基于核函数理论的系统聚类分析  

Kernel-Based Hierarchical Cluster Analysis

作　　者：陈永良[1] 李学斌[1] 

机构地区：[1]吉林大学综合信息矿产预测研究所,长春130026

出　　处：《吉林大学学报（地球科学版）》2010年第5期1211-1216,共6页Journal of Jilin University：Earth Science Edition

基　　金：国家自然科学基金项目(40872193)

摘　　要：为了完善系统聚类分析算法理论,使之具有区分数据集非线性集群特征的能力,将核函数理论和系统聚类分析算法有机结合,推导出基于核函数理论的系统聚类分析方法。其基本思路是:把样本从低维观测空间非线性变换至高维像空间,使样本变得线性可分;然后,应用核函数理论'隐式'地实现高维像空间的系统聚类分析。用Pb、Bi、Mo质量浓度作为化探异常的分类依据,对8处化探异常进行分类实验研究,在Pb、Bi、Mo两两组合的二维平面图中,8处化探异常明显地分为(1,3,8),(2,4)和(5,6,7)3个点群,用核系统聚类方法能够很好地区分出这3个点群;而传统系统聚类方法却把8处化探异常错分成(1,3,8,6)和(2,4,5,7)两个类。由此可见,核系统聚类方法的类群区分能力高于传统系统聚类方法。In order to improve the algorithmic theory and make the hierarchical cluster analysis be able to find nonlinear clusters in a data set,the authors develop a kernel-based hierarchical cluster analysis method by integrating kernel functions with the hierarchical cluster analysis algorithm.The procedure of the new cluster algorithm can be described as follows.The input samples in the low-dimensional input space are nonlinearly mapped to a high-dimensional image space where the samples are linearly separable,and then a kernel function is applied to implicitly execute the hierarchical cluster analysis in the image space.The authors conduct an experiment on the unsupervised classification of eight geochemical anomalies according to the contents of Pb,Bi,and Mo.The eight geochemical anomalies are obviously divided into the three clusters,（1,3,8）,（2,4）,and（5,6,7）,according to the three pair-wised scatter plots derived from the contents of Pb,Bi,and Mo.Kernel hierarchical cluster analysis is able to properly differentiate these three clusters while the conventional hierarchical cluster analysis improperly classifies the eight geochemical anomalies into the two classes,（1,3,8,6） and（2,4,5,7）.Therefore,the clustering ability of the new method exceeds that of the conventional hierarchical cluster algorithm.

关 键 词：核函数 聚类分析 观测空间 像空间 

分 类 号：P628.1[天文地球—地质矿产勘探]