Short-Term Traffic Prediction Based on Dynamic Tensor Completion

Short-term traffic prediction plays a critical role in many important applications of intelligent transportation systems such as traffic congestion control and smart routing, and numerous methods have been proposed to address this issue in the literature. However, most, if not all, of them suffer from the inability to fully use the rich information in traffic data. In this paper, we present a novel short-term traffic flow prediction approach based on dynamic tensor completion (DTC), in which the traffic data are represented as a dynamic tensor pattern, which is able capture more information of traffic flow than traditional methods, namely, temporal variabilities, spatial characteristics, and multimode periodicity. A DTC algorithm is designed to use the multimode information to forecast traffic flow with a low-rank constraint. The proposed method is evaluated on real-world data sets and compared with other state-of-the-art methods, and the efficacy of the proposed approach is validated on the experiments of traffic flow prediction, particularly when dealing with incomplete traffic data.

[1]  Yang Li,et al.  The Driving Safety Field Based on Driver–Vehicle–Road Interactions , 2015, IEEE Transactions on Intelligent Transportation Systems.

[2]  Eleni I. Vlahogianni,et al.  Short-term traffic forecasting: Where we are and where we’re going , 2014 .

[3]  Yin Zhang,et al.  Solving a low-rank factorization model for matrix completion by a nonlinear successive over-relaxation algorithm , 2012, Mathematical Programming Computation.

[4]  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.

[5]  Sherif Ishak,et al.  OPTIMIZATION OF DYNAMIC NEURAL NETWORKS PERFORMANCE FOR SHORT-TERM TRAFFIC PREDICTION , 2003 .

[6]  Bin Ran,et al.  Tensor completion via a multi-linear low-n-rank factorization model , 2014, Neurocomputing.

[7]  Lei Zhang,et al.  An Adaptive Longitudinal Driving Assistance System Based on Driver Characteristics , 2013, IEEE Transactions on Intelligent Transportation Systems.

[8]  Muhammad Tayyab Asif,et al.  Low-dimensional models for missing data imputation in road networks , 2013, 2013 IEEE International Conference on Acoustics, Speech and Signal Processing.

[9]  Lee D. Han,et al.  Online-SVR for short-term traffic flow prediction under typical and atypical traffic conditions , 2009, Expert Syst. Appl..

[10]  Emmanuel J. Candès,et al.  Exact Matrix Completion via Convex Optimization , 2008, Found. Comput. Math..

[11]  Fei-Yue Wang,et al.  Data-Driven Intelligent Transportation Systems: A Survey , 2011, IEEE Transactions on Intelligent Transportation Systems.

[12]  B. Recht,et al.  Tensor completion and low-n-rank tensor recovery via convex optimization , 2011 .

[13]  Wei-Chiang Hong Application of seasonal SVR with chaotic immune algorithm in traffic flow forecasting , 2010, Neural Computing and Applications.

[14]  Guangdong Feng,et al.  Traffic volume data outlier recovery via tensor model , 2013 .

[15]  Yin Wang,et al.  The retrieval of intra-day trend and its influence on traffic prediction , 2012 .

[16]  Bülent Yener,et al.  Unsupervised Multiway Data Analysis: A Literature Survey , 2009, IEEE Transactions on Knowledge and Data Engineering.

[17]  Cheol Oh,et al.  Exploring the Relationship between Data Aggregation and Predictability to Provide Better Predictive Traffic Information , 2005 .

[18]  A. Cichocki,et al.  Tensor decompositions for feature extraction and classification of high dimensional datasets , 2010 .

[19]  H. Kiers,et al.  Three-mode principal components analysis: choosing the numbers of components and sensitivity to local optima. , 2000, The British journal of mathematical and statistical psychology.

[20]  Wang Cheng-hong,et al.  A Real-time Short-term Traffic Flow Adaptive Forecasting Method Based on ARIMA Model , 2004 .

[21]  Matthew G. Karlaftis,et al.  A multivariate state space approach for urban traffic flow modeling and prediction , 2003 .

[22]  Lei Shi,et al.  STenSr: Spatio-temporal tensor streams for anomaly detection and pattern discovery , 2015, Knowledge and Information Systems.

[23]  Guangdong Feng,et al.  A Tensor Based Method for Missing Traffic Data Completion , 2013 .

[24]  Jan Niesing Simultaneous componenet and factor analysis methods for two or more groups: a comparative study. , 1997 .

[25]  Yi Zhang,et al.  Trend Modeling for Traffic Time Series Analysis: An Integrated Study , 2015, IEEE Transactions on Intelligent Transportation Systems.

[26]  Yanru Zhang,et al.  A hybrid short-term traffic flow forecasting method based on spectral analysis and statistical volatility model , 2014 .

[27]  Bin Ran,et al.  Perspectives on Future Transportation Research: Impact of Intelligent Transportation System Technologies on Next-Generation Transportation Modeling , 2012, J. Intell. Transp. Syst..

[28]  Eleni I. Vlahogianni,et al.  Spatio‐Temporal Short‐Term Urban Traffic Volume Forecasting Using Genetically Optimized Modular Networks , 2007, Comput. Aided Civ. Infrastructure Eng..

[29]  Tamara G. Kolda,et al.  Scalable Tensor Factorizations for Incomplete Data , 2010, ArXiv.

[30]  Emmanuel J. Candès,et al.  Exact Matrix Completion via Convex Optimization , 2009, Found. Comput. Math..

