Multiway Spectral Clustering: A Margin-Based Perspective

TL;DR

This paper introduces a new margin-based perspective on multiway spectral clustering, unifying analysis and guiding the development of algorithms while connecting it to statistical methods.

Contribution

It provides a novel margin-based framework that clarifies relaxation and rounding in spectral clustering and links it to other statistical techniques.

Findings

Unified analysis of spectral clustering algorithms

Guidance for designing new spectral clustering algorithms

Connections established with statistical methods like Procrustes analysis

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.