# Matrix Profile for Anomaly Detection on Multidimensional Time Series

arXiv: https://arxiv.org/abs/2409.09298 · HTML: https://mlsanity.com/paper/2409.09298/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 50 references that are in the map.
- First posted on arXiv 14 Sep 2024.

## Builds on (most cited first, 14 of 14)

- [Detecting Spacecraft Anomalies Using LSTMs and Nonparametric Dynamic Thresholding](https://mlsanity.com/paper/1802.04431/) (2018)
- [COPOD: Copula-Based Outlier Detection](https://mlsanity.com/paper/2009.09463/) (2020)
- [Extended Isolation Forest](https://mlsanity.com/paper/1811.02141/) (2018)
- [Precision and Recall for Time Series](https://mlsanity.com/paper/1803.03639/) (2018)
- [Exathlon: A Benchmark for Explainable Anomaly Detection over Time Series](https://mlsanity.com/paper/2010.05073/) (2020)
- [Toward a Foundation Model for Time Series Data](https://mlsanity.com/paper/2310.03916/) (2023)
- [RPMixer: Shaking Up Time Series Forecasting with Random Projections for Large Spatial-Temporal Data](https://mlsanity.com/paper/2402.10487/) (2024)
- [Robust PCA for Anomaly Detection in Cyber Networks](https://mlsanity.com/paper/1801.01571/) (2018)
- [Error-bounded Approximate Time Series Joins Using Compact Dictionary Representations of Time Series](https://mlsanity.com/paper/2112.12965/) (2021)
- [Adaptive Anomaly Detection in Chaotic Time Series with a Spatially Aware Echo State Network](https://mlsanity.com/paper/1909.01709/) (2019)
- [Towards a Near Universal Time Series Data Mining Tool: Introducing the Matrix Profile](https://mlsanity.com/paper/1811.03064/) (2018)
- [Sketching Multidimensional Time Series for Fast Discord Mining](https://mlsanity.com/paper/2311.03393/) (2023)
- [Hybrid Isolation Forest - Application to Intrusion Detection](https://mlsanity.com/paper/1705.03800/) (2017)
- [A Systematic Evaluation of Generated Time Series and Their Effects in Self-Supervised Pretraining](https://mlsanity.com/paper/2408.07869/) (2024)

## Built on by (most cited first, 3 of 3)

- [Empowering Time Series Forecasting with LLM-Agents](https://mlsanity.com/paper/2508.04231/) (2025)
- [TiCT: A Synthetically Pre-Trained Foundation Model for Time Series Classification](https://mlsanity.com/paper/2511.19694/) (2025)
- [Matrix Profile for Time-Series Anomaly Detection: A Reproducible Open-Source Benchmark on TSB-AD](https://mlsanity.com/paper/2604.02445/) (2026)

## Abstract (arXiv)

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