In this paper, we propose to embed edges instead of nodes using state-of-the-art neural/factorization methods (DeepWalk, node2vec, NetMF). These methods produce latent representations based on co-ocurrence statistics by simulating fixed-length random walks and then taking bags-of-vectors as the input to the Skip Gram Learning with Negative Sampling (SGNS). We commence by expressing commute times embedding as matrix factorization, and thus relating this embedding to those of DeepWalk and node2vec. Recent results showing formal links between all these methods via the spectrum of graph Laplacian, are then extended to understand the results obtained by SGNS when we embed edges instead of nodes. Since embedding edges is equivalent to embedding nodes in the line graph, we proceed to combine both existing formal characterizations of the line graphs and empirical evidence in order to explain why this embedding dramatically outperforms its nodal counterpart in multi-label classification tasks.

在本文中，我们建议使用最新的神经/分解方法（DeepWalk，node2vec，NetMF）来嵌入边缘而不是节点。这些方法通过模拟固定长度的随机游动，然后将矢量包作为负采样的“跳过革式学习”（SGNS）的输入，基于同现统计产生潜在的表示。我们首先将通勤时间嵌入表示为矩阵分解，然后将其与DeepWalk和node2vec的嵌入相关联。最近的结果显示了通过拉普拉斯图谱在所有这些方法之间的正式联系，然后扩展为了解当我们嵌入边缘而不是节点时SGNS获得的结果。由于嵌入边缘等同于在折线图中嵌入节点，