Refining Euclidean Obfuscatory Nodes Helps: A Joint-Space Graph Learning Method for Graph Neural Networks

Area of Science:

• Machine Learning
• Graph Neural Networks
• Data Mining

Background:

• Graph neural networks (GNNs) require predefined graph structures, limiting their applicability.
• Existing methods jointly learn graph structure and GNN parameters but often assume constant space curvature (Euclidean or hyperbolic).
• Constant curvature assumptions can lead to obfuscatory nodes, hindering accurate node embedding and classification.

Purpose of the Study:

• To propose a novel joint-space graph learning (JSGL) method for GNNs that handles non-constant curvatures.
• To effectively identify and refine embeddings of obfuscatory nodes in graph learning.

Main Methods:

• JSGL learns an initial graph structure using Euclidean embeddings.
• It identifies obfuscatory nodes within the Euclidean space.
• The graph topology near these obfuscatory nodes is then refined using hyperbolic space embeddings.

Main Results:

• JSGL successfully identifies obfuscatory nodes that are improperly embedded.
• The proposed method demonstrates superior performance compared to various baseline methods in experimental evaluations.
• Theoretical justification is provided for the obfuscatory node identification mechanism.

Conclusions:

• JSGL offers an effective approach for learning graph structures in the presence of non-constant curvatures.
• The joint Euclidean-hyperbolic space refinement addresses limitations of existing GNN graph learning methods.
• This method enhances the robustness and accuracy of GNNs when graph structures are initially unknown or complex.