# ABBA: Adaptive Brownian bridge-based symbolic aggregation of time series

arXiv: https://arxiv.org/abs/2003.12469 · HTML: https://mlsanity.com/paper/2003.12469/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Mar 2020.

## Built on by (most cited first, 13 of 13)

- [ECG-Byte: A Tokenizer for End-to-End Generative Electrocardiogram Language Modeling](https://mlsanity.com/paper/2412.14373/) (2024)
- [An efficient aggregation method for the symbolic representation of temporal data](https://mlsanity.com/paper/2201.05697/) (2022)
- [LLM-ABBA: Understanding time series via symbolic approximation](https://mlsanity.com/paper/2411.18506/) (2024)
- [Signal, Image, or Symbolic: Exploring the Best Input Representation for Electrocardiogram-Language Models Through a Unified Framework](https://mlsanity.com/paper/2505.18847/) (2025)
- [SymED: Adaptive and Online Symbolic Representation of Data on the Edge](https://mlsanity.com/paper/2309.03014/) (2023)
- [Clustered Federated Learning with Hierarchical Knowledge Distillation](https://mlsanity.com/paper/2512.10443/) (2025)
- [ASTRIDE: Adaptive Symbolization for Time Series Databases](https://mlsanity.com/paper/2302.04097/) (2023)
- [Data-driven prognostics based on time-frequency analysis and symbolic recurrent neural network for fuel cells under dynamic load](https://mlsanity.com/paper/2302.10771/) (2023)
- [ABBA-VSM: Time Series Classification using Symbolic Representation on the Edge](https://mlsanity.com/paper/2410.10285/) (2024)
- [QABBA: Symbolic Time-Series Compression via Integer-Quantized Aggregation](https://mlsanity.com/paper/2411.15209/) (2024)
- [TimeSliver : Symbolic-Linear Decomposition for Explainable Time Series Classification](https://mlsanity.com/paper/2601.21289/) (2026)
- [Grammar of the Wave: Towards Explainable Multivariate Time Series Event Detection via Neuro-Symbolic VLM Agents](https://mlsanity.com/paper/2603.11479/) (2026)
- [STaT: Resolving Shape Distortion in Non-Stationary Time Series via Tri-Modal Synergy](https://mlsanity.com/paper/2605.25943/) (2026)

## Abstract (arXiv)

A new symbolic representation of time series, called ABBA, is introduced. It is based on an adaptive polygonal chain approximation of the time series into a sequence of tuples, followed by a mean-based clustering to obtain the symbolic representation. We show that the reconstruction error of this representation can be modelled as a random walk with pinned start and end points, a so-called Brownian bridge. This insight allows us to make ABBA essentially parameter-free, except for the approximation tolerance which must be chosen. Extensive comparisons with the SAX and 1d-SAX representations are included in the form of performance profiles, showing that ABBA is able to better preserve the essential shape information of time series compared to other approaches. Advantages and applications of ABBA are discussed, including its in-built differencing property and use for anomaly detection, and Python implementations provided.