将矩阵轮廓扩展至多维时间序列，实现跨场景高精度异常检测
Matrix Profile for Anomaly Detection on Multidimensional Time Series
- 提出多维时间序列的矩阵轮廓压缩策略，解决高维距离张量存储难题
- 在119个数据集上验证，该方法在无监督、半监督、监督三类设置中均表现最优
- 开源完整实现，支持与TSB-AD基准对比，便于复现和研究
矩阵轮廓（Matrix Profile, MP）是一种高效的时间序列挖掘工具，在单变量时间序列异常检测中已证明有效。本文聚焦于多维时间序列异常检测问题，此类数据在实际应用中广泛存在，例如制造工厂中多个传感器采集的时变数据。传统矩阵轮廓基于单变量序列的子序列间成对距离构建n×n矩阵；而在多维情形下，需用n×n×d张量存储距离信息。本文首先分析多种将该张量压缩为轮廓向量的策略，进而研究将矩阵轮廓扩展至k近邻搜索以支持异常检测的可行性。最后，我们在119个多维时间序列异常检测数据集上，对多维矩阵轮廓与19种基线方法进行了全面比较，涵盖无监督、监督及半监督三种学习设置。实验表明，矩阵轮廓是唯一在所有设置中持续保持高性能的方法。为确保透明性并促进后续研究，我们已公开完整实现，包含对TSB-AD基准的新增评估，项目地址：https://github.com/mcyeh/mmpad_tsb
原文摘要 · Abstract (English)
The Matrix Profile (MP), a versatile tool for time series data mining, has been shown effective in time series anomaly detection (TSAD). This paper delves into the problem of anomaly detection in multidimensional time series, a common occurrence in real-world applications. For instance, in a manufacturing factory, multiple sensors installed across the site collect time-varying data for analysis. The Matrix Profile, named for its role in profiling the matrix storing pairwise distance between subsequences of univariate time series, becomes complex in multidimensional scenarios. If the input univariate time series has n subsequences, the pairwise distance matrix is a n x n matrix. In a multidimensional time series with d dimensions, the pairwise distance information must be stored in a n x n x d tensor. In this paper, we first analyze different strategies for condensing this tensor into a profile vector. We then investigate the potential of extending the MP to efficiently find k-nearest neighbors for anomaly detection. Finally, we benchmark the multidimensional MP against 19 baseline methods on 119 multidimensional TSAD datasets. The experiments covers three learning setups: unsupervised, supervised, and semi-supervised. MP is the only method that consistently delivers high performance across all setups. To ensure complete transparency and facilitate future research, our full Matrix Profile-based implementation, which includes newly added evaluations against the TSB-AD benchmark, is publicly available at: https://github.com/mcyeh/mmpad_tsb
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