Impact of regularization on spectral clustering Page 1 The Annals of Statistics 2016, Vol. 44, No.
4, 1765–1791 DOI: 10.1214/16-AOS1447 © Institute of Mathematical Statistics, 2016 IMPACT …

In this work we study the widely used\emphspectral clustering algorithms, ie partition a
graph into k clusters via (1) embedding the vertices of a graph into a low-dimensional space …

This work studies the classical spectral clustering algorithm which embeds the vertices of
some graph G=(V_G, E_G) into R^ k using k eigenvectors of some matrix of G, and applies k …

The celebrated Cheeger's Inequality (Alon and Milman 1985; Alon 1986) establishes a
bound on the edge expansion of a graph via its spectrum. This inequality is central to a rich …

Given a subset A of vertices of an undirected graph G, the cut-improvement problem asks us
to find a subset S that is similar to A but has smaller conductance. An elegant algorithm for …

The spectrum of a network or graph G=(V,E) with adjacency matrix A, consists of the
eigenvalues of the normalized Laplacian L=ID^-1/2AD^-1/2. This set of eigenvalues …

Contrastive learning has emerged as a premier method for learning representations with or
without supervision. Recent studies have shown its utility in graph representation learning …

The Cheeger inequality for undirected graphs, which relates the conductance of an
undirected graph and the second smallest eigenvalue of its normalized Laplacian, is a …

In a recent breakthrough STOC 2015 paper, a continuous diffusion process was considered
on hypergraphs (which has been refined in a recent JACM 2018 paper) to define a …

We present a simple spectral approach to the well-studied constrained clustering problem. It
captures constrained clustering as a generalized eigenvalue problem with graph …