Tensor Levenberg-Marquardt Algorithm for Multi-Relational Traffic Prediction

Traffic prediction serves as a crucial role in intelligent transportation systems for applications including routing planning and traffic control. With the advances of sensor technologies and Internet of Things (IoTs), the exploitation of traffic data motivates us to reformulate the traffic-state prediction problem based on the big-data characteristics. In order to infer multifarious traffic information, the standard one/two-relational traffic data in the vector/matrix form needs to be expanded to multi-relational traffic data in an arbitrary tensor form. However, none of the existing approaches is capable of performing traffic prediction by characterizing and tracking the inherent multi-relational nonlinear dynamics which are often encountered in the realistic time-series analysis. Furthermore, there hardly exist convergence studies on convergence condition and convergence speed pertinent to the existing traffic-prediction methods. In order to combat the aforementioned challenges, we propose a new tensor Levenberg-Marquadt algorithm (TLMA) to conduct the multi-relational nonlinear regression for traffic prediction involving tensorized data. Meanwhile, we also derive the lower-bound of the number of iterations required to make the error-norm below a specified tolerance for global convergence. Besides, we derive the conditions for our proposed TLMA to converge to the optimal solution. The convergence rates with respect to different nonlinear cost functions have been derived theoretically. The computational- and memory-complexities of our proposed new TLMA are studied as well. Finally, numerical experiments are conducted to evaluate the traffic prediction performance of our proposed new TLMA over real traffic data in comparison with other existing multi-relational prediction methods.