高维数据最优划分聚类的k-Fermat算法研究  

Research on k-Fermat algorithm for optimal partitioning clustering of high-dimensional data

作　　者：李彤[1,2] 翟永南 华英凡 LI Tong;ZHAI Yongnan;HUA Yingfan(School of Economics and Management,Dalian University of Technology,Dalian 116024,China;School of Business,Dalian University of Technology,Panjin 124221,China)

机构地区：[1]大连理工大学经济管理学院,大连116024 [2]大连理工大学商学院,盘锦124221

出　　处：《系统工程理论与实践》2024年第2期752-772,共21页Systems Engineering-Theory & Practice

基　　金：国家自然科学基金重点专项项目(72342013);辽宁省社科基金重点项目(L15AGL019)。

摘　　要：将数论中的二维数据最优集结点(广义Fermat点)向高维空间拓展,提出以高维广义Fermat点作为最优聚类中心点的划分聚类算法——k-Fermat算法.首先对Fermat点作为聚类中心点的最优性、唯一性进行理论分析,其次建立了模拟植物生长算法(PGSA)求解高维数据的Fermat点并指导聚类过程的算法体系,最后对算法复杂性进行了严格证明.为验证算法性能,采用国际公布的经典数据集,将k-Fermat算法与近年来国际重要期刊和顶级会议发表的几十种主流聚类算法进行比较,验证了本文算法的精确性和稳定性.本文改进了目前划分聚类算法中没有最优聚类中心点的理论不足,为非监督学习探索了一个新方法.In this paper,the optimal rally point of two-dimensional data(generalized Fermat point)in the number theory is extended to a high-dimensional space,and a partitioning clustering algorithm called the k-Fermat clustering algorithm is proposed,with a high-dimensional Fermat point as the optimal clustering center point.Firstly,the optimality and uniqueness of Fermat points as cluster centers are analyzed theoretically,secondly,an algorithmic system for solving Fermat point of high-dimensional data and guiding the clustering process by the plant growth simulated algorithm(PGSA)is established,and finally,the complexity of the algorithm is proved rigorously.In order to verify the performance of the algorithm,the k-Fermat algorithm is compared with dozens of mainstream clustering algorithms published in recent years in international important journals and top conferences using the classical data sets published internationally,and the accuracy and stability of the algorithm in this paper are verified.This paper improves the theoretical deficiency that there is no optimal clustering center in current partitioning clustering algorithms,and explores a new approach for unsupervised learning.

关 键 词：划分聚类 最优聚类中心 广义Fermat点 模拟植物生长算法(PGSA) k-Fermat算法 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]