Weighted Embeddings for Low-Dimensional Graph Representation

TL;DR

This paper introduces a weighted embedding method that simplifies hyperbolic geometry for graph representation, outperforming Euclidean embeddings on heterogeneous graphs while maintaining comparable computational efficiency.

Contribution

The paper presents WEmbed, a novel weighted embedding algorithm that improves low-dimensional graph representations, especially for heterogeneous data, by leveraging a simpler geometry related to hyperbolic space.

Findings

Weighted embeddings outperform Euclidean embeddings on real-world heterogeneous graphs.

WEmbed achieves higher accuracy with fewer dimensions.

Embedding time is comparable to existing Euclidean methods.

Abstract

Learning low-dimensional numerical representations from symbolic data, e.g., embedding the nodes of a graph into a geometric space, is an important concept in machine learning. While embedding into Euclidean space is common, recent observations indicate that hyperbolic geometry is better suited to represent hierarchical information and heterogeneous data (e.g., graphs with a scale-free degree distribution). Despite their potential for more accurate representations, hyperbolic embeddings also have downsides like being more difficult to compute and harder to use in downstream tasks. We propose embedding into a weighted space, which is closely related to hyperbolic geometry but mathematically simpler. We provide the embedding algorithm WEmbed and demonstrate, based on generated as well as over 2000 real-world graphs, that our weighted embeddings heavily outperform state-of-the-art Euclidean embeddings for heterogeneous graphs while using fewer dimensions. The running time of WEmbed and embedding quality for the remaining instances is on par with state-of-the-art Euclidean embedders.