分离图结构与节点属性，重建被传统方法破坏的生成信号
Aligning the Unseen in Attributed Graphs: Interplay between Graph Geometry and Node Attributes Manifold
- 将属性流形与图结构解耦，避免几何空间冲突
- 通过热核映射量化度量失真，生成可解释的结构描述符
- 发现传统方法遗漏的连接模式与异常，适合图分析研究者
在带属性图上进行表征学习的标准方法——即同时重构节点属性与图结构——存在几何缺陷，因为它强行融合两个可能不兼容的度量空间，导致破坏性对齐，使图的底层生成过程信息丢失。为恢复该信号，我们提出一种定制化的变分自编码器，将流形学习与结构对齐分离。通过量化将属性流形映射到图热核所需的度量失真，将几何冲突转化为可解释的结构描述符。实验表明，该方法能揭示传统方法无法检测的连接模式和异常，证明了后者在理论与实践上的不足。
原文摘要 · Abstract (English)
The standard approach to representation learning on attributed graphs -- i.e., simultaneously reconstructing node attributes and graph structure -- is geometrically flawed, as it merges two potentially incompatible metric spaces. This forces a destructive alignment that erodes information about the graph's underlying generative process. To recover this lost signal, we introduce a custom variational autoencoder that separates manifold learning from structural alignment. By quantifying the metric distortion needed to map the attribute manifold onto the graph's Heat Kernel, we transform geometric conflict into an interpretable structural descriptor. Experiments show our method uncovers connectivity patterns and anomalies undetectable by conventional approaches, proving both their theoretical inadequacy and practical limitations.
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