This paper introduces a novel hypergraph classification algorithm. The use of
hypergraphs in this framework has been widely studied. In previous work,
hypergraph models are typically constructed using distance or attribute based
methods. That is, hyperedges are generated by connecting a set of samples which
are within a certain distance or have a common attribute. These methods
however, do not often focus on multi-way interactions directly. The algorithm
provided in this paper looks to address this problem by constructing
hypergraphs which explore multi-way interactions of any order. We also increase
the performance and robustness of the algorithm by using a population of
hypergraphs. The algorithm is evaluated on two datasets, demonstrating
promising performance compared to a generic random forest classification
algorithm.

本文介绍了一种新颖的超图分类算法，通过构建具有任意阶多项交互的超图，并采用超图种群来提高算法的性能和鲁棒性，在两个数据集上评估并证明了其相较于通用的随机森林分类算法具有良好的性能。

基于超图群体的分类模型

A classification model based on a population of hypergraphs

Latent Graph Inference (LGI) relaxed the reliance of Graph Neural Networks
(GNNs) on a given graph topology by dynamically learning it. However, most of
LGI methods assume to have a (noisy, incomplete, improvable, ...) input graph
to rewire and can solely learn regular graph topologies. In the wake of the
success of Topological Deep Learning (TDL), we study Latent Topology Inference
(LTI) for learning higher-order cell complexes (with sparse and not regular
topology) describing multi-way interactions between data points. To this aim,
we introduce the Differentiable Cell Complex Module (DCM), a novel learnable
function that computes cell probabilities in the complex to improve the
downstream task. We show how to integrate DCM with cell complex message passing
networks layers and train it in a end-to-end fashion, thanks to a two-step
inference procedure that avoids an exhaustive search across all possible cells
in the input, thus maintaining scalability. Our model is tested on several
homophilic and heterophilic graph datasets and it is shown to outperform other
state-of-the-art techniques, offering significant improvements especially in
cases where an input graph is not provided.

本论文提出了一种基于可学习的单元概率函数和可微分单元复合模块的 Latent Topology Inference（LTI）方法，用于描述点之间的多路交互，此方法在多个同质和异质图数据集上的实验证明了其优于其他现有技术的表现，可用于在没有提供输入图形的情况下提高拓扑学习的性能。

从潜在图到潜在拓扑推断：可微分的细胞复合模块

From Latent Graph to Latent Topology Inference: Differentiable Cell  Complex Module

We introduce the beta model for random hypergraphs in order to represent the
occurrence of multi-way interactions among agents in a social network. This
model builds upon and generalizes the well-studied beta model for random
graphs, which instead only considers pairwise interactions. We provide two
algorithms for fitting the model parameters, IPS (iterative proportional
scaling) and fixed point algorithm, prove that both algorithms converge if
maximum likelihood estimator (MLE) exists, and provide algorithmic and
geometric ways of dealing the issue of MLE existence.

该研究介绍了用于表示社交网络中代理间多路交互的随机超图的 beta 模型，并提供了两种算法以适应模型参数。