Matrix Profile for Anomaly Detection on Multidimensional Time Series

TL;DR

This paper delves into the problem of anomaly detection in multidimensional time series, a common occurrence in real-world applications, and investigates the potential of extending the MP to efficiently find k-nearest neighbors for anomaly detection.

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.

Figures (12)

• Figure 1: Extending the Matrix Profile to multi-dimensional time series is a non-trivial task, given that anomalous patterns are likely to appear in only a small set of dimensions.
• Figure 2: The Matrix Profile summarizes the pairwise distance matrix of a pair of univariate time series by identifying the nearest neighbor within the matrix.
• Figure 3: In this example, based on the sorted results, the anomaly is most likely contained within the first and fourth dimensions.
• Figure 4: The Matrix Profile uses the post-sorting strategy to summarize the pairwise distance tensor from a pair of multidimensional time series.
• Figure 5: The Matrix Profile uses the pre-sorting strategy to summarize the pairwise distance tensor from a pair of multidimensional time series.

Theorems & Definitions (2)

• Definition 1
• Definition 2