Paper:

# Pruned Fast Learning Fuzzy Approach for Data-Driven Traffic Flow Prediction

## Chengdong Li^{*}, Yisheng Lv^{**}, Jianqiang Yi^{**}, and Guiqing Zhang^{*}

^{*}School of Information and Electrical Engineering, Shandong Jianzhu University

Jinan 250101, China

^{**}Institute of Automation, Chinese Academy of Sciences

Beijing 100190, China

Traffic flow prediction plays an important role in intelligent transportation systems. With the rapid growth of traffic flow data, fast and accurate traffic flow prediction methods are now required. In this paper, we propose a novel fast learning data-driven fuzzy approach for the traffic flow prediction problem. In the proposed approach, to achieve fast learning, an extreme learning machine is utilized to optimize the consequent parameters of the fuzzy rules. Further, a fuzzy rule pruning strategy that involves measuring the firing levels of the fuzzy rules is presented to obtain reduced fuzzy inference systems. To evaluate the performance of the proposed approach, it was experimentally applied to traffic flow prediction and its results compared with those of widely used methods. The experimental results verify that the proposed approach can achieve satisfactory performance. The comparisons show that the proposed approach can obtain better (sometimes similar) performances, but with a simpler structure, fewer parameters, and much faster learning speed than the other methods.

