Spectral Embedding of Weighted Graphs

• 成果类型: Article
• 署名作者: Gallagher, Ian; Jones, Andrew; Bertiger, Anna; Priebe, Carey E.; Rubin-Delanchy, Patrick
• 署名单位: University of Bristol; Microsoft; Johns Hopkins University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2023.2225239
• 发表日期: 2024
• 页码: 1923-1932
• 关键词: network; performance; DISCOVERY

摘要

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. for this article are available online.