Tensor Dirichlet Process Multinomial Mixture Model for Passenger Trajectory Clustering

Abstract: Passenger clustering based on travel records is essential for transportation operators. However, existing methods cannot easily cluster the passengers due to the hierarchical structure of the passenger trip information, namely: each passenger has multiple trips, and each trip contains multi-dimensional multi-mode information. Furthermore, existing approaches rely on an accurate specification of the clustering number to start, which is difficult when millions of commuters are using the transport systems on a daily basis. In this paper, we propose a novel Tensor Dirichlet Process Multinomial Mixture model (Tensor-DPMM), which is designed to preserve the multi-mode and hierarchical structure of the multi-dimensional trip information via tensor, and cluster them in a unified one-step manner. The model also has the ability to determine the number of clusters automatically by using the Dirichlet Process to decide the probabilities for a passenger to be either assigned in an existing cluster or to create a new cluster: This allows our model to grow the clusters as needed in a dynamic manner. Finally, existing methods do not consider spatial semantic graphs such as geographical proximity and functional similarity between the locations, which may cause inaccurate clustering. To this end, we further propose a variant of our model, namely the Tensor-DPMM with Graph. For the algorithm, we propose a tensor Collapsed Gibbs Sampling method, with an innovative step of "disband and relocating", which disbands clusters with too small amount of members and relocates them to the remaining clustering. This avoids uncontrollable growing amounts of clusters. A case study based on Hong Kong metro passenger data is conducted to demonstrate the automatic process of learning the number of clusters, and the learned clusters are better in within-cluster compactness and cross-cluster separateness.