基于粗糙集理论的模糊支持向量聚类算法的改进

摘要

Support vector clustering (SVC)is an important density based clustering algorithm,and it has many important applications in the real world.In the absence of any prior knowledge,the algorithm provides the ability to deal with arbitrary clusters,that is,the number of arbitrary contour and the number of detected data sets.However,if outliers exist in the data,the algorithm can not classify these points,which will lead to the loss of important information about the data set.To remedy these defects,the rough set theory and fuzzy set theory and support vector clustering algorithm are combined to obtain a new improved algorithm called Rough-Fuzzy support vector clustering.Rough fuzzy clustering is obtained by using the support vector as the clustering prototype.The structure features of the cluster have two main contents:the lower approximation set and the fuzzy boundary.When the support vector set is used as a spe-cial clustering,the membership degree of the fuzzy boundary can be calculated by the closeness degree between the elements.The sam-ple points in the lower approximation set are set up in the super ball obtained in the training phase of SVC algorithm.In terms of detec-ting outliers and calculating the clustering of arbitrary profiles,this paper introduces the advantages of clustering algorithm compared with the soft clustering algorithm.%支持向量聚类（SVC）是一种重要的基于密度的聚类算法，在现实世界中有很多重要的应用。在没有任何先验知识的情况下，该算法提供了处理任意簇的能力，即任意轮廓和检测类数量的数据集。然而，如果异常值存在于数据中，该算法无法将这些点进行分类，这样会导致有关数据集重要信息的丢失。为了弥补这些缺陷，将粗糙集理论和模糊集理论与支持向量聚类算法相结合得到一种新的改进算法称为粗糙-模糊支持向量聚类算法（Rough-Fuzzy Support Vector Clustering）。即通过使用支持向量作为聚类原型获得粗糙-模糊聚类。该聚类的结构特征有两个主要内容：下近似集和模糊边界。当支持向量集作为一个特殊的聚类，通过元素间的亲密程度，模糊边界的隶属度可以被计算出来。而下近似集包含的样本点建立在SVC算法训练阶段获得的超球体内。在检测异常值和计算任意轮廓的聚类方面，本文所介绍的聚类算法与软聚类算法相比拥有相当程度的优势。