Aligning the Unseen in Attributed Graphs: Interplay between Graph Geometry and Node Attributes Manifold

TL;DR

This paper introduces a novel variational autoencoder that separately models attribute and structural manifolds in attributed graphs, revealing hidden connectivity patterns and anomalies that traditional methods overlook due to geometric conflicts.

Contribution

It proposes a new approach that disentangles manifold learning from structural alignment, addressing geometric flaws in existing attributed graph representation learning methods.

Findings

Uncovers hidden connectivity patterns

Detects anomalies missed by conventional methods

Demonstrates theoretical and practical limitations of existing approaches

Abstract

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.