Provable Estimation of the Number of Blocks in Block Models

TL;DR

This paper introduces a semi-definite relaxation method for community detection in networks that accurately estimates the number of clusters without prior knowledge, outperforming existing techniques in various experiments.

Contribution

It presents a novel semi-definite relaxation approach that recovers the number of clusters and clustering matrix exactly without prior parameter knowledge.

Findings

Method accurately estimates number of clusters in simulations.

Outperforms state-of-the-art techniques in real data experiments.

Recovers clustering structure with high probability.

Abstract

Community detection is a fundamental unsupervised learning problem for unlabeled networks which has a broad range of applications. Many community detection algorithms assume that the number of clusters $r$ is known apriori. In this paper, we propose an approach based on semi-definite relaxations, which does not require prior knowledge of model parameters like many existing convex relaxation methods and recovers the number of clusters and the clustering matrix exactly under a broad parameter regime, with probability tending to one. On a variety of simulated and real data experiments, we show that the proposed method often outperforms state-of-the-art techniques for estimating the number of clusters.