A Simple Yet Effective SVD-GCN for Directed Graphs

TL;DR

This paper introduces SVD-GCN, a simple yet powerful graph neural network for directed graphs that leverages SVD and framelet techniques, demonstrating superior performance and robustness in node classification tasks.

Contribution

The paper presents a novel SVD-based GCN model for directed graphs, incorporating graph SVD-framelet and Chebyshev polynomial approximation for scalability.

Findings

SVD-GCN outperforms existing GCNs and state-of-the-art methods in node classification.

SVD-GCN exhibits strong denoising capabilities and robustness to graph data attacks.

Theoretical and empirical results confirm the effectiveness and stability of SVD-GCN.

Abstract

In this paper, we propose a simple yet effective graph neural network for directed graphs (digraph) based on the classic Singular Value Decomposition (SVD), named SVD-GCN. The new graph neural network is built upon the graph SVD-framelet to better decompose graph signals on the SVD ``frequency'' bands. Further the new framelet SVD-GCN is also scaled up for larger scale graphs via using Chebyshev polynomial approximation. Through empirical experiments conducted on several node classification datasets, we have found that SVD-GCN has remarkable improvements in a variety of graph node learning tasks and it outperforms GCN and many other state-of-the-art graph neural networks for digraphs. Moreover, we empirically demonstate that the SVD-GCN has great denoising capability and robustness to high level graph data attacks. The theoretical and experimental results prove that the SVD-GCN is effective on a variant of graph datasets, meanwhile maintaining stable and even better performance than the state-of-the-arts.