Network-Adjusted Covariates for Community Detection

TL;DR

This paper introduces a novel, tuning-free spectral clustering method using network-adjusted covariates for community detection, achieving exact recovery under certain conditions and outperforming existing methods in simulations and real networks.

Contribution

The paper proposes a new network-adjusted covariate construction method for community detection that is tuning-free, theoretically consistent, and computationally efficient, addressing limitations of prior approaches.

Findings

Exact community recovery under degree-corrected stochastic blockmodels.

Method outperforms existing approaches in simulations and real data.

Provides interpretable community structures even with isolated nodes.

Abstract

Community detection is a crucial task in network analysis that can be significantly improved by incorporating subject-level information, i.e. covariates. However, current methods often struggle with selecting tuning parameters and analyzing low-degree nodes. In this paper, we introduce a novel method that addresses these challenges by constructing network-adjusted covariates, which leverage the network connections and covariates with a unique weight to each node based on the node's degree. Spectral clustering on network-adjusted covariates yields an exact recovery of community labels under certain conditions, which is tuning-free and computationally efficient. We present novel theoretical results about the strong consistency of our method under degree-corrected stochastic blockmodels with covariates, even in the presence of mis-specification and sparse communities with bounded degrees. Additionally, we establish a general lower bound for the community detection problem when both network and covariates are present, and it shows our method is optimal up to a constant factor. Our method outperforms existing approaches in simulations and a LastFM app user network, and provides interpretable community structures in a statistics publication citation network where $30\%$ of nodes are isolated.