Lorentzian Graph Convolution Networks for Collaborative Filtering

Recently, recommendation methods based on graph convolutional networks (GCNs) have received much attention and have shown competitive performance. These methods usually perform graph convolutions of user and item embeddings in Euclidean space. However, user-item interaction graphs usually present a tree-like hierarchy in large-scale recommender systems. To better fit user and item data to the embedding space, hyperbolic space becomes a good choice, which grows exponentially in volume with radius and is well suited for embedding hierarchical data. In addition, most previous works aggregate neighborhoods through projection operations on tangent spaces, which inevitably cause distortion. In this paper, we propose a Lorentzian graph convolutional network model for collaborative filtering (LCF), which makes the learned user and item representations strictly follow hyperbolic geometry, and the learned embeddings are optimized based on margin ranking loss and geometric views. Specifically, we first pass the initialized user and item information through multiple Lorentzian graph convolutional layers, and ensure that the learned node embeddings are not out of the hyperbolic space, while capturing rich high-order neighborhood information. Then, the model is effectively learned under the composite loss function to take full advantage of the hyperbolic space. We conduct extensive experiments on three datasets and compare with many baselines. Experimental results show that our method performs better than many state-of-the-art baseline methods.