[31]  Vishal Monga,et al.  Robust Video Hashing via Multilinear Subspace Projections , 2012, IEEE Transactions on Image Processing.

[32]  Li Li,et al.  Missing traffic data: comparison of imputation methods , 2014 .

[33]  Stephen Dunne,et al.  Regime-Based Short-Term Multivariate Traffic Condition Forecasting Algorithm , 2012 .

[34]  Hisashi Kashima,et al.  Statistical Performance of Convex Tensor Decomposition , 2011, NIPS.

[35]  Hojjat Adeli,et al.  Dynamic Wavelet Neural Network Model for Traffic Flow Forecasting , 2005 .

[36]  Mariya Ishteva Numerical Methods for the Best Low Multilinear Rank Approximation of Higher-Order Tensors (Numerieke methoden voor de beste lage multilineaire rang benadering van hogere-orde tensoren) , 2009 .

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

[38]  Biswajit Basu,et al.  Real-Time Traffic Flow Forecasting Using Spectral Analysis , 2012, IEEE Transactions on Intelligent Transportation Systems.

[39]  Johan A. K. Suykens,et al.  Tensor Versus Matrix Completion: A Comparison With Application to Spectral Data , 2011, IEEE Signal Processing Letters.

[40]  Tamara G. Kolda,et al.  Link Prediction on Evolving Data Using Matrix and Tensor Factorizations , 2009, 2009 IEEE International Conference on Data Mining Workshops.

[41]  Lorenzo Mussone,et al.  A Study of Hybrid Neural Network Approaches and the Effects of Missing Data on Traffic Forecasting , 2001, Neural Computing & Applications.

[42]  L. K. Hansen,et al.  Automatic relevance determination for multi‐way models , 2009 .

[43]  Andrzej Cichocki,et al.  Era of Big Data Processing: A New Approach via Tensor Networks and Tensor Decompositions , 2014, ArXiv.

[44]  Andrzej Cichocki,et al.  Nonnegative Tensor Factorization for Continuous EEG Classification , 2007, Int. J. Neural Syst..

[45]  Tamara G. Kolda,et al.  Tensor Decompositions and Applications , 2009, SIAM Rev..

[46]  Yi Zhang,et al.  PPCA-Based Missing Data Imputation for Traffic Flow Volume: A Systematical Approach , 2009, IEEE Transactions on Intelligent Transportation Systems.

[47]  Andrzej Cichocki,et al.  Nonnegative Matrix and Tensor Factorization T , 2007 .

[48]  H. Kiers,et al.  Selecting among three-mode principal component models of different types and complexities: a numerical convex hull based method. , 2006, The British journal of mathematical and statistical psychology.

[49]  Li Li,et al.  Efficient missing data imputing for traffic flow by considering temporal and spatial dependence , 2013 .

[50]  Eleni I. Vlahogianni,et al.  Optimized and meta-optimized neural networks for short-term traffic flow prediction: A genetic approach , 2005 .

[51]  Wanli Min,et al.  Real-time road traffic prediction with spatio-temporal correlations , 2011 .

[52]  Andrzej Cichocki,et al.  Predicting traffic speed in urban transportation subnetworks for multiple horizons , 2014, 2014 13th International Conference on Control Automation Robotics & Vision (ICARCV).

[53]  Wotao Yin,et al.  Parallel matrix factorization for low-rank tensor completion , 2013, ArXiv.

[54]  L. Tucker,et al.  Some mathematical notes on three-mode factor analysis , 1966, Psychometrika.

[55]  Jieping Ye,et al.  Tensor Completion for Estimating Missing Values in Visual Data , 2009, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[56]  Demetri Terzopoulos,et al.  Multilinear subspace analysis of image ensembles , 2003, 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings..

[57]  Philip S. Yu,et al.  Incremental tensor analysis: Theory and applications , 2008, TKDD.

[58]  P. Tseng Convergence of a Block Coordinate Descent Method for Nondifferentiable Minimization , 2001 .

[59]  Eleni I. Vlahogianni,et al.  Short‐term traffic forecasting: Overview of objectives and methods , 2004 .

[60]  Wuhong Wang,et al.  Mixture Augmented Lagrange Multiplier Method for Tensor Recovery and Its Applications , 2014 .

[61]  Eleni I. Vlahogianni,et al.  Temporal aggregation in traffic data: implications for statistical characteristics and model choice , 2011 .

[62]  Mascha C. van der Voort,et al.  Combining kohonen maps with arima time series models to forecast traffic flow , 1996 .

[63]  Angshuman Guin,et al.  Multiple Imputation Scheme for Overcoming the Missing Values and Variability Issues in ITS Data , 2005 .

[64]  Zhiheng Li,et al.  A Comparison of Detrending Models and Multi-Regime Models for Traffic Flow Prediction , 2014, IEEE Intelligent Transportation Systems Magazine.

[65]  Bin Ran,et al.  Robust Missing Traffic Flow Imputation Considering Nonnegativity and Road Capacity , 2014 .

[66]  Huachun Tan,et al.  Low Multilinear Rank Approximation of Tensors and Application in Missing Traffic Data , 2014 .

[67]  Man-Chun Tan,et al.  An Aggregation Approach to Short-Term Traffic Flow Prediction , 2009, IEEE Transactions on Intelligent Transportation Systems.

[68]  Jianqiang Wang,et al.  Longitudinal collision mitigation via coordinated braking of multiple vehicles using model predictive control , 2015, Integr. Comput. Aided Eng..