Improved Graph Clustering

Abstract

Graph clustering involves the task of dividing nodes into clusters, so that the edge density is higher within clusters as opposed to across clusters. A natural, classic and popular statistical setting for evaluating solutions to this problem is the stochastic block model, also referred to as the planted partition model. In this paper we present a new algorithm--a convexified version of Maximum Likelihood--for graph clustering. We show that, in the classic stochastic block model setting, it outperforms existing methods by polynomial factors when the cluster size is allowed to have general scalings. In fact, it is within logarithmic factors of known lower bounds for spectral methods, and there is evidence suggesting that no polynomial time algorithm would do significantly better. We then show that this guarantee carries over to a more general extension of the stochastic block model. Our method can handle the settings of semi-random graphs, heterogeneous degree distributions, unequal cluster sizes, unaffiliated nodes, partially observed graphs and planted clique/coloring etc. In particular, our results provide the best exact recovery guarantees to date for the planted partition, planted k-disjoint-cliques and planted noisy coloring models with general cluster sizes; in other settings, we match the best existing results up to logarithmic factors.

This is the final version published in IEEE Transactions on Information Theory. An earlier version of this work appeared under the title "Clustering Sparse Graphs" at the Neural Information Processing Systems Conference (NIPS), 2012

References in corpus (3)

• Asymptotic analysis of the stochastic block model for modular networks and its algorithmic applications
• Graph spectra and the detectability of community structure in networks
• Guaranteed clustering and biclustering via semidefinite programming

Cited by in corpus (7)

• Evaluating Overfit and Underfit in Models of Network Community Structure
• Consistency of Spectral Hypergraph Partitioning under Planted Partition Model
• Community Detection with Side Information: Exact Recovery under the Stochastic Block Model
• Exact Recovery in the Hypergraph Stochastic Block Model: a Spectral Algorithm
• Using Two Independent Channels with Gateway for FlexRay Static Segment Scheduling
• Scalable and Robust Community Detection with Randomized Sketching
• Robust Hypergraph Clustering via Convex Relaxation of Truncated MLE