Abstract: Traditional clustering methods are two-way clustering which assumes that a cluster must be represented by a set with crisp boundary. However, assigning uncertain elements into a cluster will increase decision risk. Three-way clustering puts the identified elements into the core region and the uncertain elements into the fringe region to reduce decision risk. This paper presents a strategy for converting a two-way cluster to three-way cluster using the [ε] neighborhood of the samples. The method shrinks the two-way clustering result to get the core region and expands the two-way clustering result to get the fringe region. The experiments using the proposed method on UCI data sets show that the strategy is effective in reducing the Davies-Bouldin-Index and increasing the average silhouette coefficient and accuracy of clustering results.

Key words: three-way clustering, neighborhood, k-means clustering, k-medoid clustering, fuzzy c-means clustering

摘要： 传统的聚类方法大都是二支决策，即决策一个元素属于一个类或者不属于一个类。然而在处理不确定性信息时，强制将其中的元素划分到一个类中，往往容易带来较高的决策风险。三支决策聚类将确定的元素放入核心域中，将不确定的元素放入边界域中延迟决策，可以有效地降低决策风险。利用数学形态学中膨胀与腐蚀的思想，提出了一种使用样本的[ε]邻域将二支聚类转化为三支聚类的方法。该方法在二支聚类的结果上，利用每个类中元素的[ε]邻域收缩得到核心域，扩张得到边界域。在UCI数据集上的实验结果显示该方法可以降低聚类结果的DBI，提高聚类结果的平均轮廓系数和准确率。

关键词: 三支聚类, 邻域, k-means聚类, k-medoid聚类, fuzzy c-means聚类