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arXiv · 1102.3768

Multiway Spectral Clustering: A Margin-Based Perspective

Zhihua Zhang·Michael I. Jordan
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Abstract

Spectral clustering is a broad class of clustering procedures in which an intractable combinatorial optimization formulation of clustering is "relaxed" into a tractable eigenvector problem, and in which the relaxed solution is subsequently "rounded" into an approximate discrete solution to the original problem. In this paper we present a novel margin-based perspective on multiway spectral clustering. We show that the margin-based perspective illuminates both the relaxation and rounding aspects of spectral clustering, providing a unified analysis of existing algorithms and guiding the design of new algorithms. We also present connections between spectral clustering and several other topics in statistics, specifically minimum-variance clustering, Procrustes analysis and Gaussian intrinsic autoregression.

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Zhihua Zhang, Michael I. Jordan. 2011-02-18. Multiway Spectral Clustering: A Margin-Based Perspective. https://doi.org/10.1214/08-sts266

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