# Error-bounded Approximate Time Series Joins Using Compact Dictionary Representations of Time Series

arXiv: https://arxiv.org/abs/2112.12965 · HTML: https://mlsanity.com/paper/2112.12965/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 27 references that are in the map.
- First posted on arXiv 24 Dec 2021.

## Builds on (most cited first, 3 of 3)

- [Deep Learning for Anomaly Detection: A Survey](https://mlsanity.com/paper/1901.03407/) (2019)
- [Current Time Series Anomaly Detection Benchmarks are Flawed and are Creating the Illusion of Progress](https://mlsanity.com/paper/2009.13807/) (2020)
- [Time is of the Essence: Machine Learning-based Intrusion Detection in Industrial Time Series Data](https://mlsanity.com/paper/1809.07500/) (2018)

## Built on by (most cited first, 9 of 9)

- [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)
- [Sketching Multidimensional Time Series for Fast Discord Mining](https://mlsanity.com/paper/2311.03393/) (2023)
- [Matrix Profile for Anomaly Detection on Multidimensional Time Series](https://mlsanity.com/paper/2409.09298/) (2024)
- [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)
- [Matrix Profile XXVII: A Novel Distance Measure for Comparing Long Time Series](https://mlsanity.com/paper/2212.06146/) (2022)
- [Ego-Network Transformer for Subsequence Classification in Time Series Data](https://mlsanity.com/paper/2311.02561/) (2023)
- [Time Series Synthesis Using the Matrix Profile for Anonymization](https://mlsanity.com/paper/2311.02563/) (2023)

## Abstract (arXiv)

The matrix profile is an effective data mining tool that provides similarity join functionality for time series data. Users of the matrix profile can either join a time series with itself using intra-similarity join (i.e., self-join) or join a time series with another time series using inter-similarity join. By invoking either or both types of joins, the matrix profile can help users discover both conserved and anomalous structures in the data. Since the introduction of the matrix profile five years ago, multiple efforts have been made to speed up the computation with approximate joins; however, the majority of these efforts only focus on self-joins. In this work, we show that it is possible to efficiently perform approximate inter-time series similarity joins with error bounded guarantees by creating a compact "dictionary" representation of time series. Using the dictionary representation instead of the original time series, we are able to improve the throughput of an anomaly mining system by at least 20X, with essentially no decrease in accuracy. As a side effect, the dictionaries also summarize the time series in a semantically meaningful way and can provide intuitive and actionable insights. We demonstrate the utility of our dictionary-based inter-time series similarity joins on domains as diverse as medicine and transportation.