Consistency of anchor-based spectral clustering

Author:

de Kergorlay Henry-Louis1,Higham Desmond J1

Affiliation:

1. School of Mathematics, University of Edinburgh, Edinburgh EH9 3FD, UK

Abstract

Abstract Anchor-based techniques reduce the computational complexity of spectral clustering algorithms. Although empirical tests have shown promising results, there is currently a lack of theoretical support for the anchoring approach. We define a specific anchor-based algorithm and show that it is amenable to rigorous analysis, as well as being effective in practice. We establish the theoretical consistency of the method in an asymptotic setting where data is sampled from an underlying continuous probability distribution. In particular, we provide sharp asymptotic conditions for the number of nearest neighbors in the algorithm, which ensure that the anchor-based method can recover with high probability disjoint clusters that are mutually separated by a positive distance. We illustrate the performance of the algorithm on synthetic data and explain how the theoretical convergence analysis can be used to inform the practical choice of parameter scalings. We also test the accuracy and efficiency of the algorithm on two large scale real data sets. We find that the algorithm offers clear advantages over standard spectral clustering. We also find that it is competitive with the state-of-the-art LSC method of Chen and Cai (Twenty-Fifth AAAI Conference on Artificial Intelligence, 2011), while having the added benefit of a consistency guarantee.

Funder

Engineering and Physical Sciences Research Council

Publisher

Oxford University Press (OUP)

Subject

Applied Mathematics,Computational Theory and Mathematics,Numerical Analysis,Statistics and Probability,Analysis

Reference35 articles.

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