Spectral Embedding of Weighted Graphs

Ian Gallagher, Andrew Jones, Anna Bertiger, Carey E. Priebe and Patrick Rubin-Delanchy

Journal of the American Statistical Association, 2024, vol. 119, issue 547, 1923-1932

Abstract: When analyzing weighted networks using spectral embedding, a judicious transformation of the edge weights may produce better results. To formalize this idea, we consider the asymptotic behavior of spectral embedding for different edge-weight representations, under a generic low rank model. We measure the quality of different embeddings—which can be on entirely different scales—by how easy it is to distinguish communities, in an information-theoretical sense. For common types of weighted graphs, such as count networks or p-value networks, we find that transformations such as tempering or thresholding can be highly beneficial, both in theory and in practice. Supplementary materials for this article are available online.

Date: 2024
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DOI: 10.1080/01621459.2023.2225239

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