HL-HGAT: Heterogeneous Graph Attention Network via Hodge-Laplacian Operator.

Area of Science:

• Graph Neural Networks
• Topological Data Analysis
• Machine Learning

Background:

• Graph neural networks (GNNs) excel at capturing node relationships.
• Existing GNNs often overlook higher-order structures within graph data.
• Simplicial complexes offer a richer framework for representing complex graph structures.

Purpose of the Study:

• To introduce a novel graph representation learning approach using simplicial complexes.
• To develop a Hodge-Laplacian heterogeneous graph attention network (HL-HGAT) for learning on k-simplices.
• To enhance GNN capabilities by incorporating topological features of simplicial complexes.

Main Methods:

• Defined graph data on k-simplices within a simplicial complex framework.
• Designed HL-HGAT incorporating Hodge-Laplacian (HL) convolutional filters, simplicial projection (SP), and simplicial attention pooling (SAP) operators.
• Utilized polynomial approximation for HL-filters and transformer-based attention mechanisms for feature aggregation across simplices.

Main Results:

• Demonstrated the efficacy of HL-filters in capturing k-simplex topology via spectral domain analysis.
• Showcased the spatial localization properties of approximated HL-filters.
• Validated the model's performance across diverse applications including NP-hard problems, classification, and regression tasks.

Conclusions:

• HL-HGAT effectively learns heterogeneous signal representations across k-simplices.
• The model exhibits versatility and efficacy in handling complex graph-structured data.
• This approach advances GNNs by integrating topological information from simplicial complexes.