Tensor Z-Eigen-Decomposition And Its Application To Passenger Flow Prediction

Smart transportation plays an important role for smart city. Exploiting the patterns behind historical transportation data can help us predict the passenger flow. It can help city managers make reasonable scheduling decisions for city transport system and provide better environment for citizens.Tensor is a high-dimensional matrix. Tensor z-eigen-decomposition has been widely used in many areas. Research currently on tensor z-eigen-decompositions usually limited to single-mode product. In this paper, we consider a transformation between single-mode product and multi-mode product and extend tensor z-eigen-decomposition for multi-mode product. Furthermore, a novel definition of multivariate transfer tensor and multi-mode symmetric tensor is provided. Tensor z-eigen-decomposition theory is extended for these new definitions and discuss the conditions which make tensor z-eigenvalue decomposition uniquely.A multivariate transfer tensor model is constructed in this paper, and the model incorporated the effect of time and interaction among the lines is used to predict for future passenger flow. In order to consider the influence of weather and holidays, the multivariate transfer model is expanded by adding two order that represent the information of weather and holiday respectively. The z-eigentensor by the decomposition of the expanded multivariate transfer tensor indicates stationary distribution of a multivariate Markov chain and its elements show the possibility of passenger flow in a specific time period.