Abstract: FCM is a classical clustering algorithm,which is widely used in pattern reorganization,data mining and so on.It is an optimization algorithm based on gradient descending.It is sensitive to the initial condition and liable to be trapped in a local optimum.Space smoothing allows a local search heuristics to escape from a poor,local optimum.In this paper,we construct a series of smoothed search spaces with space smoothing strategy,and runs FCM in every search space.FCMS（FCM based on Multi-Space）uses the solution in the former search space as an initial solution for the current space.Through such way,FCMS could jump out of the local optimum“traps”,and improve the probability of getting global optimum.This paper gives out displacement strategy for space smoothing,and experiment results indicate that smoothing search space is very efficient to FCM.

Key words: clustering analysis, multi-space, FCM

摘要： FCM是经典的聚类算法,广泛地应用于模式识别、数据挖掘等领域。FCM算法是一种梯度下降优化算法,对初始解敏感并且容易获得局部最优解。空间平滑能够避免启发式局部搜索算法掉入局部最优解。采用空间平滑策略构造一系列光滑程度不同的搜索空间,在不同的搜索空间中执行FCM算法,并利用前层搜索空间的聚类结果来引导本层搜索空间的聚类。FCMS（FCM based
on multi-Space）能够跳过局部最优解的“陷阱”,增大获得全局最优解的概率,达到提高聚类质量的目的。给出了等距法空间平滑策略,并通过实验对比了FCMS算法与FCM算法的聚类质量。实验结果表明,空间平滑对FCM算法非常有效。

关键词: 聚类分析, 多空间, FCM