Time series clustering using elastic distances

Holder, Christopher (2025) Time series clustering using elastic distances. Doctoral thesis, University of East Anglia.

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Abstract

In recent years, time series data has become increasingly ubiquitous, emerging across numerous domains such as astronomy, biology, engineering, finance, manufacturing, medicine, meteorology, and more. A time series is an ordered sequence of real valued observations. The most common form of ordering is in the time domain. Although the concept of a time series is not limited to time-based ordering, the fact that human experience is inherently bound to the passage of time makes time-domain data particularly prevalent. As a result, nearly any recorded phenomenon can be represented as a time series.

The widespread generation of time series data, coupled with the desire to analyse and derive insights from it, has sparked significant interest in time series machine learning tasks. Among these, time series clustering (TSCL) has emerged as one of the most prominent fields. TSCL aims to group time series into clusters where the series within a cluster exhibit homogeneity, while those outside the cluster are heterogeneous. As an unsupervised task, TSCL requires no manual labelling, making it versatile and applicable to a wide range of time series datasets. It is often employed as a key tool for exploratory data analysis.

One of the most common approaches to clustering time series data is to adapt traditional clustering algorithms (e.g., k-means, k-medoids, DBSCAN, agglomerative clustering) by replacing conventional distance measures with elastic ones. Elastic distances account for misalignment between time series during distance computation—when similar events occur but are recorded at different time intervals in each series. By accounting for misalignment, elastic distances significantly improve the quality of the similarity measure between time series.

Dynamic Time Warping (DTW) has become the most widely used elastic distance in TSCL literature. However, other elastic distances have demonstrated superior performance in related fields, such as time series classification. Despite this, the TSCL community has been slow to adopt these alternatives. This thesis addresses this gap by conducting the most comprehensive review of elastic distances for TSCL. We evaluate 12 different elastic distances, nine of which had not been previously applied to TSCL. Our empirical analysis reveal that many of these unconsidered elastic distances significantly outperform DTW for TSCL tasks.

Building on these findings, we propose novel elastic distance-based algorithms, including the Elastic Barycentre Average, the Elastic Unsupervised Proportional Weighting (EUPW) ensemble scheme, the Elastic Clustering Ensemble (ECE), and the k-means end-to-end Elastic Stochastic subgradient Barycentre Average (KESBA) clusterer.

This thesis demonstrates the benefits of incorporating previously unexplored elastic distances into established TSCL algorithms, introduces new elastic-based averaging techniques, and presents the development of state-of-the-art elastic-based partition and ensemble clustering methods. Together, these contributions advance TSCL performance and lay the foundation for future innovations in the field.

Item Type:	Thesis (Doctoral)
Faculty \ School:	Faculty of Science > School of Computing Sciences
Depositing User:	Kitty Laine
Date Deposited:	04 Nov 2025 14:10
Last Modified:	04 Nov 2025 14:10
URI:	https://ueaeprints.uea.ac.uk/id/eprint/100897
DOI:

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