# Learning Edge Representations via Low-Rank Asymmetric Projections

## TL;DR

This paper introduces a novel graph embedding method that explicitly models directed edges and uses a graph likelihood objective, resulting in more concise, accurate representations that outperform previous methods in link prediction tasks.

## Contribution

The paper presents a new approach combining explicit edge modeling and a graph likelihood objective, improving embedding quality and efficiency for directed graphs.

## Key findings

- Achieves up to 76% error reduction in link prediction.
- Produces embeddings 10 times smaller with higher accuracy.
- Effectively models directed edges in graph embeddings.

## Abstract

We propose a new method for embedding graphs while preserving directed edge information. Learning such continuous-space vector representations (or embeddings) of nodes in a graph is an important first step for using network information (from social networks, user-item graphs, knowledge bases, etc.) in many machine learning tasks. Unlike previous work, we (1) explicitly model an edge as a function of node embeddings, and we (2) propose a novel objective, the "graph likelihood", which contrasts information from sampled random walks with non-existent edges. Individually, both of these contributions improve the learned representations, especially when there are memory constraints on the total size of the embeddings. When combined, our contributions enable us to significantly improve the state-of-the-art by learning more concise representations that better preserve the graph structure. We evaluate our method on a variety of link-prediction task including social networks, collaboration networks, and protein interactions, showing that our proposed method learn representations with error reductions of up to 76% and 55%, on directed and undirected graphs. In addition, we show that the representations learned by our method are quite space efficient, producing embeddings which have higher structure-preserving accuracy but are 10 times smaller.