Multiway Spectral Clustering: A Margin-based Perspective
Zhihua Zhang, Michael I. Jordan · 2008
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. Key words and phrases: Spectral clustering, spectral relaxation, graph partitioning, reproducing kernel Hilbert space, large-margin classification, Gaussian intrinsic autoregression. 1.