Abstract:

The fuzzy C-means (FCM) clustering algorithm is one of the widely used clustering algorithms based on the minimization of objective function. Several clustering algorithms, such as AFCM algorithm and GK algorithm, are the extension and improvement of FCM clustering algorithm. This paper introduces Total-Bregman divergence into the FCM clustering framework and proposes an algorithm named fuzzy clustering algorithm based on total-Bregman divergence (TBD-FCM), which is an improvement of the fuzzy clustering algorithm based on Bregman divergence. Then this paper analyzes the convergence properties of this algorithm. In experiment part, several clustering results on the datasets from the UCI repository have been shown to prove the effectiveness and the convergence properties of clustering algorithm.

Key words: clustering algorithm, fuzzy clustering, Total-Bregman divergence

摘要：

模糊C均值（fuzzy C-means, FCM）聚类算法是一种常用的基于目标函数最小化的聚类算法。目前已经提出了相当数量的聚类算法是对模糊C均值聚类算法的改进，例如AFCM算法、GK算法等。对最近发表的基于Bregman距离的模糊聚类算法进行了改进，通过在FCM模糊聚类框架中引入Total-Bregman距离提升了聚类算法的聚类性能。同时对基于Total-Bregman距离的模糊聚类算法的收敛性质进行了理论分析。实验部分对来自UCI数据库的几个数据集进行了聚类，证明了算法的有效性和收敛性。

关键词: 聚类算法, 模糊聚类, Total-Bregman距离