Low-Rank Graph Neural Networks Inspired by the Weak-balance Theory in Social Networks

Graph Neural Networks (GNNs) have achieved state-of-the-art performance on node classification tasks by exploiting both the graph structures and node features. Generally, most existing GNNs depend on the implicit homophily assumption that nodes belonging to the same class are more likely to be connected. However, GNNs may fail to model heterophilious graphs where nodes with different labels tend to be linked, as shown in recent studies. To address this issue, we propose a generic GNN applicable to both homophilious and heterophilious graphs, namely Low-Rank Graph Neural Network (LRGNN). In detail, we aim at computing a coefficient matrix such that the sign of each coefficient reveals whether the corresponding two nodes belong to the same class, which is similar to the sign inference problem. In Signed Social Networks (SSNs), the sign inference problem can be modeled as a low-rank matrix factorization (LRMF) problem due to the global low-rank structure described by the weak balance theory. In this paper, we show that signed graphs are naturally generalized weakly-balanced when considering node classification tasks. Motivated by this observation, we propose to leverage LRMF to recover a coefficient matrix from a partially observed signed adjacency matrix. To effectively capture the node similarity, we further incorporate the low-rank representation (LRR) method. Our theoretical result shows that under our update rule of node representations, LRR obtained by solving a subspace clustering problem can recover the subspace structure of node representations. To solve the corresponding optimization problem, we utilize an iterative optimization algorithm with a convergence guarantee and develop a neural-style initialization manner that enables fast convergence. Finally, extensive experimental evaluation on both real-world and synthetic graphs has validated the superior performance of LRGNN over various state-of-the-art GNNs. In particular, LRGNN can offer clear performance gains in a scenario when the node features are not informative enough.