SCHash: Speedy Simplicial Complex Neural Networks via Randomized Hashing

Xuan Tan, Wei Wu, Chuan Luo

Abstract: Graphs, as a non-linear data structure, are ubiquitous in practice, and efficient graph analysis can benefit important information retrieval applications in the era of big data. Currently, one of the fundamental graph mining problems is graph embedding, which aims to represent the graph as a low-dimensional feature vector with the content and structural information in the graph preserved. Although the graph embedding technique has evolved considerably, traditional methods mainly focus on node pairwise relationship in graphs, which makes the representational power of such schemes limited. Recently, a number of works have explored the simplicial complexes, which describe the higher-order interactions between nodes in the graphs, and further proposed several Graph Neural Network (GNN) algorithms based on simplicial complexes. However, these GNN approaches are highly inefficient in terms of running time and space, due to massive parameter learning. In this paper, we propose a simple and speedy graph embedding algorithm dubbed SCHash. Through adopting the Locality Sensitive Hashing (LSH) technique, SCHash captures the higher-order information derived from the simplicial complex in the GNN framework, and it can achieve a good balance between accuracy and efficiency. Our extensive experiments clearly show that, in terms of accuracy, the performance of our proposed SCHash algorithm is comparable to that of state-of-the-art GNN algorithms; also, SCHash achieves higher accuracy than the existing LSH algorithms. In terms of efficiency, SCHash runs faster than GNN algorithms by 2 ~ 4 orders of magnitude, and is more efficient than the existing LSH algorithms.