Performance of a community detection algorithm based on semidefinite programming

TL;DR

This paper investigates a semidefinite programming-based community detection algorithm in graphs, demonstrating its efficiency, robustness, and near-optimal performance in identifying planted partitions within stochastic block models.

Contribution

It provides a detailed analysis of a semidefinite programming approach for community detection, highlighting its practical speed, robustness, and quasi-optimal detection capabilities.

Findings

Algorithm is very fast, solving large problems in seconds.

Semidefinite programming approach is robust to model variations.

The method achieves near-optimal detection performance.

Abstract

The problem of detecting communities in a graph is maybe one the most studied inference problems, given its simplicity and widespread diffusion among several disciplines. A very common benchmark for this problem is the stochastic block model or planted partition problem, where a phase transition takes place in the detection of the planted partition by changing the signal-to-noise ratio. Optimal algorithms for the detection exist which are based on spectral methods, but we show these are extremely sensible to slight modification in the generative model. Recently Javanmard, Montanari and Ricci-Tersenghi (arXiv:1511.08769) have used statistical physics arguments, and numerical simulations to show that finding communities in the stochastic block model via semidefinite programming is quasi optimal. Further, the resulting semidefinite relaxation can be solved efficiently, and is very robust with respect to changes in the generative model. In this paper we study in detail several practical aspects of this new algorithm based on semidefinite programming for the detection of the planted partition. The algorithm turns out to be very fast, allowing the solution of problems with $O(10^5)$ variables in few second on a laptop computer.