Perfect Spectral Clustering with Discrete Covariates
This addresses the problem of separating latent network structure from observed covariate homophily for researchers in network analysis, offering a novel theoretical guarantee in spectral clustering.
The paper tackles community detection in networks with discrete node covariates, where edge formation depends on both latent block model structure and homophily on observed covariates, and proposes a spectral algorithm that achieves perfect clustering with high probability on large, sparse networks.
Among community detection methods, spectral clustering enjoys two desirable properties: computational efficiency and theoretical guarantees of consistency. Most studies of spectral clustering consider only the edges of a network as input to the algorithm. Here we consider the problem of performing community detection in the presence of discrete node covariates, where network structure is determined by a combination of a latent block model structure and homophily on the observed covariates. We propose a spectral algorithm that we prove achieves perfect clustering with high probability on a class of large, sparse networks with discrete covariates, effectively separating latent network structure from homophily on observed covariates. To our knowledge, our method is the first to offer a guarantee of consistent latent structure recovery using spectral clustering in the setting where edge formation is dependent on both latent and observed factors.