The isomorphism problem is a fundamental problem in network analysis, which involves capturing both low-order and high-order structural information. In terms of extracting low-order structural information, graph isomorphism algorithms analyze the structural equivalence to reduce the solver space dimension, which demonstrates its power in many applications, such as protein design, chemical pathways, and community detection. For the more commonly occurring high-order relationships in real-life scenarios, the problem of hypergraph isomorphism, which effectively captures these high-order structural relationships, cannot be straightforwardly addressed using graph isomorphism methods. Besides, the existing hypergraph kernel methods may suffer from high memory consumption or inaccurate sub-structure identification, thus yielding sub-optimal performance. In this paper, to address the abovementioned problems, we first propose the hypergraph Weisfiler-Lehman test algorithm for the hypergraph isomorphism test problem by generalizing the Weisfiler-Lehman test algorithm from graphs to hypergraphs. Secondly, based on the presented algorithm, we propose a general hypergraph Weisfieler-Lehman kernel framework and implement two instances, which are Hypergraph Weisfeiler-Lehamn Subtree Kernel and Hypergraph Weisfeiler-Lehamn Hyperedge Kernel. In order to fulfill our research objectives, a comprehensive set of experiments was meticulously designed, including seven graph classification datasets and 12 hypergraph classification datasets. Results on hypergraph classification datasets show significant improvements compared to other typical kernel-based methods, which demonstrates the effectiveness of the proposed methods. In our evaluation, we found that our proposed methods outperform the second-best method in terms of runtime, running over 80 times faster when handling complex hypergraph structures.

翻译：同构问题是网络分析中的一个基本问题，它涉及捕获低阶和高阶结构信息。在提取低阶结构信息方面，图同构算法分析结构等价性以降低求解器空间维度，这在蛋白质设计、化学路径和社区检测等众多应用中展示了其强大能力。对于现实场景中更常见的高阶关系，超图同构问题能够有效捕获这些高阶结构关系，但无法直接使用图同构方法解决。此外，现有的超图核方法可能面临内存消耗大或子结构识别不准确的问题，从而导致性能次优。本文为了解决上述问题，首先通过将Weisfeiler-Lehman测试算法从图推广到超图，提出了用于超图同构测试问题的超图Weisfeiler-Lehman测试算法。其次，基于该算法，我们提出了一个通用的超图Weisfeiler-Lehman核框架，并实现了两个实例：超图Weisfeiler-Lehman子树核与超图Weisfeiler-Lehman超边核。为实现研究目标，我们精心设计了一系列全面的实验，包括7个图分类数据集和12个超图分类数据集。在超图分类数据集上的结果表明，与其他典型核方法相比，所提方法取得了显著改进，验证了其有效性。在评估中，我们发现所提方法在运行时间上优于第二名方法，处理复杂超图结构时速度提升超过80倍。