基于超图的持续嵌入同调在图分类领域的应用  

Applications of Persistent Embedding Homology onn Hypergraphs in Graph Classification

作　　者：任智昊 刘艺 赵梓伊 刘秀贵[1] Ren Zhihao;Liu Yi;Zhao Ziyi;Liu Xiugui(School of Mathematical Sciences,Nankai University,Tianjin 300071,China)

机构地区：[1]南开大学数学科学学院,天津300071

出　　处：《南开大学学报(自然科学版)》2025年第1期12-17,共6页Journal of Nankai University(Natural Sience)

摘　　要：图数据作为一种广泛存在于各学科中的数据形式,其分类问题一直是图数据研究中的一个重要课题.基于超图的持续同调理论,一种新的图分类模型被提出.该模型通过在一般无向图上构建持续超图,进而计算其嵌入同调作为特征进行机器学习,以实现图分类的目标.该图分类模型在多个数据集的测试中取得了较好的效果.Graph data is a widely existing form of data in various disciplines,and graph classification is an important issue in graph data research.A graph classification model is proposed based on persistent homology theory of hypergraphs.Specifically,it involves constructing persistent hypergraphs on general undirected graphs and using the computed persistent hypergraph embeddings as features for machine learning,thereby achieving the goal of graph classification.The established graph classification model was tested on multiple datasets and achieved good results.

关 键 词：持续同调 图分类 超图 

分 类 号：O189.2[理学—数学]