# An efficient aggregation method for the symbolic representation of temporal data

arXiv: https://arxiv.org/abs/2201.05697 · HTML: https://mlsanity.com/paper/2201.05697/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 57 references that are in the map.
- First posted on arXiv 14 Jan 2022.

## Builds on (most cited first, 5 of 5)

- [A review on outlier/anomaly detection in time series data](https://mlsanity.com/paper/2002.04236/) (2020)
- [Accelerated Hierarchical Density Clustering](https://mlsanity.com/paper/1705.07321/) (2017)
- [Time Series Forecasting Using LSTM Networks: A Symbolic Approach](https://mlsanity.com/paper/2003.05672/) (2020)
- [A Mixture of Generalized Hyperbolic Distributions](https://mlsanity.com/paper/1305.1036/) (2013)
- [ABBA: Adaptive Brownian bridge-based symbolic aggregation of time series](https://mlsanity.com/paper/2003.12469/) (2020)

## Built on by (most cited first, 7 of 7)

- [LLM-ABBA: Understanding time series via symbolic approximation](https://mlsanity.com/paper/2411.18506/) (2024)
- [Persistence-Based Discretization for Learning Discrete Event Systems from Time Series](https://mlsanity.com/paper/2301.05041/) (2023)
- [ASTRIDE: Adaptive Symbolization for Time Series Databases](https://mlsanity.com/paper/2302.04097/) (2023)
- [Time-to-Pattern: Information-Theoretic Unsupervised Learning for Scalable Time Series Summarization](https://mlsanity.com/paper/2308.13722/) (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)
- [STaT: Resolving Shape Distortion in Non-Stationary Time Series via Tri-Modal Synergy](https://mlsanity.com/paper/2605.25943/) (2026)

## Abstract (arXiv)

Symbolic representations are a useful tool for the dimension reduction of temporal data, allowing for the efficient storage of and information retrieval from time series. They can also enhance the training of machine learning algorithms on time series data through noise reduction and reduced sensitivity to hyperparameters. The adaptive Brownian bridge-based aggregation (ABBA) method is one such effective and robust symbolic representation, demonstrated to accurately capture important trends and shapes in time series. However, in its current form the method struggles to process very large time series. Here we present a new variant of the ABBA method, called fABBA. This variant utilizes a new aggregation approach tailored to the piecewise representation of time series. By replacing the k-means clustering used in ABBA with a sorting-based aggregation technique, and thereby avoiding repeated sum-of-squares error computations, the computational complexity is significantly reduced. In contrast to the original method, the new approach does not require the number of time series symbols to be specified in advance. Through extensive tests we demonstrate that the new method significantly outperforms ABBA with a considerable reduction in runtime while also outperforming the popular SAX and 1d-SAX representations in terms of reconstruction accuracy. We further demonstrate that fABBA can compress other data types such as images.