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.
"Multiway Spectral Clustering: A Margin-Based Perspective." Statist. Sci. 23 (3) 383 - 403, August 2008. https://doi.org/10.1214/08-STS266