Low-Rank Robust Subspace Tensor Clustering for Metro Passenger Flow Modeling

Tensor clustering has become an important topic, specifically in spatiotemporal modeling, because of its ability to cluster spatial modes (e.g., stations or road segments) and temporal modes (e.g., time of day or day of the week). Our motivating example is from subway passenger flow modeling, where similarities between stations are commonly found. However, the challenges lie in the innate high-dimensionality of tensors and also the potential existence of anomalies. This is because the three tasks, that is, dimension reduction, clustering, and anomaly decomposition, are intercorrelated with each other, and treating them in a separate manner will render a suboptimal performance. Thus, in this work, we design a tensor-based subspace clustering and anomaly decomposition technique for simultaneous outlier-robust dimension reduction and clustering for high-dimensional tensors. To achieve this, a novel low-rank robust subspace clustering decomposition model is proposed by combining Tucker decomposition, sparse anomaly decomposition, and subspace clustering. An effective algorithm based on Block Coordinate Descent is proposed to update the parameters. Prudent experiments prove the effectiveness of the proposed framework via the simulation study, with a gain of +25% clustering accuracy over benchmark methods in a hard case. The interrelations of the three tasks are also analyzed via ablation studies, validating the interrelation assumption. Moreover, a case study in station clustering based on real passenger flow data is conducted, with quite valuable insights discovered.