Simplicial Complex Neural Networks.

Area of Science:

• Graph learning
• Network science
• Machine learning

Background:

• Graph-structured data is prevalent in various domains.
• Existing graph learning models primarily utilize direct graph information (edges/hyperedges).
• Indirect or hidden relations within graph data are often overlooked.

Purpose of the Study:

• To propose a general framework, the Simplicial Complex Neural (SCN) network.
• To leverage both direct and indirect graph information for enhanced graph learning.
• To improve representation learning for nodes, edges, and higher-order structures.

Main Methods:

• Constructing a simplicial complex incorporating direct and indirect graph information.
• Learning simplex representations through layer-by-layer simplicial complex propagation.
• Deriving theoretical bounds for the simplicial complex filter and generalization error.

Main Results:

• Simultaneous representation learning for nodes (0-simplex), edges (1-simplex), and triangles (2-simplex).
• Demonstrated superior performance compared to existing graph and hypergraph network approaches.
• Achieved promising results in node, edge, and triangle classification tasks.

Conclusions:

• The Simplicial Complex Neural network effectively integrates diverse relational information in graphs.
• SCN offers a powerful approach for representation learning on complex graph structures.
• The proposed method shows significant potential for advancing graph learning applications.