现有的超图网络表示方法需要分析全批量节点和超边以实现跨层递归扩展邻域, 这会带来巨大的计算开销, 且因过度扩展导致更低的泛化精度. 为解决这一问题, 提出一种基于重要性采样的超图表示方法. 首先, 它将节点和超边看作是两组符合特定概率测度的独立同分布样本, 用积分形式解释超图的结构特征交互; 其次, 设计带可学习参数的邻域重要性采样规则, 根据节点和超边的物理关系和特征计算采样概率, 逐层递归采集固定数目的对象, 构造一个更小的采样邻接矩阵; 最终, 利用蒙特卡洛方法近似估计整个超图的空间特征. 此外, 借鉴PINN的优势, 将需要缩减的方差作为物理约束加入到超图神经网络中, 以获取更具泛化能力的采样规则. 多个数据集上的广泛实验表明, 所提出的方法能够获得更准确的超图表示结果, 同时具有更快的收敛速度.
Existing hypergraph network representation methods need to analyze the full batch nodes and hyperedges to recursively extend the neighbors across layers, which brings huge computational costs and leads to lower generalization accuracy due to over-expansion. To solve this problem, this study proposes a hypergraph network representation method based on importance sampling. First, the method treats nodes and hyperedges as two sets of independent identically distributed samples that satisfy specific probability measures and interprets the structural feature interactions of the hypergraph in an integral form. Second, it designs a neighbor importance sampling rule with learnable parameters and calculates sampling probabilities based on the physical relations and features of nodes and hyperedges. A fixed number of objects are recursively acquired layer by layer to construct a smaller sampled adjacency matrix. Finally, the spatial features of the entire hypergraph are approximated using Monte Carlo methods. In addition, with the advantage of physically informed neural networks, the sampling variance that needs to be reduced is added to the hypergraph neural network as a physical constraint to obtain sampling rules with better generalization capability. Extensive experiments on multiple datasets show that the method proposed in this study can obtain more accurate hypergraph representation results with a faster convergence rate.