Matrix Profile for Anomaly Detection on Multidimensional Time Series

TL;DR

This paper extends the Matrix Profile technique to multidimensional time series anomaly detection, analyzing strategies for tensor condensation, extending MP for k-nearest neighbors, and benchmarking against 19 methods.

Contribution

It introduces a novel approach for applying Matrix Profile to multidimensional data, including tensor condensation strategies and comprehensive benchmarking.

Findings

MP consistently outperforms 19 baseline methods across datasets.

Extending MP to multidimensional data is effective for anomaly detection.

The implementation and evaluations are publicly available at the provided GitHub link.

Abstract

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