Spectral Embedding of Weighted Graphs
研究加权图谱嵌入时边权变换对社区检测效果的影响，发现温和化或阈值化等变换能显著提升效果，对网络分析研究者有参考价值。
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.