# Matrix Profile Goes MAD: Variable-Length Motif And Discord Discovery in Data Series

arXiv: https://arxiv.org/abs/2008.13447 · HTML: https://mlsanity.com/paper/2008.13447/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Aug 2020.

## Built on by (most cited first, 10 of 10)

- [Do Deep Neural Networks Contribute to Multivariate Time Series Anomaly Detection?](https://mlsanity.com/paper/2204.01637/) (2022)
- [Robust and Explainable Autoencoders for Unsupervised Time Series Outlier Detection---Extended Version](https://mlsanity.com/paper/2204.03341/) (2022)
- [Series2Graph: Graph-based Subsequence Anomaly Detection for Time Series](https://mlsanity.com/paper/2207.12208/) (2022)
- [VUS: Effective and Efficient Accuracy Measures for Time-Series Anomaly Detection](https://mlsanity.com/paper/2502.13318/) (2025)
- [dCAM: Dimension-wise Class Activation Map for Explaining Multivariate Data Series Classification](https://mlsanity.com/paper/2207.12165/) (2022)
- [MSAD: A Deep Dive into Model Selection for Time series Anomaly Detection](https://mlsanity.com/paper/2510.26643/) (2025)
- [k-Graph: A Graph Embedding for Interpretable Time Series Clustering](https://mlsanity.com/paper/2502.13049/) (2025)
- [IRMAC: Interpretable Refined Motifs in Binary Classification for Smart Grid Applications](https://mlsanity.com/paper/2109.13732/) (2021)
- [Detect, Explain, Interpret: An End-to-End Benchmark for Time Series Anomaly Detection, Explainability and Interpretability](https://mlsanity.com/paper/2610.01168/) (2026)
- [Retrieval Over Training: Similarity search-based Model Selection for Time Series Anomaly Detection](https://mlsanity.com/paper/2610.20243/) (2026)

## Abstract (arXiv)

In the last fifteen years, data series motif and discord discovery have emerged as two useful and well-used primitives for data series mining, with applications to many domains, including robotics, entomology, seismology, medicine, and climatology. Nevertheless, the state-of-the-art motif and discord discovery tools still require the user to provide the relative length. Yet, in several cases, the choice of length is critical and unforgiving. Unfortunately, the obvious brute-force solution, which tests all lengths within a given range, is computationally untenable. In this work, we introduce a new framework, which provides an exact and scalable motif and discord discovery algorithm that efficiently finds all motifs and discords in a given range of lengths. We evaluate our approach with five diverse real datasets, and demonstrate that it is up to 20 times faster than the state-of-the-art. Our results also show that removing the unrealistic assumption that the user knows the correct length, can often produce more intuitive and actionable results, which could have otherwise been missed. (Paper published in Data Mining and Knowledge Discovery Journal - 2020)