  Graph Comparative Learning (GCL) is a self-supervised method that combines
the advantages of Graph Convolutional Networks (GCNs) and comparative learning,
making it promising for learning node representations. However, the GCN
encoders used in these methods rely on the Fourier transform to learn fixed
graph representations, which is inherently limited by the uncertainty principle
involving spatial and spectral localization trade-offs. To overcome the
inflexibility of existing methods and the computationally expensive
eigen-decomposition and dense matrix multiplication, this paper proposes an
Adaptive Spectral Wavelet Transform-based Self-Supervised Graph Neural Network
(ASWT-SGNN). The proposed method employs spectral adaptive polynomials to
approximate the filter function and optimize the wavelet using contrast loss.
This design enables the creation of local filters in both spectral and spatial
domains, allowing flexible aggregation of neighborhood information at various
scales and facilitating controlled transformation between local and global
information. Compared to existing methods, the proposed approach reduces
computational complexity and addresses the limitation of graph convolutional
neural networks, which are constrained by graph size and lack flexible control
over the neighborhood aspect. Extensive experiments on eight benchmark datasets
demonstrate that ASWT-SGNN accurately approximates the filter function in
high-density spectral regions, avoiding costly eigen-decomposition.
Furthermore, ASWT-SGNN achieves comparable performance to state-of-the-art
models in node classification tasks.
