非均匀随机图中的距离保持嵌入
Distance-Preserving Embeddings in Inhomogeneous Random Graphs
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- Johns Hopkins University（约翰斯·霍普金斯大学）
- Georgia Institute of Technology（佐治亚理工学院）
机构由 AI 辅助整理，请以论文原文为准。
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中文总结 AI 辅助
研究非均匀随机图中距离保持嵌入，基于地标嵌入分析最短路径近似，扩展失真保证到全局平均并统一分析，引入GNN增强变体，使模型能从小图学习并推广到大型真实网络，保持或超越经典嵌入保真度。
中文摘要 AI 辅助
图机器学习为理解复杂网络和学习有意义的节点表示提供了强大工具。然而，设计能最小化局部和全局功能（如最短路径长度）失真的嵌入是一个核心挑战。以往距离保持嵌入的失真保证本质上是最坏情况，产生过于悲观的界限。为解决此问题，我们分析了基于地标嵌入在非均匀随机图上的最短路径近似。通过保留到一小组称为地标的参考节点的最短路径，基于地标的方法有效地充当虚拟图扳手。我们将这些保证扩展到全局、组件范围的平均值，并通过新颖的度量三明治框架统一了有限类型和连续潜在空间的分析。最后，我们引入了一种GNN增强变体，用灵活的、结构感知的神经替代物取代了刚性的、计算昂贵的精确最短路径查询。
英文摘要
Graph machine learning provides powerful tools for understanding complex networks and learning meaningful node representations. A central challenge, however, is designing embeddings with minimal distortion of both local and global functionals, such as shortest path lengths. Prior distortion guarantees for distance-preserving embeddings are worst-case in nature, producing overly pessimistic bounds that fail to capture the structure of typical large-scale networks. To address this, we analyze shortest-path approximation via landmark-based embeddings on inhomogeneous random graphs, a general model with type-dependent edge probabilities. By retaining shortest paths to a small set of reference nodes called landmarks, landmark-based methods effectively function as virtual graph spanners, where structural heterogeneity and controlled neighborhood expansion modeled via multi-type branching processes enable significantly tighter dimension-distortion trade-offs than classical worst-case bounds. We extend these guarantees to global, component-wide averages and unify the analysis across finite-type and continuous latent spaces through a novel metric sandwiching framework, establishing universal distortion bounds for general $L^2$ kernel models, including heavy-tailed and power-law networks. Finally, we introduce a GNN-augmented variant that replaces rigid, computationally expensive exact shortest-path queries with flexible, structure-aware neural surrogates. By leveraging the inherent alignment between graph neural message-passing and the dynamic programming principles of shortest-path algorithms, our approach demonstrates that models trained on small-scale random graphs learn to extract universal distance-preserving features, achieving robust generalization to large-scale, real-world networks that match or exceed the fidelity of classical, exact landmark-based embeddings.
