Multiway Spectral Clustering: A Margin-Based Perspective

Details Multiway Spectral Clustering: A Margin-Based Perspective Multiway Spectral Clustering: A Margin-Based Perspective

2011-02-18

arxiv.org/abs/1102.3768v1

Statistical Science 2008, Vol. 23, No. 3, 383-403

Statistics

Methodology

Published in at http://dx.doi.org/10.1214/08-STS266 the Statistical Science (http://www.imstat.org/sts/) by the Institute of M

Scientific paper

10.1214/08-STS266

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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