快速模糊分割算法

Fast fuzzy partitioning algorithm

针对全局模糊最优划分(FGOP)或接近全局模糊最优划分的快速增量模糊分割算法进行研究。通过确定算法中的最佳模糊分割k=2,3,…,k_(max),计算出每个分区相应的有效性指标,由此得到数据k_(max),k_(max)的最佳分割目标函数值相对接近k_(max)-1簇的最佳分割目标函数值。分类归并前,进行数据标准化,将几个有效性指标应用到标准化数据的分区中。给出标准化数据和初始数据所用的有效性指标之间的简单关系,提议的算法找到具有最恰当数量簇的最优分割。该算法在数个合成数据集和几个UCI(加州大学欧文分校)数据存储库的真实数据集上进行测试,效果得到了验证。

A fast fuzzy partitioning algorithm is able to find either a fuzzy globally optimal partition or a fuzzy locally optimal partition close to the global one was proposed.Since fuzzy k optimal partitions with k=2,3,…,kmax clusters were determined successively,it was possible to calculate corresponding validity indices for every obtained partition and kmax defined.The objective function value of optimal partition kmax clusters was relatively close to that of kmax-1 clusters.Before clustering,the data were normalized,and several validity indices were applied to partitions of the normalized data.Simple relationships between used validity indices on normalized and original data were given as well.The proposed algorithm is able to find optimal partitions with the most appropriate number of clusters.The algorithm was verified on numerous synthetic datasets and several real datasets from the UCI data repository.