基于灰关系分析的模糊聚类

Grey Relational Analysis for Fuzzy Clustering

灰关系分析（Grey relational analysis,GRA））能够度量参考样本和比较样本间的相似性而广泛应用于聚类算法中,但目前基于GRA的聚类方法对灰关系阈值的设定采用尝试法,难以刻画信息的完全度。为此,本文将灰关系分析所学习的相似性度量嵌入到流行的模糊聚类算法中,从而提出了基于灰关系分析的模糊聚类方法。分析了灰关系性质和核机理论相似性基础之上,由灰色理论中的灰关系衍生出一种新型核——灰关系核,同时,也由核机理论诱导出一种新的灰关系度量,从而构建了灰关系分析和核机理论间的一条联系纽带。UCI数据集上的模拟实验验证了基于灰关系分析的模糊聚类方法和所提灰关系度量的有效性。

Grey relational analysis（GRA） can measure the similarity between the reference samples and the comparative samples,thus is widely applied in the clustering algorithms;however,the state-of-the-art clustering algorithms based on GRA set the grey relation threshold using try-and-error method,and could not conduct the real fuzziness.To solve this,this paper embeds the similarity measure learned by GRA into the popular fuzzy clustering methods,and proposes a fuzzy clustering method based on GRA.Based on the analysis on the similarity between grey relation and kernel method,the paper derivates a novel kernel—grey relation kernel,simultaneously,induces a novel grey relation metric by the kernel method.As a result,a bridge between GRA and kernel method is built.Simulation experiments on UCI benchmark datasets verify the effectiveness of the proposed algorithm and metric.