BScNets: Block Simplicial Complex Neural Networks

Abstract

Simplicial neural networks (SNNs) have recently emerged as a new direction in graph learning which expands the idea of convolutional architectures from node space to simplicial complexes on graphs. Instead of predominantly assessing pairwise relations among nodes as in the current practice, simplicial complexes allow us to describe higher-order interactions and multi-node graph structures. By building upon connection between the convolution operation and the new block Hodge-Laplacian, we propose the first SNN for link prediction. Our new Block Simplicial Complex Neural Networks (BScNets) model generalizes existing graph convolutional network (GCN) frameworks by systematically incorporating salient interactions among multiple higher-order graph structures of different dimensions. We discuss theoretical foundations behind BScNets and illustrate its utility for link prediction on eight real-world and synthetic datasets. Our experiments indicate that BScNets outperforms the state-of-the-art models by a significant margin while maintaining low computation costs. Finally, we show utility of BScNets as a new promising alternative for tracking spread of infectious diseases such as COVID-19 and measuring the effectiveness of the healthcare risk mitigation strategies.

Zoo guide to network embedding

“…The literature on simplicial complexes embedding and simplicial neural networks is rapidly growing [152]. It includes simplicial and cell complex neural networks [153][154][155][156][157][158][159] and geometric LEs embedding [160]. Simple graphs can also be described as higher-order set-of-sets formed by node neighbourhoods, for which recently a new graph embedding has been proposed (HATS) [161].…”

Link Prediction in Multilayer Networks via Cross-Network Embedding

“…GAT introduces self-attention to assign different importance to each pair of nodes (Veličković et al 2018). Chen et al generalized GCN to simplicial complexes by integrating interactions among multiple higherorder graph structures (Chen, Gel, and Poor 2022).…”

TopoGCL: Topological Graph Contrastive Learning

“…However, since the agreement analysis among representations is typically assessed using cosine similarity of the related embeddings, these contrasting approaches cannot systematically account for similarity of higher-order graph properties, for instance, simultaneous matching among subgraphs of varying sizes and orders. In turn, such polyadic node interactions, including various network motifs and other multi-node graph substructures, often play the key role in graph learning tasks, especially, in conjunction with prediction of protein functions in protein-protein interactions and fraud detection in financial networks (Benson, Gleich, and Leskovec 2016;Chen, Gel, and Poor 2022). Interestingly, as shown by (You et al 2020), subgraphs also tend to play the uniformly consistent role in the data augmentation step of GCL across all types of the considered graphs, from bioinformatics to social networks.…”