基于矩阵特征值分析的模糊聚类有效性指标

许多有效性指标已经被提出量化地估计和评价模糊聚类算法对于给定数据集的划分结果.但是由于不合理的结构和极大的时间耗费,迄今这些有效性指标几乎都无法满足应用的一般性需求.为此,提出一个基于Gerschgorin圆盘定律估计的聚类有效性指标来估计模糊聚类的类数.先由模糊聚类划分的结果得到一个相关性矩阵,接着求出该矩阵的所有特征值和特征向量,然后基于经典Gerschgorin圆盘定律估计最优的类数.为了检验提出的指标在模糊聚类中的有效性,把模糊聚类算法应用到带有不同特征的3个人工数据集和3个真实的数据集,并比较提出的指标和2个最常用的模糊聚类有效性指标.实验结果证明了所提出的有效性指标能够发现被聚类数据集的固有结构,从而得出更加准确的类数.

Matrix Eigenvalue Analysis-Based Clustering Validity Index

Many validity indices have been proposed for quantitatively assessing the performance of fuzzy clustering algorithms.But so far these validity indices work with little satisfaction due to their unreasonable structures and low efficiency in applications.In this paper,a Gerschgorin disk estimation-based criterion was proposed to estimate the correct number of clusters.Firstly,a correlation matrix was derived from the fuzzy clustering results,and then the eigenvalue decomposition was performed to obtain all eigenvalues and eigenvectors of the matrix.Finally,based on the classical Gerschgorin disk theorem,the optimal number of clusters was estimated.To validate the proposed criterion in fuzzy clustering,a group of the most used validity indices were applied to three synthetic datasets and three real datasets with different characteristics,and compared with the proposed criterion.The experimental results verify that the proposed criterion can discover the inherit natures among the clustered patterns and suggest more accurate number of clusters.