Paper Info
Title
A Sparse Completely Positive Relaxation of the Modularity Maximization for Community Detection.
Abstract
In this paper, we consider the community detection problem under either the stochastic block model (SBM) assumption or the degree-correlated SBM assumption. The modularity maximization formulation for the community detection problem is NP-hard in general. In this paper, we propose a sparse and low-rank completely positive relaxation for the modularity maximization problem, we then develop an efficient row-by-row (RBR)-type block coordinate descent algorithm to solve the relaxation and prove an O(1/root N) convergence rate to a stationary point, where N is the number of iterations. A fast rounding scheme is constructed to retrieve the community structure from a solution to the above relaxation. Nonasymptotic high probability bounds on the misclassification rate are established to justify our approach. We further develop an asynchronous parallel RBR algorithm to speed up the convergence. Extensive numerical experiments on both synthetic and real world networks show that the proposed approach enjoys advantages in both clustering accuracy and numerical efficiency. Our numerical results indicate that the newly proposed method is a competitive alternative for the community detection problem on sparse networks with over 50 million nodes.
Year
DOI
Venue
2017
10.1137/17M1141904
SIAM JOURNAL ON SCIENTIFIC COMPUTING
Keywords
Field
DocType
community detection,degree-correlated stochastic block model,completely positive relaxation,proximal block coordinate descent method,nonasymptotic error bound
Convergence (routing),Mathematical optimization,Algorithm,Stochastic block model,Rounding,Stationary point,Rate of convergence,Coordinate descent,Cluster analysis,Mathematics,Maximization
Journal
Volume
Issue
ISSN
40
5
1064-8275
Citations 
PageRank 
References 
0
0.34
15
Authors
4
Name
Order
Citations
PageRank
Junyu Zhang164.70
Haoyang Liu200.34
Zaiwen Wen393440.20
Shuzhong Zhang42808181.66