Graph Neural Networks for Recommender Systems

Graph neural networks (GNN) have gained an increasing popularity in data science field because of their ability to represent highly complex and diverse structures in biology, physics, sociology and other fields. However, due to their oversmoothing and homophily limitations (prevailing connections among same-type graph nodes are required), GNNs applications are still limited. Sheaf convolutional network (SCN) is an advanced type of GNN, originating from topology, that overcomes these challenges, but, to our knowledge, has not yet been fully applied to the recommender systems (RS), which are popular for many problems in academic and industry settings. Our contribution is a novel application of SCN to a recommender system (RS) using multivariate sheaves and evaluation of the results in comparison to alternative advanced and widely used models such as Light Graph Convolutional Network (LightGCN), Neural Graph Collaborative Filtering (NGCF), and Graph Attention Network (GAT). We show that multidimensional Sheaf Convolutional Network (mdSCN) outperforms one-dimentional SCN with statistical significance on two out of three 10k-edge datasets. Diagonal mdSCN outperforms all other non-mdSCN models on the same datasets. mdSCN performance improves embeddings for more sparse (<10% values) datasets and are for sure of interest of a lighter adaptation for larger datasets which are common in RS.