Multi-scale signed graph convolutional network based on framelet.

Area of Science:

• Graph Neural Networks
• Signal Processing on Graphs
• Machine Learning

Background:

• Spectral graph convolutional networks (GCNs) excel in node classification and link prediction.
• Existing GCNs primarily focus on unsigned graphs, limiting their application to signed and directed graph data.
• Graph framelets provide multiresolution analysis for graph signals, but their application to signed graphs is underexplored.

Purpose of the Study:

• To propose an efficient framelet-based GCN tailored for signed (including directed) graphs.
• To leverage the magnetic signed Laplace matrix for multiresolution analysis of signed graph signals.
• To enhance the performance of GCNs on complex graph structures.

Main Methods:

• Developed a magnetic signed graph framelet system for excavating low-pass and high-pass information.
• Implemented framelet-based convolution in both real and complex domains using a complex-valued magnetic Laplacian.
• Employed Chebyshev polynomial approximation to accelerate framelet transform and mitigate computational complexity.

Main Results:

• The proposed Framelet-MSGCN effectively handles signed, directed, and weighted graph data.
• Extensive experiments demonstrated superior performance compared to state-of-the-art algorithms on four real-world datasets.
• Achieved significant improvements in five link prediction tasks.

Conclusions:

• The proposed framelet-based GCN offers an efficient and effective solution for analyzing complex signed graph data.
• The magnetic signed graph framelet system provides a powerful tool for multiscale graph signal processing.
• This work advances the capabilities of GCNs in handling diverse and intricate graph structures.