模糊聚类计算的最佳算法

An Optimal Algorithm for Fuzzy Classification Problem

给出模糊关系传递闭包在对应模糊图上的几何意义 ,并提出一个基于图连通分支计算的模糊聚类最佳算法 .对任给的 n个样本 ,新算法最坏情况下的时间复杂性函数 T(n)满足 O(n)≤ T(n)≤ O(n2 ) .与经典的基于模糊传递闭包计算的模糊聚类算法的 O(n3 log n)计算时间相比 ,新算法至少降低了 O(nlog n)时间因子 .理论分析与计算机实验表明 ,新算法对大规模数据进行模糊聚类计算的实际计算时间 ,在实际应用中是可以被接受的 .

In this paper, the geometric meaning of the transitive closure of a fuzzy relation in corresponding fuzzy graph is first given. An optimal algorithm, which is based on the computation of graph connected components, for fuzzy classification problem is proposed. For any given n samples, the worst case time complexity T(n) of the algorithm satisfies that O(n)≤T(n)≤O(n 2) . Compared with the classic fuzzy classification algorithm, which is based on the computation of the transitive closure of a given relative matrix and of the O(n 3 log n) time, the new algorithm decreases O(n log n) time factor at least. The theoretic analysis and computer performance show that the real computing time of the new algorithm is acceptable when it is used for fuzzy classification on large data.