GSPNet: Graph Spectral Projection Network using Learnable Spectral Transformation.

Area of Science:

• Graph Neural Networks
• Machine Learning
• Spectral Graph Theory

Background:

• Spectral graph convolutional networks (SGCNs) are prominent for graph-structured data learning.
• SGCNs utilize graph spectral transformations, approximating filters with polynomial propagation for efficiency.
• This polynomial approximation in SGCNs often introduces non-trivial propagation errors.

Purpose of the Study:

• To theoretically analyze the propagation matrix in SGCNs and quantify its inherent error.
• To propose a novel network, Graph Spectral Projection Network (GSPNet), to address SGCN propagation errors.
• To demonstrate GSPNet's capability to learn improved spectral transformations for enhanced graph learning.

Main Methods:

• Theoretical analysis of the propagation matrix in SGCNs, deriving an explicit error bound.
• Development of the Graph Spectral Projection Network (GSPNet) with a learned spectral transformation.
• Empirical evaluation of GSPNet on standard graph datasets against existing SGCN models.

Main Results:

• The study confirms significant propagation errors in standard SGCN polynomial approximations.
• GSPNet successfully learns a propagation matrix that surpasses the limitations of polynomial propagation.
• Experimental results show GSPNet achieving superior performance compared to current SGCN models.

Conclusions:

• SGCN polynomial propagation inherently introduces errors that can be theoretically bounded.
• GSPNet offers a viable solution by learning an optimized spectral transformation, mitigating these errors.
• GSPNet demonstrates promising potential for advancing graph learning tasks beyond conventional SGCNs.