密度峰值聚类算法(Clustering by fast search and find of density peaks,DPC)的截断距离参数需人工干预,且参数选取对聚类结果产生较大的影响.为解决这一问题,提出了一种基于改进果蝇优化的密度峰值聚类算法.通过Tent混沌映射初始化...密度峰值聚类算法(Clustering by fast search and find of density peaks,DPC)的截断距离参数需人工干预,且参数选取对聚类结果产生较大的影响.为解决这一问题,提出了一种基于改进果蝇优化的密度峰值聚类算法.通过Tent混沌映射初始化果蝇种群,利用Tent混沌序列随机性、遍历性和规律性的特点来提高初始种群的多样性,增强算法的全局探索能力;并引入动态步长因子与柯西变异策略对基本果蝇优化算法(Fruit Fly Optimization Algorithm,FOA)的更新机制进行改进,加强局部勘探能力,帮助算法跳出局部最优;利用随机算法收敛准则从理论上对改进FOA算法的收敛性进行分析;在6个基准测试函数上进行实验仿真,结果表明改进的FOA算法具有更快的收敛速度及更高的求解精度;将改进FOA算法与DPC算法融合成新算法,利用改进FOA算法较强的寻优能力找到最佳截断距离并实现最终的聚类.实验结果表明,新算法在UCI数据集及人工数据集上的聚类性能均有改善,相较于DPC算法、FOA-DPC算法、FADPC算法及ACS-FSDP算法具有更优的性能指标,有效抑制了手动选取截断距离参数带来的影响问题.展开更多
This work is about a splitting method for solving a nonconvex nonseparable optimization problem with linear constraints,where the objective function consists of two separable functions and a coupled term.First,based o...This work is about a splitting method for solving a nonconvex nonseparable optimization problem with linear constraints,where the objective function consists of two separable functions and a coupled term.First,based on the ideas from Bregman distance and Peaceman–Rachford splitting method,the Bregman Peaceman–Rachford splitting method with different relaxation factors for the multiplier is proposed.Second,the global and strong convergence of the proposed algorithm are proved under general conditions including the region of the two relaxation factors as well as the crucial Kurdyka–Łojasiewicz property.Third,when the associated Kurdyka–Łojasiewicz property function has a special structure,the sublinear and linear convergence rates of the proposed algorithm are guaranteed.Furthermore,some preliminary numerical results are shown to indicate the effectiveness of the proposed algorithm.展开更多
Let Sigma (infinity)(n=1) X-n be a series of independent random variables with at least one non-degenerate X-n, and let F-n be the distribution function of its partial sums S-n = Sigma (n)(k=1) X-k. Motivated by Hilde...Let Sigma (infinity)(n=1) X-n be a series of independent random variables with at least one non-degenerate X-n, and let F-n be the distribution function of its partial sums S-n = Sigma (n)(k=1) X-k. Motivated by Hildebrand's work in [1], the authors investigate the a.s. convergence of Sigma (infinity)(n=1) X-n under a hypothesis that Sigma (infinity)(n=1) rho (X-n, c(n)) = infinity whener Sigma (infinity)(n=1) c(n) diverges, where the notation rho (X,c) denotes the Levy distance between the random variable X and the constant c. The principal result of this paper shows that the hypothesis is the condition under which the convergence of F-n(x(0)) with the limit value 0 < L-0 < 1, together with the essential convergence of Sigma (infinity)(n=1) X-n, is both sufficient and necessary in order for the series Sigma (infinity)(n=1) X-n to a.s. coverage. Moreover, if the essential convergence of Sigma (infinity)(n=1) X-n is strengthened to limsup(n=infinity) P(\S-n\ < K) = 1 for some K > 0, the hypothesis is already equivalent to the a.s. convergence of Sigma (infinity)(n=1) X-n. Here they have not only founded a very general limit theorem, but improved the related result in Hildebrand([1]) as well.展开更多
文摘密度峰值聚类算法(Clustering by fast search and find of density peaks,DPC)的截断距离参数需人工干预,且参数选取对聚类结果产生较大的影响.为解决这一问题,提出了一种基于改进果蝇优化的密度峰值聚类算法.通过Tent混沌映射初始化果蝇种群,利用Tent混沌序列随机性、遍历性和规律性的特点来提高初始种群的多样性,增强算法的全局探索能力;并引入动态步长因子与柯西变异策略对基本果蝇优化算法(Fruit Fly Optimization Algorithm,FOA)的更新机制进行改进,加强局部勘探能力,帮助算法跳出局部最优;利用随机算法收敛准则从理论上对改进FOA算法的收敛性进行分析;在6个基准测试函数上进行实验仿真,结果表明改进的FOA算法具有更快的收敛速度及更高的求解精度;将改进FOA算法与DPC算法融合成新算法,利用改进FOA算法较强的寻优能力找到最佳截断距离并实现最终的聚类.实验结果表明,新算法在UCI数据集及人工数据集上的聚类性能均有改善,相较于DPC算法、FOA-DPC算法、FADPC算法及ACS-FSDP算法具有更优的性能指标,有效抑制了手动选取截断距离参数带来的影响问题.
基金supported by the National Natural Science Foundation of China(No.12171106)the Natural Science Foundation of Guangxi Province(Nos.2020GXNSFDA238017 and 2018GXNSFFA281007).
文摘This work is about a splitting method for solving a nonconvex nonseparable optimization problem with linear constraints,where the objective function consists of two separable functions and a coupled term.First,based on the ideas from Bregman distance and Peaceman–Rachford splitting method,the Bregman Peaceman–Rachford splitting method with different relaxation factors for the multiplier is proposed.Second,the global and strong convergence of the proposed algorithm are proved under general conditions including the region of the two relaxation factors as well as the crucial Kurdyka–Łojasiewicz property.Third,when the associated Kurdyka–Łojasiewicz property function has a special structure,the sublinear and linear convergence rates of the proposed algorithm are guaranteed.Furthermore,some preliminary numerical results are shown to indicate the effectiveness of the proposed algorithm.
文摘Let Sigma (infinity)(n=1) X-n be a series of independent random variables with at least one non-degenerate X-n, and let F-n be the distribution function of its partial sums S-n = Sigma (n)(k=1) X-k. Motivated by Hildebrand's work in [1], the authors investigate the a.s. convergence of Sigma (infinity)(n=1) X-n under a hypothesis that Sigma (infinity)(n=1) rho (X-n, c(n)) = infinity whener Sigma (infinity)(n=1) c(n) diverges, where the notation rho (X,c) denotes the Levy distance between the random variable X and the constant c. The principal result of this paper shows that the hypothesis is the condition under which the convergence of F-n(x(0)) with the limit value 0 < L-0 < 1, together with the essential convergence of Sigma (infinity)(n=1) X-n, is both sufficient and necessary in order for the series Sigma (infinity)(n=1) X-n to a.s. coverage. Moreover, if the essential convergence of Sigma (infinity)(n=1) X-n is strengthened to limsup(n=infinity) P(\S-n\ < K) = 1 for some K > 0, the hypothesis is already equivalent to the a.s. convergence of Sigma (infinity)(n=1) X-n. Here they have not only founded a very general limit theorem, but improved the related result in Hildebrand([1]) as well.
