基于随机分布与高斯分布数据集的不同距离下的FCM算法比较

Comparison of FCM Algorithms at Different Distances Based on Random Distribution and Gaussian Distribution Data Sets

首先,本文给出了Euclidean Distance(欧式距离)、(Manhattan Distance)曼哈顿距离、Chebyshev Distance(切比雪夫距离)、Minkowski Distance(闵可夫斯基距离)、标准化欧氏距离(Standardized Euclidean distance)、马氏距离(Mahalanobis Distance)和Morphology Similarity Distance)形状相似距离下的FCM算法的公式和取得最佳c-划分的条件。之后,为比较这些算法的好坏,我们对针对随机分布和具有几何特征的高斯分布的数据集应用这些算法分别作了聚类,并对结果进行分析,得到在当数据为随机分布时,形状相似距离相比于欧式距离、曼哈顿距离以及其他距离更为合适。然而不同距离下的高斯分布数据集的聚类结果并无大差异。

First,this article gives the formula of the FCM algorithm under Euclidean Distance,Manhattan Distance,Chebyshev Distance,Minkowski Distance,Standardized Euclidean Distance,Mahalanobis Distance,and Morphology Similarity Distance and the conditions for obtaining the optimal c-partition.Then,in order to compare the effect of these algorithms,we applied these algorithms to the data sets with random distribution and Gaussian distribution with geometric characteristics to perform clustering.With the analysis of the results,Morphology Similarity Distance is more suitable than European Distance,Manhattan Distances,and other distances when the data is randomly distributed.However,the clustering results of Gaussian Distribution datasets at different distances are not significantly different.