A Regularized Graph Neural Network Based on Approximate Fractional Order Gradients

Zijian Liu, Yaning Wang, Yang Luo and Chunbo Luo
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Zijian Liu: School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China
Yaning Wang: School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China
Yang Luo: School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China
Chunbo Luo: School of Information and Communication Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China

Mathematics, 2022, vol. 10, issue 8, 1-20

Abstract: Graph representation learning is a significant challenge in graph signal processing (GSP). The flourishing development of graph neural networks (GNNs) provides effective representations for GSP. To effectively learn from graph signals, we propose a regularized graph neural network based on approximate fractional order gradients (FGNN). The regularized graph neural network propagates the information between neighboring nodes. The approximation strategy for calculating fractional order derivatives avoids falling into fractional order extrema and overcomes the high computational complexity of fractional order derivatives. We further prove that such an approximation is feasible and FGNN is unbiased towards the global optimization solution. Extensive experiments on citation and community networks show that the proposed FGNN has improved recognition accuracy and convergence speed than vanilla FGNN. The five datasets of different sizes and domains confirm the great scalability of our proposed method.

Keywords: graph neural networks; unbiased approximation; citation network; community network; fractional order derivatives; node classification (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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