标题： 基于稀疏和低秩张量优化的交通流数据补全与异常诊断 显示英文标题

标题： Traffic Flow Data Completion and Anomaly Diagnosis via Sparse and Low-Rank Tensor Optimization

摘要： 从传感系统收集的时空交通时间序列（如交通速度数据）通常不完整，存在大量损坏和缺失值。 海量数据隐藏着潜在的数据结构，这给数据恢复问题带来了重大挑战，例如挖掘数据的潜在时空相关性以及识别异常数据。 本文提出了一种基于Tucker分解的稀疏低秩高阶张量优化模型（TSLTO），用于数据填补和异常诊断。 我们将交通张量数据分解为低秩和稀疏张量，并基于Tucker分解建立稀疏低秩高阶张量优化模型。 通过利用非光滑分析工具研究张量函数的最优条件，我们设计了用于求解该模型的ADMM优化算法。 最后，在合成数据和真实世界数据集（广州市交通速度数据集）上进行了数值实验。 与几种现有代表性算法的数值比较表明，所提出的算法在交通流数据恢复和异常诊断任务中具有更高的准确性和效率。 显示英文摘要

摘要： Spatiotemporal traffic time series, such as traffic speed data, collected from sensing systems are often incomplete, with considerable corruption and large amounts of missing values. A vast amount of data conceals implicit data structures, which poses significant challenges for data recovery issues, such as mining the potential spatio-temporal correlations of data and identifying abnormal data. In this paper, we propose a Tucker decomposition-based sparse low-rank high-order tensor optimization model (TSLTO) for data imputation and anomaly diagnosis. We decompose the traffic tensor data into low-rank and sparse tensors, and establish a sparse low-rank high-order tensor optimization model based on Tucker decomposition. By utilizing tools of non-smooth analysis for tensor functions, we explore the optimality conditions of the proposed tensor optimization model and design an ADMM optimization algorithm for solving the model. Finally, numerical experiments are conducted on both synthetic data and a real-world dataset: the urban traffic speed dataset of Guangzhou. Numerical comparisons with several representative existing algorithms demonstrate that our proposed approach achieves higher accuracy and efficiency in traffic flow data recovery and anomaly diagnosis tasks.