- [1] E. I. Vlahogianni, M. G. Karlaftis, and J. C. Golias, “Short-term traffic forecasting: Where we are and where we are going,” Transportation Research Part C: Emerging Technologies, Vol.43, pp. 3-19, 2014.
- [2] C. Chen, Y. Wang, L. Li, J. Hu, and Z. Zhang, “The retrieval of intra-day trend and its influence on traffic prediction,” Transportation Research Part C: Emerging technologies, Vol.22, pp. 103-118, 2012.
- [3] M. M. Hamed, H. R. Al-Masaeid, and Z. M. B. Said, “Short-term prediction of traffic volume in urban arterials,” J. of Transportation Engineering, Vol.121, No.3, pp. 249-254, 1995.
- [4] M. Van Der Voort, M. Dougherty, and S. Watson, “Combining Kohonen maps with ARIMA time series models to forecast traffic flow,” Transportation Research Part C: Emerging Technologies, Vol.4, No.5, pp. 307-318, 1996.
- [5] B. Williams, “Multivariate vehicular traffic flow prediction: evaluation of ARIMAX modeling,” Transportation Research Record: J. of the Transportation Research Board, Vol.1776, pp. 194-200, 2001.
- [6] B. M. Williams and L. A. Hoel, “Modeling and forecasting vehicular traffic flow as a seasonal ARIMA process: Theoretical basis and empirical results,” J. of Transportation Engineering, Vol.129, No.6, pp. 664-672, 2003.
- [7] S. Lee and D. Fambro, “Application of subset autoregressive integrated moving average model for short-term freeway traffic volume forecasting,” Transportation Research Record: J. of the Transportation Research Board, Vol.1678, pp. 179-188, 1999.
- [8] F. Moretti, S. Pizzuti, S. Panzieri, and M. Annunziato, “Urban traffic flow forecasting through statistical and neural network bagging ensemble hybrid modeling,” Neurocomputing, Vol.167, pp. 3-7, 2015.
- [9] E. I. Vlahogianni, M. G. Karlaftis, and J. C. Golias, “Optimized and meta-optimized neural networks for short-term traffic flow prediction: a genetic approach,” Transportation Research Part C: Emerging Technologies, Vol.13, No.3, pp. 211-234, 2005.
- [10] K. Y. Chan, T. S. Dillon, J. Singh, and E. Chang, “Neural-network-based models for short-term traffic flow forecasting using a hybrid exponential smoothing and Levenberg-Marquardt algorithm,” IEEE Trans. on Intelligent Transportation Systems, Vol.13, No.2, pp. 644-654, 2012.
- [11] P. Dell’Acqua, F. Bellotti, R. Berta, and A. De Gloria, “Time-aware multivariate nearest neighbor regression methods for traffic flow prediction,” IEEE Trans. on Intelligent Transportation Systems, Vol.16, No.6, pp. 3393-3402, 2015.
- [12] W. C. Hong, “Traffic flow forecasting by seasonal SVR with chaotic simulated annealing algorithm,” Neurocomputing, Vol.74, No.12, pp. 2096-2107, 2011.
- [13] W. C. Hong, Y. Dong, F. Zheng, and S. Y. Wei, “Hybrid evolutionary algorithms in a SVR traffic flow forecasting model,” Applied Mathematics and Computation, Vol.217, No.15, pp. 6733-6747, 2011.
- [14] W. C. Hong, Y. Dong, F. Zheng, and C. Y. Lai, “Forecasting urban traffic flow by SVR with continuous ACO,” Applied Mathematical Modelling, Vol.35, No.3, pp. 1282-1291, 2011.
- [15] Y. Lv, Y. Duan, W. Kang, Z. Li, and F. Y. Wang, “Traffic flow prediction with big data: A deep learning approach,” IEEE Trans. on Intelligent Transportation Systems, Vol.16, No.2, pp. 865-873, 2015.
- [16] L. Dimitriou, T. Tsekeris, and A. Stathopoulos, “Adaptive hybrid fuzzy rule-based system approach for modeling and predicting urban traffic flow,” Transportation Research Part C: Emerging Technologies, Vol.16, No.5, pp. 554-573, 2008.
- [17] H. Yin, S. Wong, J. Xu, and C. K. Wong, “Urban traffic flow prediction using a fuzzy-neural approach,” Transportation Research Part C: Emerging Technologies, Vol.10, No.2, pp. 85-98, 2002.
- [18] L. I. Rui, J. Y. Chen, Y. J. Liu, and Z. K. Wang, “WPANFIS: combine fuzzy neural network with multiresolution for network traffic prediction,” The J. of China Universities of Posts and Telecommunications, Vol.17, No.4, pp. 88-93, 2010.
- [19] J. Abdi, B. Moshiri, B. Abdulhai, and A. K. Sedigh, “Forecasting of short-term traffic-flow based on improved neurofuzzy models via emotional temporal difference learning algorithm,” Engineering Applications of Artificial Intelligence, Vol. 25, No.5, pp. 1022-1042, 2012.
- [20] M. C. Tan, S. C. Wong, J. M. Xu, Z. R. Guan, and P. Zhang, “An aggregation approach to short-term traffic flow prediction,” IEEE Trans. on Intelligent Transportation Systems, Vol.10, No.1, pp. 60-69, 2009.
- [21] L. A. Zadeh, “Fuzzy sets,” Information and Control, Vol.8, No.3, pp. 338-353, 1965.
- [22] L. A. Zadeh, “Fuzzy logic - a personal perspective,” Fuzzy Sets and Systems, Vol.281, pp. 4-20, 2015.
- [23] W. Pedrycz and H. Izakian, “Cluster-centric fuzzy modeling,” IEEE Trans. on Fuzzy Systems, Vol.22, No.6, pp. 1585-1597, 2014.
- [24] C. Li, J. Yi, and G. Zhang, “On the monotonicity of interval type-2 fuzzy logic systems,” IEEE Trans. on Fuzzy Systems, Vol.22, No.5, pp. 1197-1212, 2014.
- [25] G. B. Huang, Q. Y. Zhu, and C. K. Siew, “Extreme learning machine: theory and applications,” Neurocomputing, Vol.70, No.1, pp. 489-501, 2006.
- [26] G. B. Huang, H. Zhou, X. Ding, and R. Zhang, “Extreme learning machine for regression and multiclass classification,” IEEE Trans. on Systems, Man, and Cybernetics, Part B: Cybernetics, Vol.42, No.2, pp. 513-529, 2012.
- [27] G. B. Huang and L. Chen, “Convex incremental extreme learning machine,” Neurocomputing, Vol.70, No.16, pp. 3056-3062, 2007.
- [28] G. B. Huang, X. Ding, and H. Zhou, “Optimization method based extreme learning machine for classification,” Neurocomputing, Vol.74, No.1, pp. 155-163, 2010.
- [29] Z. L. Sun, K. F. Au, and T. M. Choi, “A neuro-fuzzy inference system through integration of fuzzy logic and extreme learning machines,” IEEE Trans. on Systems, Man, and Cybernetics, Part B: Cybernetics, Vol.37, No.5, pp. 1321-1331, 2007.
- [30] H. J. Rong, G. B. Huang, N. Sundararajan, and P. Saratchandran, “Online sequential fuzzy extreme learning machine for function approximation and classification problems,” IEEE Trans. on Systems, Man, and Cybernetics, Part B: Cybernetics, Vol.39, No.4, pp. 1067-1072, 2009.
- [31] S. O. Olatunji, A. Selamat, and A. Abdulraheem, “A hybrid model through the fusion of type-2 fuzzy logic systems and extreme learning machines for modelling permeability prediction,” Information Fusion, Vol.16, pp. 29-45, 2014.
- [32] Z. Deng, K. S. Choi, L. Cao, and S. Wang, “T2fela: type-2 fuzzy extreme learning algorithm for fast training of interval type-2 TSK fuzzy logic system,” IEEE Trans. on Neural Networks and Learning Systems, Vol.25, No.4, pp. 664-676, 2014.
- [33] J. S. R. Jang, “ANFIS: adaptive-network-based fuzzy inference system,” IEEE Trans. on Systems, Man and Cybernetics, Vol.23, No.3, pp. 665-685, 1993.
- [34] Y. H. Joo, H. S. Hwang, K. B. Kim, and K. B. Woo, “Fuzzy system modeling by fuzzy partition and GA hybrid schemes,” Fuzzy Sets and Systems, Vol.86, No.3, pp. 279-288, 1997.
- [35] J. Yao, M. Dash, S. T. Tan, and H. Liu, “Entropy-based fuzzy clustering and fuzzy modeling,” Fuzzy Sets and Systems, Vol.113, No.3, pp. 381-388, 2000.
- [36] G. H. Golub and C. F. Van Loan, “Matrix Computations (4th Edition),” Maryland, The Johns Hopkins University Press, 2013.
- [37] G. Quintana-Orti, E. S. Quintana-Orti, and A. Petitet, “Efficient solution of the rank-deficient linear least squares problem,” SIAM J. on Scientific Computing, Vol.20, No.3, pp. 1155-1163, 1998.
- [38] V N. Vapnik, “Statistical Learning Theory,” New York, Wiley, 1998.