This paper presents a comprehensive study on clustering: exiting methods and
developments made at various times. Clustering is defined as an unsupervised learning …

Substantial progress has been made recently on develo** provably accurate and efficient
algorithms for low-rank matrix factorization via nonconvex optimization. While conventional …

Spectral methods have emerged as a simple yet surprisingly effective approach for
extracting information from massive, noisy and incomplete data. In a nutshell, spectral …

Recovering low-rank structures via eigenvector perturbation analysis is a common problem
in statistical machine learning, such as in factor analysis, community detection, ranking …

There have been rapid developments in model-based clustering of graphs, also known as
block modelling, over the last ten years or so. We review different approaches and …

Abstract The Davis–Kahan theorem is used in the analysis of many statistical procedures to
bound the distance between subspaces spanned by population eigenvectors and their …

The stochastic block model with two communities, or equivalently the planted bisection
model, is a popular model of random graph exhibiting a cluster behavior. In the symmetric …

We analyze the performance of spectral clustering for community extraction in stochastic
block models. We show that, under mild conditions, spectral clustering applied to the …

New phase transition phenomena have recently been discovered for the stochastic block
model, for the special case of two non-overlap** symmetric communities. This gives raise …

The random dot product graph (RDPG) is an independent-edge random graph that is
analytically tractable and, simultaneously, either encompasses or can successfully …