2024/10/08 by Thomas Bläsius, Bläsius, Thomas, Jean-Pierre von der Heydt +5
Computer Science · #Advanced Graph Neural Networks #Bayesian Modeling and Causal Inference #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #Graph Theory and Algorithms #Machine Learning (cs.LG) #Social and Information Networks (cs.SI)
paper · pdf · doi:10.48550/arxiv.2410.06042
openalex publication_date 2024/10/08 · openalex created_date 2024/10/12 · openalex updated_date 2026/07/28
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.