ICLR 2025

Published as a conference paper at ICLR 2025
CORESET SPECTRAL CLUSTERING
Ben Jourdan1, Gregory Schwartzman2, Peter Macgregor3, and He Sun1
1University of Edinburgh, UK
2Japan Advanced Institute of Science and Technology (JAIST), Japan
3University of St Andrews, UK
ben.jourdan@ed.ac.uk, greg@jaist.ac.jp, prm4@st-andrews.ac.uk,
h.sun@ed.ac.uk
ABSTRACT
Coresets have become an invaluable tool for solving k-means and kernel k-means clustering
problems on large datasets with small numbers of clusters. On the other hand, spectral clustering
works well on sparse graphs and has recently been extended to scale efficiently to large numbers
of clusters. We exploit the connection between kernel k-means and the normalised cut problem
to combine the benefits of both. Our main result is a coreset spectral clustering algorithm
for graphs that clusters a coreset graph to infer a good labelling of the original graph. We
prove that an α-approximation for the normalised cut problem on the coreset graph is an O(α)-
approximation on the original. We also improve the running time of the state-of-the-art coreset
algorithm for kernel k-means on sparse kernels, from ˜O(nk) to ˜O(n · min{k, davg}), where
davg is the average number of non-zero entries in each row of the n × n kernel matrix. Our
experiments confirm our coreset algorithm is asymptotically faster on large real-world graphs
with many clusters, and show that our clustering algorithm overcomes the main challenge faced
by coreset kernel k-means on sparse kernels which is getting stuck in local optima.
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INTRODUCTION
Kernel k-means and spectral clustering are two popular algorithms which are capable of learning
non-linear decision boundaries between clusters. For this reason, they have been applied to many
practical problems in machine learning, including in the fields of medical research and network
science (Gönen & Margolin, 2014; Kuo et al., 2014; White & Smyth, 2005).
Given a data set X, both kernel k-means and spectral clustering ...