论文标题
图形嵌入中的歧管结构
Manifold structure in graph embeddings
论文作者
论文摘要
图形的统计分析通常始于嵌入，即表示其节点为空间点的过程。在实践中，如何选择嵌入维度是一个细微的决定，但是从理论上讲，真实维度的概念通常可以使用。在光谱嵌入中，该维度可能很高。但是，本文表明，现有的随机图模型，包括Graphon和其他潜在位置模型，可以预测数据应靠近较低的维度集合。因此，可以通过采用利用隐藏歧管结构的方法来规避维度的诅咒。
Statistical analysis of a graph often starts with embedding, the process of representing its nodes as points in space. How to choose the embedding dimension is a nuanced decision in practice, but in theory a notion of true dimension is often available. In spectral embedding, this dimension may be very high. However, this paper shows that existing random graph models, including graphon and other latent position models, predict the data should live near a much lower-dimensional set. One may therefore circumvent the curse of dimensionality by employing methods which exploit hidden manifold structure.
