# A Review and Evaluation of Elastic Distance Functions for Time Series Clustering

arXiv: https://arxiv.org/abs/2205.15181 · HTML: https://mlsanity.com/paper/2205.15181/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 58 references that are in the map.
- First posted on arXiv 30 May 2022.

## Builds on (most cited first, 9 of 9)

- [The UCR Time Series Archive](https://mlsanity.com/paper/1810.07758/) (2018)
- [Benchmarking Multivariate Time Series Classification Algorithms](https://mlsanity.com/paper/2007.13156/) (2020)
- [HIVE-COTE 2.0: a new meta ensemble for time series classification](https://mlsanity.com/paper/2104.07551/) (2021)
- [Should we really use post-hoc tests based on mean-ranks?](https://mlsanity.com/paper/1505.02288/) (2015)
- [sktime: A Unified Interface for Machine Learning with Time Series](https://mlsanity.com/paper/1909.07872/) (2019)
- [A review on distance based time series classification](https://mlsanity.com/paper/1806.04509/) (2018)
- [A Benchmark Study on Time Series Clustering](https://mlsanity.com/paper/2004.09546/) (2020)
- [Nonsmooth Analysis and Subgradient Methods for Averaging in Dynamic Time Warping Spaces](https://mlsanity.com/paper/1701.06393/) (2017)
- [Elastic Similarity and Distance Measures for Multivariate Time Series](https://mlsanity.com/paper/2102.10231/) (2021)

## Built on by (most cited first, 14 of 14)

- [Bake off redux: a review and experimental evaluation of recent time series classification algorithms](https://mlsanity.com/paper/2304.13029/) (2023)
- [aeon: a Python toolkit for learning from time series](https://mlsanity.com/paper/2406.14231/) (2024)
- [ShapeDBA: Generating Effective Time Series Prototypes using ShapeDTW Barycenter Averaging](https://mlsanity.com/paper/2309.16353/) (2023)
- [CLaP -- State Detection from Time Series](https://mlsanity.com/paper/2504.01783/) (2025)
- [On time series clustering with k-means](https://mlsanity.com/paper/2410.14269/) (2024)
- [Rock the KASBA: Blazingly Fast and Accurate Time Series Clustering](https://mlsanity.com/paper/2411.17838/) (2024)
- [SE-shapelets: Semi-supervised Clustering of Time Series Using Representative Shapelets](https://mlsanity.com/paper/2304.03292/) (2023)
- [Convolutional and Deep Learning based techniques for Time Series Ordinal Classification](https://mlsanity.com/paper/2306.10084/) (2023)
- [ReLATE: Resilient Learner Selection for Multivariate Time-Series Classification Against Adversarial Attacks](https://mlsanity.com/paper/2503.07882/) (2025)
- [Castor: Competing shapelets for fast and accurate time series classification](https://mlsanity.com/paper/2403.13176/) (2024)
- [Clustering of timed sequences -- Application to the analysis of care pathways](https://mlsanity.com/paper/2404.15379/) (2024)
- [Effectiveness of High-Dimensional Distance Metrics on Solar Flare Time Series](https://mlsanity.com/paper/2511.01873/) (2025)
- [CROCS: A Two-Stage Clustering Framework for Behaviour-Centric Consumer Segmentation with Smart Meter Data](https://mlsanity.com/paper/2601.10494/) (2026)
- [Soft-MSM: Differentiable Context-Aware Elastic Alignment for Time Series](https://mlsanity.com/paper/2605.00069/) (2026)

## Abstract (arXiv)

Time series clustering is the act of grouping time series data without recourse to a label. Algorithms that cluster time series can be classified into two groups: those that employ a time series specific distance measure; and those that derive features from time series. Both approaches usually rely on traditional clustering algorithms such as k-means. Our focus is on distance based time series that employ elastic distance measures, i.e. distances that perform some kind of realignment whilst measuring distance. We describe nine commonly used elastic distance measures and compare their performance with k-means and k-medoids clustering. Our findings are surprising. The most popular technique, dynamic time warping (DTW), performs worse than Euclidean distance with k-means, and even when tuned, is no better. Using k-medoids rather than k-means improved the clusterings for all nine distance measures. DTW is not significantly better than Euclidean distance with k-medoids. Generally, distance measures that employ editing in conjunction with warping perform better, and one distance measure, the move-split-merge (MSM) method, is the best performing measure of this study. We also compare to clustering with DTW using barycentre averaging (DBA). We find that DBA does improve DTW k-means, but that the standard DBA is still worse than using MSM. Our conclusion is to recommend MSM with k-medoids as the benchmark algorithm for clustering time series with elastic distance measures. We provide implementations in the aeon toolkit, results and guidance on reproducing results on the associated GitHub repository.