Perfect Spectral Clustering with Discrete Covariates

Jonathan Hehir; Xiaoyue Niu; Aleksandra Slavkovic

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arXiv · 2205.08047

Perfect Spectral Clustering with Discrete Covariates

Jonathan Hehir·Xiaoyue Niu·Aleksandra Slavkovic

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Abstract

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.

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BibTeX RIS

Jonathan Hehir, Xiaoyue Niu, Aleksandra Slavkovic. 2022-05-17. Perfect Spectral Clustering with Discrete Covariates. https://arxiv.org/abs/2205.08047

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