Network Embedding by Walking on the Line Graph

Abstract

In this paper, we propose to embed edges instead of nodes using state-of-the-art neural/factorization methods (DeepWalk, node2vec). 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.