Hypergraph neural networks (HGNN) have recently become attractive and
received significant attention due to their excellent performance in various
domains. However, most existing HGNNs rely on first-order approximations of
hypergraph connectivity patterns, which ignores important high-order
information. To address this issue, we propose a novel adjacency-tensor-based
Tensorized Hypergraph Neural Network (THNN). THNN is a faithful hypergraph
modeling framework through high-order outer product feature message passing and
is a natural tensor extension of the adjacency-matrix-based graph neural
networks. The proposed THNN is equivalent to an high-order polynomial
regression scheme, which enable THNN with the ability to efficiently extract
high-order information from uniform hypergraphs. Moreover, in consideration of
the exponential complexity of directly processing high-order outer product
features, we propose using a partially symmetric CP decomposition approach to
reduce model complexity to a linear degree. Additionally, we propose two simple
yet effective extensions of our method for non-uniform hypergraphs commonly
found in real-world applications. Results from experiments on two widely used
hypergraph datasets for 3-D visual object classification show the promising
performance of the proposed THNN.

提出了一种基于张量的高阶超图神经网络模型，它利用高阶外积特征传递实现了对高阶信息的有效提取，并通过部分对称 CP 分解方法降低了模型复杂度；在两个三维视觉对象分类数据集上进行的实验结果表明了其性能优越性。