第14卷第5期 智能系统学报 Vol.14 No.5 2019年9月 CAAI Transactions on Intelligent Systems Sep.2019 D0:10.11992/tis.201810002 网络出版地址：http:/kns.cnki.net/kcms/detail/23.1538.tp.20190527.1407.010.html 公理化模糊共享近邻自适应谱聚类算法 储德润，周治平 (江南大学物联网技术应用教育部工程研究中心，江苏无锡214122) 摘要：针对传统的谱聚类算法通常利用高斯核函数作为相似性度量，且单纯以距离决定相似性不能充分表现 原始数据中固有的模糊性、不确定性和复杂性，导致聚类性能降低的问题。提出了一种公理化模糊共享近邻自 适应谱聚类算法，首先结合公理化模糊集理论提出了一种模糊相似性度量方法，利用识别特征来衡量更合适的 数据成对相似性，然后采用共享近邻的方法发现密集区域样本点分布的结构和密度信息，并且根据每个点所处 领域的稠密程度自动调节参数，从而生成更强大的亲和矩阵，进一步提高聚类准确率。实验表明，相较于距 离谱聚类、自适应谱聚类、模糊聚类方法和地标点谱聚类，所提算法有着更好的聚类性能。 关键词：机器学习；数据挖掘；聚类分析；模糊聚类；谱聚类；公理化模糊集理论；共享最近邻：尺度参数 中图分类号：TP18文献标志码：A文章编号：1673-4785(2019)05-0897-08 中文引用格式：储德润，周治平.公理化模糊共享近邻自适应谱聚类算法机.智能系统学报，2019,14(5)：897-904 英文引用格式：CHU Derun,ZHOU Zhiping.Shared nearest neighbor adaptive spectral clustering algorithm based on axiomatic fuzzy set theory(J.CAAI transactions on intelligent systems,2019,14(5):897904. Shared nearest neighbor adaptive spectral clustering algorithm based on axiomatic fuzzy set theory CHU Derun,ZHOU Zhiping (Engineering Research Center of Internet of Things Technology Applications Ministry of Education,Jiangnan University,Wuxi 214122.China) Abstract:For the traditional spectral clustering algorithm,the Gaussian kernel function is usually used as the similarity measure.However,the similarity of distance cannot fully express the ambiguity,uncertainty,and complexity inherent in the original data,resulting in the reduction of clustering performance.To solve this problem,we propose an axiomatic fuzzy set shared nearest neighbor adaptive spectral clustering algorithm.First,the proposed algorithm uses a fuzzy sim- ilarity measurement method based on axiomatic fuzzy set theory to measure more suitable data pairwise similarity by identifying features.Then,the structure and density information of sample point distribution in a dense area is obtained using the method of sharing the nearest neighbor,and the parameter o is automatically adjusted according to the density degree of each point in the domain,thereby generating a more powerful affinity matrix to further increase the accuracy rate of clustering.Experimental results show that the proposed algorithm has better clustering performance than dis- tance spectral clustering,adaptive spectral clustering,fuzzy clustering,and landmark spectral clustering. Keywords:machine learning,data mining,clustering analysis,fuzzy clustering,spectral clustering;axiomatic fuzzy set theory;shared nearest neighbor;scale parameter 聚类技术作为机器学习领域中的一种无监督挥着重要的作用。在过去的几十年中，许多聚类 技术，在检测数据的内在结构和潜在知识方面发 方法得到了发展，如基于分区的方法(k-means)、 基于模型的方法、基于密度的方法、层次聚类方 收稿日期：2018-10-03.网络出版日期：201905-28 通信作者：储德润.E-mail:CDR0727@163.com 法、模糊聚类方法(fuzzy c-means)和基于图的方DOI: 10.11992/tis.201810002 网络出版地址: http://kns.cnki.net/kcms/detail/23.1538.tp.20190527.1407.010.html 公理化模糊共享近邻自适应谱聚类算法 储德润，周治平 （江南大学 物联网技术应用教育部工程研究中心，江苏 无锡 214122） 摘 要：针对传统的谱聚类算法通常利用高斯核函数作为相似性度量，且单纯以距离决定相似性不能充分表现 原始数据中固有的模糊性、不确定性和复杂性，导致聚类性能降低的问题。提出了一种公理化模糊共享近邻自 适应谱聚类算法，首先结合公理化模糊集理论提出了一种模糊相似性度量方法，利用识别特征来衡量更合适的 数据成对相似性，然后采用共享近邻的方法发现密集区域样本点分布的结构和密度信息，并且根据每个点所处 领域的稠密程度自动调节参数 σ，从而生成更强大的亲和矩阵，进一步提高聚类准确率。实验表明，相较于距 离谱聚类、自适应谱聚类、模糊聚类方法和地标点谱聚类，所提算法有着更好的聚类性能。 关键词：机器学习；数据挖掘；聚类分析；模糊聚类；谱聚类；公理化模糊集理论；共享最近邻；尺度参数 中图分类号：TP18 文献标志码：A 文章编号：1673−4785(2019)05−0897−08 中文引用格式：储德润, 周治平. 公理化模糊共享近邻自适应谱聚类算法 [J]. 智能系统学报, 2019, 14(5): 897–904. 英文引用格式：CHU Derun, ZHOU Zhiping. Shared nearest neighbor adaptive spectral clustering algorithm based on axiomatic fuzzy set theory[J]. CAAI transactions on intelligent systems, 2019, 14(5): 897–904. Shared nearest neighbor adaptive spectral clustering algorithm based on axiomatic fuzzy set theory CHU Derun，ZHOU Zhiping (Engineering Research Center of Internet of Things Technology Applications Ministry of Education, Jiangnan University, Wuxi 214122, China) Abstract: For the traditional spectral clustering algorithm, the Gaussian kernel function is usually used as the similarity measure. However, the similarity of distance cannot fully express the ambiguity, uncertainty, and complexity inherent in the original data, resulting in the reduction of clustering performance. To solve this problem, we propose an axiomatic fuzzy set shared nearest neighbor adaptive spectral clustering algorithm. First, the proposed algorithm uses a fuzzy sim￾ilarity measurement method based on axiomatic fuzzy set theory to measure more suitable data pairwise similarity by identifying features. Then, the structure and density information of sample point distribution in a dense area is obtained using the method of sharing the nearest neighbor, and the parameter σ is automatically adjusted according to the density degree of each point in the domain, thereby generating a more powerful affinity matrix to further increase the accuracy rate of clustering. Experimental results show that the proposed algorithm has better clustering performance than dis￾tance spectral clustering, adaptive spectral clustering, fuzzy clustering, and landmark spectral clustering. Keywords: machine learning; data mining; clustering analysis; fuzzy clustering; spectral clustering; axiomatic fuzzy set theory; shared nearest neighbor; scale parameter 聚类技术作为机器学习领域中的一种无监督 技术，在检测数据的内在结构和潜在知识方面发 挥着重要的作用。在过去的几十年中，许多聚类 方法得到了发展，如基于分区的方法 (k-means)、 基于模型的方法、基于密度的方法、层次聚类方 法、模糊聚类方法 (fuzzy c-means) 和基于图的方 收稿日期：2018−10−03. 网络出版日期：2019−05−28. 通信作者：储德润. E-mail：CDR0727@163.com. 第 14 卷第 5 期 智 能 系 统 学 报 Vol.14 No.5 2019 年 9 月 CAAI Transactions on Intelligent Systems Sep. 2019