With the increasing popularity of graph-based methods for dimensionality reduction and representation learning, node embedding functions have become important objects of study in the literature. In this paper, we take an axiomatic approach to understanding node embedding methods, first stating three properties for embedding dissimilarity networks, then proving that all three cannot be satisfied simultaneously by any node embedding method. Similar to existing results on the impossibility of clustering under certain axiomatic assumptions, this points to fundamental difficulties inherent to node embedding tasks. Once these difficulties are identified, we then relax these axioms to allow for certain node embedding methods to be admissible in our framework.

翻译：随着以图表为基础的减少维度和代表性学习方法越来越受欢迎,节点嵌入功能已成为文献中的重要研究对象。在本文件中,我们采取不言而喻的方法来理解节点嵌入方法,首先说明嵌入不同网络的三种特性,然后证明这三种方法不能同时用任何节点嵌入方法来满足所有三种方法。这与某些不言而喻的假设下不可能集群的现有结果类似,也指出了节点嵌入任务所固有的基本困难。一旦发现这些困难,我们就放松这些轴心,以便允许某些节点嵌入方法在我们的框架内被接受。