arXiv:2605.00716cs.LGcs.SI2026-05被引 2

用对数比值坐标学习可解释的图嵌入,让节点特征显式反映结构组成关系。

Aitchison Embeddings for Learning Compositional Graph Representations

论文配图:Aitchison Embeddings for Learning Compositional Graph Representations
图 1 · 摘自论文原文
  • 基于艾奇森几何,将节点表示为单纯形上的混合成分,用ILR坐标映射到欧氏空间。
  • 在节点分类和链接预测上性能媲美主流方法,且嵌入本身具可解释性。
  • 支持成分删减后几何保持一致,可探查不同结构成分对预测的影响。

表示学习是图机器学习的核心,支撑链接预测与节点分类等任务。然而,大多数图嵌入难以解释,无法揭示特征与图结构的关系。许多网络天然具有角色混合视角:节点可被描述为潜在原型因子的混合。受此启发,我们提出一种基于艾奇森几何的组合式图嵌入框架,该几何是用于比较混合物的标准几何。节点被表示为单纯形值的组合,并通过保距对数比值(ILR)坐标嵌入,保留艾奇森距离的同时,在欧氏空间中实现无约束优化。这带来了内在可解释的嵌入,其几何结构反映原型间的相对权衡,并在成分受限时仍保持一致行为;我们考虑固定与可学习的ILR基。在节点分类和链接预测任务中,该方法性能媲美强基线,同时通过构造即具备可解释性,而非事后补充。此外,子组合一致性使得成分删减与重归一化后仍保持良好几何结构,我们利用此特性通过子组合降维来探究原型组如何影响表示与预测。

原文摘要 · Abstract (English)

Representation learning is central to graph machine learning, powering tasks such as link prediction and node classification. However, most graph embeddings are hard to interpret, offering limited insight into how learned features relate to graph structure. Many networks naturally admit a role-mixture view, where nodes are best described as mixtures over latent archetypal factors. Motivated by this structure, we propose a compositional graph embedding framework grounded in Aitchison geometry, the canonical geometry for comparing mixtures. Nodes are represented as simplex-valued compositions and embedded via isometric log-ratio (ILR) coordinates, which preserve Aitchison distances while enabling unconstrained optimization in Euclidean space. This yields intrinsically interpretable embeddings whose geometry reflects relative trade-offs among archetypes and supports coherent behavior under component restriction; we consider both fixed and learnable ILR bases. Across node classification and link prediction, our method achieves competitive performance with strong baselines while providing explainability by construction rather than post-hoc. Finally, subcompositional coherence enables principled component restriction: removing and renormalizing subsets preserves a well-defined geometry, which we exploit via subcompositional dimensionality removal to probe how archetype groups influence representations and predictions.

图嵌入可解释性组合表示艾奇森几何

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