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Improving Spectral Clustering using the Asymptotic Value of the Normalised Cut

By David Hofmeyr

Abstract

Spectral clustering is a popular and versatile clustering method based on a relaxation of the normalised graph cut objective. Despite its popularity, however, there is no single agreed upon method for tuning the important scaling parameter, nor for determining automatically the number of clusters to extract. Popular heuristics exist, but corresponding theoretical results are scarce. In this paper we investigate the asymptotic value of the normalised cut for an increasing sample assumed to arise from an underlying probability distribution, and based on this result provide recommendations for improving spectral clustering methodology. A corresponding algorithm is proposed with strong empirical performance.Comment: An updated version has been accepted to Journal of Computational and Graphical Statistic

Topics: Statistics - Machine Learning
Publisher: 'Informa UK Limited'
Year: 2019
DOI identifier: 10.1080/10618600.2019.1593180
OAI identifier: oai:arXiv.org:1703.09975

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