基于势博弈的聚类算法

Clustering Algorithm Based on Initial Clustering

摘要: 针对聚类过程中初始聚类选取方法的不同会影响其最终聚类结果，且传统的聚类算法很难得到稳定的聚类的问题，提出一种新颖的以模糊c均值作为初始聚类的基于势博弈的聚类算法(简称FS-IBRC)。该算法结合模糊c均值算法，以欧氏距离作为相似性度量，不断迭代更新隶属度矩阵和聚类中心，直至目标函数收敛从而得到较优的初始聚类结果。在此基础上，将数据聚类问题转化为寻找势博弈模型的纯纳什均衡问题，这对应于稳定的聚类。进而给出了解决这种基于势博弈模型聚类的算法，即迭代的最佳响应算法。最后，将FS-IBRC算法和一般初始化算法(S-IBRC)分别在两个不同的人工数据集上测试并实现。

Abstract: Aiming at the problem that the different initial cluster selection methods in the clustering process will affect the final clustering results, and the traditional clustering algorithm is difficult to obtain stable clustering, a novel method using fuzzy c-means as the initial clustering is proposed. Clustering algorithm is based on potential game (Referred to as FS-IBRC). The algorithm combines the fuzzy c-means algorithm with Euclidean distance as the similarity measure, and iteratively updates the membership matrix and clustering center until the objective function converges to obtain a better initial clustering result. On this basis, the data clustering problem is transformed into a pure Nash equilibrium problem of finding a potential game model, which corresponds to stable clustering. Furthermore, an algorithm for solving this clustering based on the potential game model is given, that is, the iterative optimal response algorithm. Finally, the FS-IBRC algorithm and the general initialization algorithm (S-IBRC) were tested and implemented on two different artificial data sets.