Tensor clustering has become an important topic, specifically in
spatio-temporal modeling, due to its ability to cluster spatial modes (e.g.,
stations or road segments) and temporal modes (e.g., time of the 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, i.e., dimension reduction,
clustering, and anomaly decomposition, are inter-correlated to 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 simultaneously 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
than 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 the station clustering based on real
passenger flow data is conducted, with quite valuable insights discovered.

本研究提出了一种基于张量的子空间聚类和异常分解技术，旨在同时实现高维张量的异常鲁棒降维和聚类。通过结合 Tucker 分解、稀疏异常分解和子空间聚类，提出了一个新的低秩鲁棒子空间聚类分解模型，并通过块坐标下降算法更新参数。实验证明，该方法在模拟研究中相比基准方法在难案例中提高了 + 25% 的聚类准确率，同时通过消融研究分析了三个任务之间的相互关系，并通过基于真实乘客流量数据的车站聚类案例研究发现了有价值的见解。