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

翻译：矩阵轮廓（Matrix Profile，MP）作为一种通用时间序列数据挖掘工具，已被证明在时间序列异常检测（TSAD）中颇具成效。本文深入研究了多维时间序列中的异常检测问题——这是现实应用中常见的场景。例如，在制造工厂中，部署在各处的多个传感器会收集时变数据用于分析。矩阵轮廓得名于其对存储单变量时间序列子序列间成对距离的矩阵进行轮廓分析的功能，该功能在多维场景下变得复杂。若输入的单变量时间序列包含n个子序列，则成对距离矩阵为n×n矩阵。而在具有d个维度的多维时间序列中，成对距离信息必须存储于n×n×d张量中。本文首先分析了将该张量压缩为轮廓向量的不同策略。继而研究了扩展MP以高效搜索k近邻进行异常检测的潜力。最后，我们在119个多维TSAD数据集上，将多维MP与19种基线方法进行了基准对比。实验涵盖三种学习范式：无监督、监督及半监督。MP是唯一在所有范式下始终取得优异性能的方法。为确保完全透明并促进未来研究，我们基于矩阵轮廓的完整实现代码（含新增的针对TSB-AD基准的评估功能）已公开于：https://github.com/mcyeh/mmpad_tsb