Spectral Embedding of Weighted Graphs
Spectral Embedding of Weighted Graphs
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DOI：
10.1080/01621459.2023.2225239
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发表时间：
2019-10
影响因子：
3.7
通讯作者：
Ian Gallagher;Andrew Jones;A. Bertiger;C. Priebe;Patrick Rubin-Delanchy
中科院分区：
文献类型：
--
作者：
Ian Gallagher;Andrew Jones;A. Bertiger;C. Priebe;Patrick Rubin-Delanchy
当使用谱嵌入分析加权网络时，边权重的明智变换可能会产生更好的结果。为了形式化这个想法，我们考虑了谱嵌入的渐近行为不同的边权重表示，在一个通用的低秩模型。我们衡量不同嵌入的质量--可以在完全不同的尺度上--通过在信息理论的意义上区分社区的难易程度。对于常见类型的加权图，例如计数网络或p值网络，我们发现，无论是在理论上还是在实践中，诸如回火或阈值化之类的变换都是非常有益的。
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-theoretic 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.