DeepSCNN: a simplicial convolutional neural network for deep learning

Abstract

Graph convolutional neural networks (GCNs) are deep learning methods for processing graph-structured data. Usually, GCNs mainly consider pairwise connections and ignore higher-order interactions between nodes. Recently, simplices have been shown to encode not only pairwise relations between nodes but also encode higher-order interactions between nodes. Researchers have been concerned with how to design simplicial-based convolutional neural networks. The existing simplicial neural networks can achieve good performance in tasks such as missing value imputation, graph classification, and node classification. However, due to issues of gradient vanishing, over-smoothing, and over-fitting, they are typically limited to very shallow models. Therefore, we innovatively propose a simplicial convolutional neural network for deep learning (DeepSCNN). Firstly, simplicial edge sampling technology (SES) is introduced to prevent over-fitting caused by deepening network layers. Subsequently, initial residual connection technology is added to simplicial convolutional layers. Finally, to verify the validity of the DeepSCNN, we conduct missing data imputation and node classification experiments on citation networks. Additionally, we compare the experimental performance of the DeepSCNN with that of simplicial neural networks (SNN) and simplicial convolutional networks (SCNN). The results show that our proposed DeepSCNN method outperforms SNN and SCNN.