一种基于属性空间相似性的模糊聚类算法

模糊C均值(FCM)聚类算法及其相关改进算法基于最大模糊隶属度原则确定聚类结果，没有充分利用迭代后的模糊隶属度矩阵和簇类中心的样本属性特征信息，影响聚类准确度。针对这个问题，该文提出一种新的改进思路:改进FCM算法输出定类原则。给出二元属性拓扑子空间中属性相似度的定义，最终提出一种基于属性空间相似性的改进FCM算法(FCM-SAS):首先，选择FCM算法聚类后模糊隶属度低于聚类置信度的样本作为存疑样本；然后，计算存疑样本与聚类后聚类中心的属性相似度；最后，基于最大属性相似度原则更新存疑样本的簇类标签。通过UCI数据集实验，证明算法不仅有效，还较一些基于最大模糊隶属度原则定类的改进算法具有更优的聚类评价指标。

A Novel Fuzzy Clustering Algorithm Based on Similarity of Attribute Space

With the attribute feature information of the fuzzy membership matrix and cluster centers after the iteration not fully utilized, the results of Fuzzy C-Means (FCM) Clustering and related modified algorithms are determined based on the principle of maximum fuzzy membership, causing bad influence on the clustering accuracy. To solve this problem, the improvement ideas are proposed: to improve classification principle of FCM. The formula definition of attribute similarity in binary topological subspaces is given. Then, the improved FCM algorithm based on the Similarity of Attribute Space (FCM-SAS) is proposed: First, samples with fuzzy membership degree lower than the clustering reliability are selected as suspicious samples. Next, the attribute similarity between the suspicious samples and the cluster centers after clustering are calculated. Finally, cluster labels of suspicious samples based on the principle of maximum attribute similarity are updated. The validity and superiority of the proposed algorithm is verified by the UCI sample set experiments and comparisons with other modified algorithms based on the principle of maximum fuzzy membership.