用张量伪骨架分解提升高维数据异常检测鲁棒性
Robust Anomaly Detection via Tensor Pseudoskeleton Decomposition
- 基于张量鲁棒主成分分析，利用伪骨架分解提取低秩结构
- 在纽约出租车数据上检测异常事件，准确率优于现有方法
- 适合处理大规模高维时空数据的异常检测任务
异常检测在现代数据驱动应用中至关重要，涵盖欺诈交易识别、网络防护及传感器系统监控等场景。传统基于距离、密度或聚类的方法在高维张量数据上面临挑战，因维度间复杂依赖会放大噪声并增加计算复杂度。本文提出在张量鲁棒主成分分析框架内，采用张量Chidori伪骨架分解，以提取低Tucker秩结构并分离稀疏异常，增强检测鲁棒性。建立了收敛性与估计误差的理论结果，证明了方法的稳定性和准确性。在纽约市出租车行程的真实时空数据上进行数值实验，验证了该方法在检测城市异常事件方面优于现有基准方法。结果表明，张量伪骨架分解有望提升大规模高维数据中的异常检测性能。
原文摘要 · Abstract (English)
Anomaly detection plays a critical role in modern data-driven applications, from identifying fraudulent transactions and safeguarding network infrastructure to monitoring sensor systems for irregular patterns. Traditional approaches, such as distance, density, or cluster-based methods, face significant challenges when applied to high dimensional tensor data, where complex interdependencies across dimensions amplify noise and computational complexity. To address these limitations, this paper leverages Tensor Chidori pseudoskeleton decomposition within a tensor-robust principal component analysis framework to extract low Tucker rank structure while isolating sparse anomalies, ensuring robustness to anomaly detection. We establish theoretical results regarding convergence, and estimation error, demonstrating the stability and accuracy of the proposed approach. Numerical experiments on real-world spatiotemporal data from New York City taxi trip records validate the effectiveness of the proposed method in detecting anomalous urban events compared to existing benchmark methods. Our results suggest that tensor pseudoskeleton decomposition may offer potential for enhancing anomaly detection in large-scale, high-dimensional data.
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