Bilateral Filtering Graph Convolutional Network for Multi-relational Social Recommendation in the Power-law Networks

Abstract

In recent years, advances in Graph Convolutional Networks (GCNs) have given new insights into the development of social recommendation. However, many existing GCN-based social recommendation methods often directly apply GCN to capture user-item and user-user interactions, which probably have two main limitations: (a) Due to the power-law property of the degree distribution, the vanilla GCN with static normalized adjacency matrix has limitations in learning node representations, especially for the long-tail nodes; (b) multi-typed social relationships between users that are ubiquitous in the real world are rarely considered. In this article, we propose a novel Bilateral Filtering Heterogeneous Attention Network (BFHAN), which improves long-tail node representations and leverages multi-typed social relationships between user nodes. First, we propose a novel graph convolutional filter for the user-item bipartite network and extend it to the user-user homogeneous network. Further, we theoretically analyze the correlation between the convergence values of different graph convolutional filters and node degrees after stacking multiple layers. Second, we model multi-relational social interactions between users as the multiplex network and further propose a multiplex attention network to capture distinctive inter-layer influences for user representations. Last but not least, the experimental results demonstrate that our proposed method outperforms several state-of-the-art GCN-based methods for social recommendation tasks.