针对传统密度峰值聚类算法(Clustering by fast search and find of density peaks,CFSFDP)簇心选择不佳、非簇心点分配不准确导致的聚类效果差问题,提出一种融合可拓关联函数的密度峰值聚类算法,通过引入平均差异度衡量样本密度选取簇...针对传统密度峰值聚类算法(Clustering by fast search and find of density peaks,CFSFDP)簇心选择不佳、非簇心点分配不准确导致的聚类效果差问题,提出一种融合可拓关联函数的密度峰值聚类算法,通过引入平均差异度衡量样本密度选取簇心;基于k邻域思想提出雏形簇概念并建立物元模式下的节域和经典域;利用可拓关联函数定量衡量未分配点相对各雏形簇的隶属程度,从而实现精准聚类.将该算法和其他几种聚类算法在人工数据集和UCI标准数据集上分别进行对比实验,实验结果表明本文算法对任意形状任意密度数据集的聚类效果更好,优于其他算法.展开更多
Let X and Y be metrizable topological linear spaces. In this paper, the following results are proved. (1) If X and Y are complete, g: X→Y is a point closed u. s. c.,and symmetric process with F(X)=Y,then either F(X) ...Let X and Y be metrizable topological linear spaces. In this paper, the following results are proved. (1) If X and Y are complete, g: X→Y is a point closed u. s. c.,and symmetric process with F(X)=Y,then either F(X) is meager in Y,or else F is an open muRifunction with F(X)=Y. (2) If X is complete, and F: X→Y is a process with a subclosed graph, then F is I s. c.. We also discuss topological multi-homomorphisms between topological linear spaces.展开更多
The purpose of this paper is to reconsider the utility representation problem of preferences,Sev-eral representation theorems are obtained on general choice spaces.Preferences having continuous utility functions are c...The purpose of this paper is to reconsider the utility representation problem of preferences,Sev-eral representation theorems are obtained on general choice spaces.Preferences having continuous utility functions are characterized by their continuities and countable satiation.It is showed that on a pairwise separable choice space,the sufficient and necessary condition for a preference to be represented by a contin-uous utility function is that the preference is continuous and countably satiable.For monotone prefer-ences,we obtain that any space has continuous utility representations.展开更多
文摘针对传统密度峰值聚类算法(Clustering by fast search and find of density peaks,CFSFDP)簇心选择不佳、非簇心点分配不准确导致的聚类效果差问题,提出一种融合可拓关联函数的密度峰值聚类算法,通过引入平均差异度衡量样本密度选取簇心;基于k邻域思想提出雏形簇概念并建立物元模式下的节域和经典域;利用可拓关联函数定量衡量未分配点相对各雏形簇的隶属程度,从而实现精准聚类.将该算法和其他几种聚类算法在人工数据集和UCI标准数据集上分别进行对比实验,实验结果表明本文算法对任意形状任意密度数据集的聚类效果更好,优于其他算法.
基金This paper was reported at the 5th National Functional Analysis Conference held at Nanjing in Nov.,1990.
文摘Let X and Y be metrizable topological linear spaces. In this paper, the following results are proved. (1) If X and Y are complete, g: X→Y is a point closed u. s. c.,and symmetric process with F(X)=Y,then either F(X) is meager in Y,or else F is an open muRifunction with F(X)=Y. (2) If X is complete, and F: X→Y is a process with a subclosed graph, then F is I s. c.. We also discuss topological multi-homomorphisms between topological linear spaces.
基金This work is supported by the natural science foundation.
文摘The purpose of this paper is to reconsider the utility representation problem of preferences,Sev-eral representation theorems are obtained on general choice spaces.Preferences having continuous utility functions are characterized by their continuities and countable satiation.It is showed that on a pairwise separable choice space,the sufficient and necessary condition for a preference to be represented by a contin-uous utility function is that the preference is continuous and countably satiable.For monotone prefer-ences,we obtain that any space has continuous utility representations.
