Robust Graph Structure Learning with the Alignment of Features and Adjacency Matrix

To improve the robustness of graph neural networks (GNN), graph structure learning (GSL) has attracted great interest due to the pervasiveness of noise in graph data. Many approaches have been proposed for GSL to jointly learn a clean graph structure and corresponding representations. To extend the previous work, this paper proposes a novel regularized GSL approach, particularly with an alignment of feature information and graph information, which is motivated mainly by our derived lower bound of node-level Rademacher complexity for GNNs. Additionally, our proposed approach incorporates sparse dimensional reduction to leverage low-dimensional node features that are relevant to the graph structure. To evaluate the effectiveness of our approach, we conduct experiments on real-world graphs. The results demonstrate that our proposed GSL method outperforms several competitive baselines, especially in scenarios where the graph structures are heavily affected by noise. Overall, our research highlights the importance of integrating feature and graph information alignment in GSL, as inspired by our derived theoretical result, and showcases the superiority of our approach in handling noisy graph structures through comprehensive experiments on real-world datasets.

Stability and Generalization of $\ell_p$-Regularized Stochastic Learning for GCN

Graph convolutional networks (GCN) are viewed as one of the most popular representations among the variants of graph neural networks over graph data and have shown powerful performance in empirical experiments. That $\ell_2$-based graph smoothing enforces the global smoothness of GCN, while (soft) $\ell_1$-based sparse graph learning tends to promote signal sparsity to trade for discontinuity. This paper aims to quantify the trade-off of GCN between smoothness and sparsity, with the help of a general $\ell_p$-regularized $(1<p\leq 2)$ stochastic learning proposed within. While stability-based generalization analyses have been given in prior work for a second derivative objectiveness function, our $\ell_p$-regularized learning scheme does not satisfy such a smooth condition. To tackle this issue, we propose a novel SGD proximal algorithm for GCNs with an inexact operator. For a single-layer GCN, we establish an explicit theoretical understanding of GCN with the $\ell_p$-regularized stochastic learning by analyzing the stability of our SGD proximal algorithm. We conduct multiple empirical experiments to validate our theoretical findings.