Preliminaries

Graph Neural Networks is a deep learning method that takes graph data as input. Graph Neural Networks can be divided into Convolutional Graph Neural Networks, Recurrent Graph Neural Networks, Graph Auto-Encoders, and Spatial-Temporal Graph Neural Networks. Convolutional.

Graph Neural Networks can be decomposed into two branches:  Spectral-based GNNs where graph spectral theory was applied to learn node representations, and spatial-based GNNs based on local-dependence assumption of graph structured data that graph convolution is defined in the spatial domain as aggregating and transforming local information. Thus, spectral-based GNNs extends classical signal processing to graph data, designing graph filters in the frequency domain by borrowing from graph signal analysis, and realizing graph convolution whereas spatial-based GNNs describe the pairwise relations between objects. 

Although GNNs show excellent performance in handling graph data, the potential higher-order relations among objects will be lost if there are simply represented by a graph. Hypergraph Neural Networks recognized as a flexible modeling tool for complex and higher-order data, including a vertex set and a hyperedge set. Objects are considered vertices, multiple vertices are connected to form a hyperedge representing higher-order relations.