用加权空间嵌入图节点，比传统方法更高效准确。
Weighted Embeddings for Low-Dimensional Graph Representation
- 提出加权空间嵌入算法WEmbed，介于欧氏与双曲几何之间
- 在2000多个真实图上表现优于顶尖欧氏嵌入，且维数更低
- 计算快、易用，适合处理层次化异构图数据
从符号数据中学习低维数值表示是机器学习的重要课题。尽管欧氏空间嵌入常见，但近年研究发现双曲几何更适合表达层次结构和异质数据（如度分布呈幂律的图）。然而，双曲嵌入计算复杂、下游任务难应用。本文提出加权空间嵌入，其数学形式更简单，与双曲几何密切相关。我们提出了WEmbed算法，并基于生成图及超过2000个真实世界图验证：该方法在异构图上显著优于当前最优欧氏嵌入，且使用更少维度。在剩余实例上，WEmbed运行时间与嵌入质量均与顶级欧氏嵌入器相当。
原文摘要 · Abstract (English)
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.
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