Filtering , 1984 .

[12]  L. Chua,et al.  A generalized canonical piecewise-linear representation , 1990 .

[13]  Leo Breiman,et al.  Hinging hyperplanes for regression, classification, and function approximation , 1993, IEEE Trans. Inf. Theory.

[14]  Gary A. Davis,et al.  Nonparametric Regression and Short‐Term Freeway Traffic Forecasting , 1991 .

[15]  Zuo Zhang,et al.  Short-Term Traffic Flow Forecasting Based on MARS , 2008, 2008 Fifth International Conference on Fuzzy Systems and Knowledge Discovery.

[16]  Leon O. Chua,et al.  Canonical piecewise-linear analysis , 1983 .

[17]  J. M. Tarela,et al.  A representation method for PWL functions oriented to parallel processing , 1990 .