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arXiv 2404.04403stat.MEcs.AI
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用于地铁客流建模的低秩鲁棒子空间张量聚类

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

School of Computing and Augmented Intelligence, Arizona State University（亚利桑那州立大学计算与增强智能学院）；Cologne Institute for Information Systems, University of Cologne（科隆大学科隆信息系统研究所）；EWI gGmbH, University of Cologne（科隆大学能源经济研究所）；Department of Industrial Engineering, Tsinghua University（清华大学工业工程系）；Department of Industrial Engineering and Decision Analytics, Hong Kong University of Science and Technology（香港科技大学工业工程与决策分析学系）；Information Hub, Hong Kong University of Science and Technology (Guangzhou)（香港科技大学（广州）信息枢纽）

Jiuyun Hu, Ziyue Li, Chen Zhang, Fugee Tsung, Hao Yan

备注：
Conditionally Accepted in INFORMS Journal of Data Science
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AI总结：

针对地铁客流高维张量中的聚类、降维与异常分解耦合问题，提出融合 Tucker 分解、稀疏异常分解和子空间聚类的低秩鲁棒模型，并用块坐标下降求解，显著提升困难情形下的聚类准确率。

摘要：

张量聚类已成为一个重要课题，尤其是在时空建模中，因为它能够对空间模态（例如车站或路段）和时间模态（例如一天中的时刻或一周中的日期）进行聚类。我们的启发性示例来自地铁客流建模，其中车站之间的相似性普遍存在。然而，挑战在于张量固有的高维性以及异常值的潜在存在。这是因为降维、聚类和异常分解这三项任务相互关联，若以彼此分离的方式处理，将导致次优性能。因此，本研究设计了一种基于张量的子空间聚类与异常分解技术，用于同时实现高维张量的抗异常值降维和聚类。为此，通过结合 Tucker 分解、稀疏异常分解和子空间聚类，提出了一种新颖的低秩鲁棒子空间聚类分解模型。研究提出了一种基于块坐标下降的有效算法来更新参数。严谨的实验通过模拟研究证明了所提框架的有效性：在一个困难情形下，其聚类准确率比基准方法高出 +25%。研究还通过消融实验分析了三项任务之间的相互关系，验证了相互关系假设。此外，还基于真实客流数据开展了车站聚类案例研究，并发现了相当有价值的洞见。

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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