基于目标函数优化的无向加权图粗糙模糊聚类算法  

Rough fuzzy clustering algorithm of undirected weighted graph based on objective function optimization

作　　者：何文倩 刘士虎[1] 宋敏 杨昔阳[2] HE Wen-qian;LIU Shi-hu;SONG Min;YANG Xi-yang(School of Mathematics and Computer Science,Yunnan Minzu University,Kumming 650500,China;School of Mathematics and Computer Science,Quanzhou Normal University,Quanzhou 362000,China)

机构地区：[1]云南民族大学数学与计算机科学学院,云南昆明650504 [2]泉州师范学院数学与计算机科学学院,福建泉州362000

出　　处：《云南民族大学学报（自然科学版）》2022年第5期577-587,607,共12页Journal of Yunnan Minzu University:Natural Sciences Edition

基　　金：国家自然科学基金(61966039);福建省自然科学基金(2021J01001);云南省教育厅科学研究基金(2022Y471)。

摘　　要：研究了无向加权图数据基于目标函数优化的粗糙模糊聚类算法.该算法对图的结构信息和边权重信息进行结合,确定顶点的综合结构相似性.采用粗糙集思想分别设计了类的上下近似集的模糊中心表示.提出参与聚类过程的一种基于等价关系R的属性相似性度量方法,并建立一种新的目标函数迭代优化机制,以此为基础建立了无向加权图数据模糊聚类的算法模型.算法应用在4个无向加权图数据中,实验对比结果证明了该算法具有较好聚类效果.算法还可以通过求有效性指标的最小值,选择对应的最佳聚类数.In this paper, the rough fuzzy clustering algorithm of undirected weighted graph data based on objective function optimization is studied. The structural information and edge weight information of the graph data were combined to determine the comprehensive structural similarity for vertices. The fuzzy center representations of upper and lower approximation sets for clusters are designed respectively by using rough set idea. An attribute similarity measurement based on equivalent relation R is proposed to participate in the clustering process and a new iterative optimization mechanism of objective function is established, on which fuzzy clustering algorithm model is established. The algorithm is applied to four undirected weighted graph data, and experimental comparison result confirmed that the algorithm has better clustering effect. The corresponding best cluster number is selected by finding the minimum value for the validity index.

关 键 词：无向加权图数据 粗糙集 模糊聚类 综合结构相似性 属性相似性 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]