Network-adjusted covariates for community detection

Y Hu and W Wang

Biometrika, 2024, vol. 111, issue 4, 1221-1240

Abstract: SummaryCommunity detection is a crucial task in network analysis that can be significantly improved by incorporating subject-level information, ie, covariates. Existing methods have shown the effectiveness of using covariates on the low-degree nodes, but rarely discuss the case where communities have significantly different density levels, ie, multiscale networks. In this paper, we introduce a novel method that addresses this challenge by constructing network-adjusted covariates, which leverage the network connections and covariates with a node-specific weight for each node. This weight can be calculated without tuning parameters. We present novel theoretical results on the strong consistency of our method under degree-corrected stochastic blockmodels with covariates, even in the presence of misspecification and multiple sparse communities. Additionally, we establish a general lower bound for the community detection problem when both the network and covariates are present, and it shows that our method is optimal for connection intensity up to a constant factor. Our method outperforms existing approaches in simulations and a LastFM app user network. We then compare our method with others on a statistics publication citation network where 30% of nodes are isolated, and our method produces reasonable and balanced results. Our method is implemented in the R package NAC.

Keywords: Community detection; Degree-corrected stochastic blockmodel; ℓ∞ norm; Node attribute; Random matrix theory; Spectral clustering (search for similar items in EconPapers)
Date: 2024
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