Tensor Dirichlet Process Multinomial Mixture Model for Passenger
  Trajectory Clustering
Ziyue Li Hao Yan Chen Zhang Andi Wang Wolfgang Ketter Lijun Sun Fugee Tsung
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.