ASWT-SGNN: Adaptive Spectral Wavelet Transform-based Self-Supervised Graph Neural Network

TL;DR

This paper introduces ASWT-SGNN, a novel self-supervised graph neural network that uses adaptive spectral wavelet transforms to improve flexibility and efficiency in learning node representations without costly eigen-decomposition.

Contribution

The paper proposes an adaptive spectral wavelet transform approach for GNNs, enabling flexible neighborhood aggregation and reducing computational complexity compared to existing methods.

Findings

Achieves high accuracy in node classification on benchmark datasets.

Avoids eigen-decomposition by approximating spectral filters with adaptive polynomials.

Demonstrates improved flexibility and efficiency over traditional GCNs.

Abstract

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.