利用模糊熵约束的模糊C均值聚类算法

Fuzzy C Means Clustering Algorithm by Using Fuzzy Entropy Constraint

针对传统的模糊C均值聚类算法求解隶属度公式仅仅考虑距离因素和算法对噪声数据敏感的问题,通过引入模糊熵约束,给出一种模糊C均值聚类算法.该算法引入模糊熵作为模糊C均值聚类算法的约束条件,重新给出了模糊C均值聚类算法的隶属度和聚类中心求解新公式,与原算法公式相比,新公式不仅考虑了距离因素,而且还考虑了数据集分布特性,并对同一个数据对象隶属于所有聚类中心的隶属度进行相关性计算,使得整个隶属度求解公式具有高斯分布特性,从而可以抑制噪声数据对聚类中心的影响.最后,采用UCI数据集,实验验证了该算法与传统FCM聚类算法及其派生算法相比,进一步提高了聚类的准确率和抗噪性.

In view of the issues of traditional fuzzy C means （FCM） clustering algorithm, which only considers distance factors in membership formula and are sensitive to noise data,a fuzzy C means clustering algorithm is presented by introducing the fuzzy entropy as the constraint. In the algorithm, the fuzzy entropy is introduced as constraint condition of fuzzy C means clustering algorithm, and the new formulas of solving memberships and clustering centers are given. Compared with the original algorithm formulas, the new formulas not only consider the distance factor,but also the distribution features of the data set. Memberships of the same data object belonged to all clustering centers are given correlation calculations, making the whole membership solution formula with Gaussian dis- tribution characteristics and reducing the influence of noise data to clustering centers. In the end, the experiments validate that the algo- rithm further improves the clustering accuracy and noise immunity by using UCI data sets.