基于模糊相容关系的聚类粒度分析

Granular Analysis in Clustering Based on Fuzzy Tolerance Relation

聚类操作实质上是在样本点之间定义一种等价关系,属于同一类的任意两个样本点被看作是等价的,然而基于传统的等价关系聚类存在缺陷,不能解决异类有交集聚类问题。分析了基于等价关系聚类粒度分析不足的原因,利用模糊相容关系分析聚类粒度,提出了基于模糊相容关系的聚类粒度分析方法,通过模糊相容关系合成与分解,确定最优聚类粒度;再将有交集样本的覆盖转化为矩阵,定义覆盖矩阵距离概念,通过覆盖的合并和分割,找到与覆盖距离最小的划分,进而提出覆盖的最优划分算法解决异类间交集的归属问题。无线电信号监测数据聚类实验结果,表明了这种聚类粒度分析方法的可行性和有效性。

Clustering defines an equivalence relation between the samples in nature, while two sample points are equivalent if they belong to one class, but classical equivalence relation can not overcome clustering which different classes have intersection. The disadvantages of granular analysis in clustering based on the equivalence relation were pointed out, then, granular analysis in clustering based on the fuzzy tolerance relation was proposed. The best granularity was chosen by compositing and decomposing the fuzzy tolerance relations. After giving the best analysis granularity, the covering which different classes have intersection was transferred into the matrix, the distance of the matrixes was defined. By merging and separating subsets of the covering according to minimal distance, the best partitions could be found, then, the best partition algorithm of the covering was proposed. The results of the experiment about clustering short wave communication signal show the feasibility and efficiency of the algorithm.