基于商空间的非均匀粒度聚类分析

An Analysis of Uneven Granules Clustering Based on Quotient Space

采用距离度量空间的手段讨论了商空间的模糊粒度聚类,结合信息融合技术用不同粒度合成聚类结果,认为聚类可以以非均匀粒度来描述样本集。据此提出了使用 Gaussian 型函数定义商空间的距离函数的模糊聚类算法(FCluster 算法),算法用距离表示信息粒度,不需要定义隶属函数和求出相似矩阵,并且不需要讨论参数的选择。仿真实验说明了算法可以很直观地从不同粒度(距离)观察聚类结果,大大降低了计算复杂度和空间复杂度,适于处理大数据量的样本,并且 Gaussian 型函数定义的距离对试验样本可以达到很好的效果。

The fuzzy granules clustering based on the quotient space is discussed by the metric space. The cluster is a combination of information obtained from different granules in information fusion. Clustering with uneven granules in this way represents samples sets. By this means, a fuzzy clustering (FCluster) is proposed. In the clustering, the distance measure function, which is defined with Gaussian function between samples, is employed other than membership functions, fuzzy matrix, and the Gaussian width parameters are ignored. As the experiment showed, the approach advantage is: (1) the cluster is observed in different viewpoints; (2) the computational and special cost is saved; (3) it is efficient for the large number of observations; (4) Gaussian distance is able to achieve better accuracy to the synthetic control chart time series data sets.