Network embedding is a method of learning a low-dimensional vector representation of network vertices under the condition of preserving different types of network properties. Previous studies mainly focus on preserving structural information of vertices at a particular scale, like neighbor information or community information, but cannot preserve the hierarchical community structure, which would enable the network to be easily analyzed at various scales. Inspired by the hierarchical structure of galaxies, we propose the Galaxy Network Embedding (GNE) model, which formulates an optimization problem with spherical constraints to describe the hierarchical community structure preserving network embedding. More specifically, we present an approach of embedding communities into a low-dimensional spherical surface, the center of which represents the parent community they belong to. Our experiments reveal that the representations from GNE preserve the hierarchical community structure and show advantages in several applications such as vertex multi-class classification, network visualization, and link prediction. The source code of GNE is available online.

中文翻译：

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分层社区结构网络上的网络嵌入

网络嵌入是在保留不同类型网络属性的条件下，学习网络顶点的低维向量表示的方法。以前的研究主要集中在保留特定尺度的顶点结构信息，如邻居信息或社区信息，但不能保留分层的社区结构，这使得网络易于在各种尺度上进行分析。受星系层次结构的启发，我们提出了 Galaxy Network Embedding (GNE) 模型，该模型制定了一个具有球形约束的优化问题来描述保留网络嵌入的层次社区结构。更具体地说，我们提出了一种将社区嵌入低维球面的方法，其中的中心代表他们所属的父社区。我们的实验表明，来自 GNE 的表示保留了分层社区结构，并在顶点多类分类、网络可视化和链接预测等多种应用中显示出优势。GNE 的源代码可在线获取。