k-means clustering for persistent homology

Yueqi Cao (), Prudence Leung and Anthea Monod
Additional contact information
Yueqi Cao: Imperial College London, South Kensington Campus
Prudence Leung: Imperial College London, South Kensington Campus
Anthea Monod: Imperial College London, South Kensington Campus

Advances in Data Analysis and Classification, 2025, vol. 19, issue 1, No 5, 95-119

Abstract: Abstract Persistent homology is a methodology central to topological data analysis that extracts and summarizes the topological features within a dataset as a persistence diagram. It has recently gained much popularity from its myriad successful applications to many domains, however, its algebraic construction induces a metric space of persistence diagrams with a highly complex geometry. In this paper, we prove convergence of the k-means clustering algorithm on persistence diagram space and establish theoretical properties of the solution to the optimization problem in the Karush–Kuhn–Tucker framework. Additionally, we perform numerical experiments on both simulated and real data of various representations of persistent homology, including embeddings of persistence diagrams as well as diagrams themselves and their generalizations as persistence measures. We find that k-means clustering performance directly on persistence diagrams and measures outperform their vectorized representations.

Keywords: Alexandrov geometry; Karush–Kuhn–Tucker optimization; k-means clustering; Persistence diagrams; Persistent homology; 46M20; 46N30; 51F99 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11634-023-00578-y Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:advdac:v:19:y:2025:i:1:d:10.1007_s11634-023-00578-y

Ordering information: This journal article can be ordered from
http://www.springer. ... ds/journal/11634/PS2

DOI: 10.1007/s11634-023-00578-y

Access Statistics for this article

Advances in Data Analysis and Classification is currently edited by H.-H. Bock, W. Gaul, A. Okada, M. Vichi and C. Weihs

More articles in Advances in Data Analysis and Classification from Springer, German Classification Society - Gesellschaft für Klassifikation (GfKl), Japanese Classification Society (JCS), Classification and Data Analysis Group of the Italian Statistical Society (CLADAG), International Federation of Classification Societies (IFCS)
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().