Hypergraphs provide an effective modeling approach for modeling high-order
relationships in many real-world datasets. To capture such complex
relationships, several hypergraph neural networks have been proposed for
learning hypergraph structure, which propagate information from nodes to
hyperedges and then from hyperedges back to nodes. However, most existing
methods focus on information propagation between hyperedges and nodes,
neglecting the interactions among hyperedges themselves. In this paper, we
propose HeIHNN, a hyperedge interaction-aware hypergraph neural network, which
captures the interactions among hyperedges during the convolution process and
introduce a novel mechanism to enhance information flow between hyperedges and
nodes. Specifically, HeIHNN integrates the interactions between hyperedges into
the hypergraph convolution by constructing a three-stage information
propagation process. After propagating information from nodes to hyperedges, we
introduce a hyperedge-level convolution to update the hyperedge embeddings.
Finally, the embeddings that capture rich information from the interaction
among hyperedges will be utilized to update the node embeddings. Additionally,
we introduce a hyperedge outlier removal mechanism in the information
propagation stages between nodes and hyperedges, which dynamically adjusts the
hypergraph structure using the learned embeddings, effectively removing
outliers. Extensive experiments conducted on real-world datasets show the
competitive performance of HeIHNN compared with state-of-the-art methods.

我们提出了一种名为 HeIHNN 的超边交互感知超图神经网络，旨在捕捉超边之间的相互作用，并引入了一种新的机制来增强超边和节点之间的信息流动。经过广泛的实验，在真实世界的数据集上，HeIHNN 相比现有方法表现出具有竞争力的性能。

超边交互感知的超图神经网络

Hyperedge Interaction-aware Hypergraph Neural Network

Higher-order motif structures and multi-vertex interactions are becoming
increasingly important in studies that aim to improve our understanding of
functionalities and evolution patterns of networks. To elucidate the role of
higher-order structures in community detection problems over complex networks,
we introduce the notion of a Superimposed Stochastic Block Model (SupSBM). The
model is based on a random graph framework in which certain higher-order
structures or subgraphs are generated through an independent hyperedge
generation process, and are then replaced with graphs that are superimposed
with directed or undirected edges generated by an inhomogeneous random graph
model. Consequently, the model introduces controlled dependencies between edges
which allow for capturing more realistic network phenomena, namely strong local
clustering in a sparse network, short average path length, and community
structure. We proceed to rigorously analyze the performance of a number of
recently proposed higher-order spectral clustering methods on the SupSBM. In
particular, we prove non-asymptotic upper bounds on the misclustering error of
spectral community detection for a SupSBM setting in which triangles or
3-uniform hyperedges are superimposed with undirected edges. As part of our
analysis, we also derive new bounds on the misclustering error of higher-order
spectral clustering methods for the standard SBM and the 3-uniform hypergraph
SBM. Furthermore, for a non-uniform hypergraph SBM model in which one directly
observes both edges and 3-uniform hyperedges, we obtain a criterion that
describes when to perform spectral clustering based on edges and when on
hyperedges, based on a function of hyperedge density and observation quality.

本研究旨在探究超级叠加随机块模型 (SupSBM) 在解决复杂网络社区检测问题中的作用。研究者提出使用新模型可以更精确地捕获局部聚类、短平均路径和社区结构等更真实的网络现象，并进一步证明多个高阶谱聚类方法的性能在该模型下是满足特定的误分类错误率上界的。

基于叠加随机块模型的高阶谱聚类

Higher-Order Spectral Clustering under Superimposed Stochastic Block  Model

Graph models have long been used in lieu of real data which can be expensive
and hard to come by. A common class of models constructs a matrix of
probabilities, and samples an adjacency matrix by flipping a weighted coin for
each entry. Examples include the Erd\H{o}s-R\'{e}nyi model, Chung-Lu model, and
the Kronecker model. Here we present the HyperKron Graph model: an extension of
the Kronecker Model, but with a distribution over hyperedges. We prove that we
can efficiently generate graphs from this model in order proportional to the
number of edges times a small log-factor, and find that in practice the runtime
is linear with respect to the number of edges. We illustrate a number of useful
features of the HyperKron model including non-trivial clustering and highly
skewed degree distributions. Finally, we fit the HyperKron model to real-world
networks, and demonstrate the model's flexibility with a complex application of
the HyperKron model to networks with coherent feed-forward loops.

通过超边的分布式 Kronecker 模型，我们可以快速、高效地生成具有非平凡聚类和高度不对称度分布的图形，从而可以将此模型成功应用于实际的网络数据中