HiGCN: Higher-order Graph Convolutional Network with Flower-Petals Laplacians on Simplicial Complexes

Abstract

Vanilla graph neural networks (GNNs) built on pairwise interaction networks have recently achieved remarkable success in various tasks. However, these GNNs cannot capture latent higher-order interactions inherent in complex systems, and the expressive power of GNNs was proved to be limited. Meanwhile, simplicial complexes (SCs) are a powerful tool to model higher-order interactions with elegant mathematical theories. But existing simplicial GNNs are limited by high complexity and low flexibility, and it remains elusive to quantify the strength of higher-order interactions. In this paper, we creatively construct a higher-order flower-petals (FP) model and introduce FP Laplacians for SCs. Additionally, we propose a higher-order graph convolutional network (HiGCN) based on the FP Laplacians, which can capture intrinsic features at different topology scales. Learnable graph filters (group of parameters) are employed in every FP Laplacian domain to find different patterns, and the filters’ weights quantify the strength of the higher-order interactions. We theoretically demonstrate HiGCN’s superior expressive power, and numerical experiments on classical graph datasets show that our model has achieved state-of-the-art (SOTA). In general, our work is an important step toward studying the higher-order mechanism in complex networks.

Yiming Huang

Undergraduate

My research interests include network science, vital node identification, and topological deep learning.

Yujie Zeng

Undergraduate

My research interests include network science, higher-order network and vital node identification.

Linyuan Lü

Professor

Professor, doctoral supervisor, winner of the National Natural Science Foundation of Outstanding Youth Science Fund.