无向图的伪欧氏吸引-排斥嵌入
Pseudo-Euclidean Attract-Repel Embeddings for Undirected Graphs
摘要：
点积嵌入取一个图并为节点构造向量，使得两个向量之间的点积给出边的强度。点积有一个强传递性的假设，然而，现实世界中生成图的许多重要力量导致了非传递关系。我们通过将节点嵌入到伪欧几里德空间中来消除传递性假设-给每个节点一个吸引和排斥向量。两个节点之间的内积是通过取吸引向量中的点积并减去排斥向量中的点积来定义的。伪欧几里德嵌入可以有效地压缩网络，允许多个最近邻的概念，每个最近邻都有自己的解释，并且可以“开槽”到现有的模型中，例如指数族嵌入或图神经网络，以获得更好的链接预测。
英文摘要：
Dot product embeddings take a graph and construct vectors for nodes such that dot products between two vectors give the strength of the edge. Dot products make a strong transitivity assumption, however, many important forces generating graphs in the real world lead to non-transitive relationships. We remove the transitivity assumption by embedding nodes into a pseudo-Euclidean space - giving each node an attract and a repel vector. The inner product between two nodes is defined by taking the dot product in attract vectors and subtracting the dot product in repel vectors. Pseudo-Euclidean embeddings can compress networks efficiently, allow for multiple notions of nearest neighbors each with their own interpretation, and can be `slotted' into existing models such as exponential family embeddings or graph neural networks for better link prediction.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
