Abstract: The difference in magnitude between the intra-class distance and the inter-class distance results in the inability to directly fuse the two types of distances, which in turn affects the FCM clustering model design. First of all, this paper comprehensively reviews the classical and improved FCM clustering model, and the relationship model between intra-class distance and inter-class distance trace is constructed. The insufficiency of the existing FCM clustering model is analyzed from two aspects: the inconsistency and the magnitude difference of the distance between classes. Again, the Gaussian kernel distance is used to replace the traditional Euclidean distance to characterize the distance between classes, an intra-class distance balancing method is presented to minimize the difference between intra-class compactness and inter-class separation, and the FCM clustering model based on Gaussian kernel and its algorithm are redesigned. Finally, an example is given to prove the effectiveness and superiority of this method.

Key words: fuzzy C-means clustering algorithm (FCM), cluster analysis, Gaussian kernel

摘要： 类内距离和类间距离数值量级差异性导致两类距离无法直接融合,进而影响了FCM聚类模型设计。首先,本文全面回顾了经典和改进型的FCM聚类模型,构建了类内距离和类间距离迹的关系模型,分别从类内类间距离的变化不一致性和量级差异性两个方面分析了现有FCM聚类模型的不足;其次,运用高斯核距离替代传统的欧式距离来表征类内类间距离,基于最小化类内紧凑度与类间分离度差的思想,设计了类内类间距离平衡方法,提出了一种改进的FCM聚类目标函数与算法;最后,运用算例说明了本方法的有效性和优越性。

关键词: FCM, 聚类分析, 高斯核