Simple Multigraph Convolution Networks

TL;DR

The paper tackles the efficiency-accuracy trade-off in multigraph convolution by learning credible cross-view interactions. It introduces SMGCN, which uses two topology extractors—edge-level $\mathbf{E}$ and subgraph-level $\mathbf{S}$—and a simple high-order polynomial expansion to perform cross-view message passing within a spectral convolution framework. This approach preserves spectral-convolution properties while significantly reducing the number of parameters compared to full cross-view polynomial expansions like MIMO-GCN. Empirical results on ACM and DBLP show state-of-the-art performance with lower computational cost, and the authors provide publicly available code for reproducibility.

Abstract

Existing multigraph convolution methods either ignore the cross-view interaction among multiple graphs, or induce extremely high computational cost due to standard cross-view polynomial operators. To alleviate this problem, this paper proposes a Simple MultiGraph Convolution Networks (SMGCN) which first extracts consistent cross-view topology from multigraphs including edge-level and subgraph-level topology, then performs polynomial expansion based on raw multigraphs and consistent topologies. In theory, SMGCN utilizes the consistent topologies in polynomial expansion rather than standard cross-view polynomial expansion, which performs credible cross-view spatial message-passing, follows the spectral convolution paradigm, and effectively reduces the complexity of standard polynomial expansion. In the simulations, experimental results demonstrate that SMGCN achieves state-of-the-art performance on ACM and DBLP multigraph benchmark datasets. Our codes are available at https://github.com/frinkleko/SMGCN.

Figures (5)

• Figure 1: Overview of the proposed SMGCN.
• Figure 2: Triangle-based weighted similarity matrix generation. Self-loop is omitted in this figure.
• Figure 3: Parameters of models on ACM and DBLP dataset.
• Figure 4: Visualization of node embedding learned by our method on ACM dataset.
• Figure 5: Visualization of $\mathbf{T}^{(1)}$ and $\mathbf{T}^{(2)}$ learned by our method on ACM dataset. Yellow boxes represent nodes in the same connecting component.