Adaptive frequency-based fully hyperbolic graph neural networks

Graph Convolutional Networks (GCNs) have attracted broad attention from industry and academia, for their excellent expressive power in terms of modeling the irregular data, e.g., skeletal data and graph-structured data. The most effective existing model may be the fully hyperbolic graph neural network. However, it involves a large number of parameters, thus consuming considerable computing resources. In this paper, we propose a model based on adaptive frequency filter and corresponding optimizer in hyperbolic space. The adaptive frequency can learn the different frequency components of the embeddings of the nodes in graph, which adaptively adjust the beneficial signals of high-frequency and low-frequency. And the optimizer is based on a subset of the orthogonal constraint, which is dedicated for the adaptive frequency with less parameters. Moreover, our model bridges the gap of hyperbolic space and the spectral space for exploring the underlying semantics of the node and relation embeddings of graph. Consequently, our model needs only to optimize the less parameters in hyperbolic space and meanwhile prevent the distortion caused by conventional manifold GCN. Experimental results show that our method achieves substantial improvements and outperforms the state-of-the-art performance in terms of node classification.