Beyond Node Embedding: A Direct Unsupervised Edge Representation Framework for Homogeneous Networks

TL;DR

This paper introduces a novel unsupervised method for directly embedding edges in homogeneous networks by converting the network into a weighted line graph, improving edge mining tasks.

Contribution

It proposes the first direct unsupervised edge embedding approach using weighted line graphs and collective homophily, independent of node embeddings.

Findings

Effective for link prediction tasks

Generates meaningful edge embeddings without relying on node embeddings

Connects edge embeddings to node centrality measures

Abstract

Network representation learning has traditionally been used to find lower dimensional vector representations of the nodes in a network. However, there are very important edge driven mining tasks of interest to the classical network analysis community, which have mostly been unexplored in the network embedding space. For applications such as link prediction in homogeneous networks, vector representation (i.e., embedding) of an edge is derived heuristically just by using simple aggregations of the embeddings of the end vertices of the edge. Clearly, this method of deriving edge embedding is suboptimal and there is a need for a dedicated unsupervised approach for embedding edges by leveraging edge properties of the network. Towards this end, we propose a novel concept of converting a network to its weighted line graph which is ideally suited to find the embedding of edges of the original network. We further derive a novel algorithm to embed the line graph, by introducing the concept of collective homophily. To the best of our knowledge, this is the first direct unsupervised approach for edge embedding in homogeneous information networks, without relying on the node embeddings. We validate the edge embeddings on three downstream edge mining tasks. Our proposed optimization framework for edge embedding also generates a set of node embeddings, which are not just the aggregation of edges. Further experimental analysis shows the connection of our framework to the concept of node centrality.