Hyperbolic multichannel graph convolutional network for social recommendation

Social recommendations enhance the quality of recommendations by integrating social network information. Existing methods predominantly rely on pairwise relationships to uncover potential user preferences. However, they usually overlook the exploration of higher-order user relations. Moreover, because social relation graphs often exhibit scale-free graph structures, directly embedding them in Euclidean space will lead to significant distortion. To this end, we propose a novel graph neural network framework with hypergraph and hyperbolic embedding learning, namely HMGCN. Specifically, we first construct hypergraphs over user-item interactions and social networks, and then perform graph convolution on the hypergraphs. At the same time, a multi-channel setting is employed in the convolutional network, with each channel encoding its corresponding hypergraph to capture different high-order user relation patterns. In addition, we feed the item embeddings and the obtained high-order user embeddings into a hyperbolic graph convolutional network to extract user and item representations, enabling the model to better capture the hierarchical structure of their complex relationships. Experimental results on three public datasets, namely FilmTrust, LastFM, and Yelp, demonstrate that the model achieves more comprehensive user and item representations, more accurate fitting and processing of graph data, and effectively addresses the issues of insufficient user relationship extraction and data embedding distortion in social recommendation models.