一种基于流形距离核的谱聚类和量子聚类融合算法  

A fusion algorithm of spectral clustering and quantum clustering based on manifold distance kernel

作　　者：马宇红 李兴义 薛生倩 王小小 MA Yu-hong;LI Xing-yi;XUE Sheng-qian;WANG Xiao-xiao(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,Gansu,China;Editorial Department of the University Journal,Northwest Normal University,Lanzhou 730070,Gansu,China)

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070 [2]西北师范大学学报编辑部,甘肃兰州730070

出　　处：《西北师范大学学报（自然科学版）》2023年第2期37-46,共10页Journal of Northwest Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(51368055)。

摘　　要：谱聚类是一种基于图谱划分理论的聚类算法,本质上是将聚类问题转化为图的最优划分问题;量子聚类可以充分挖掘数据样本的内在信息,是一种基于划分的无监督聚类算法.为了充分发挥谱聚类算法和量子聚类算法的优势,本文提出了一种基于流形距离核的谱聚类和量子聚类融合算法(MFD-NJW-QC).首先,计算数据集的流形距离核矩阵,构造相应的拉普拉斯矩阵;其次,根据拉普拉斯矩阵的若干最大特征值对应的特征向量构造新数据集,并使用量子聚类算法对新构造的数据集进行聚类,从而得到原始数据的类标签;最后,基于7个人工数据集和5个UCI数据集验证MFD-NJW-QC算法的聚类性能.结果显示,MFD-NJW-QC算法能够明显提高聚类性能,尤其对于具有流形结构,且类簇大小不平衡、密度分布不均匀的数据集优势更为突出.Spectral clustering is a clustering algorithm based on graph partition theory,which essentially transforms the clustering problem into the optimal graph partition problem,and quantum clustering can fully explore the intrinsic information of data samples,so it is an unsupervised clustering algorithm based on partition.In order to give full play to the advantages of spectral clustering and quantum clustering,a fusion algorithm of spectral clustering and quantum clustering based on manifold distance kernel(MFD-NJW-QC)is proposed.Firstly,the manifold distance kernel matrix of the dataset is calculated,and the corresponding Laplacian matrix is constructed by the manifold distance kernel matrix.Secondly,a new dataset is constructed according to the eigenvectors corresponding to several maximum eigenvalues of the Laplacian matrix,and the newly constructed dataset is clustered by quantum clustering algorithm,so as to obtain the class labels of the original data.Finally,the clustering performance of the MFD-NJW-QC algorithm is verified by experiments based on 7 artificial data sets and 5 UCI data sets.The results show that the MFD-NJW-QC algorithm can significantly improve the clustering performance,especially for those datasets with manifold structure,uneven cluster size and uneven density distribution.

关 键 词：流形距离核 谱聚类 量子聚类 拉普拉斯矩阵 特征向量 

分 类 号：TP181[自动化与计算机技术—控制理论与控制工程]