基于聚类算法的有限制单纯形均匀随机抽样研究

Research on Restricted Simplex Uniform Random Sampling Based on Clustering Algorithm

针对单纯形在抽样算法设计方案中无法适用复杂限制情况下的条件分布以及满足高维情形要求,需要提出一种行之有效的抽样算法,即Gibbs抽样算法,来为有限制单纯形均匀随机抽样提供一个可靠算法框架,同时为了获得有限制单纯形上均匀分布的代表点,此研究引入了3种聚类算法。从数值模拟结果可以看出,提出的抽样方法能够获取到较为均匀的样本,能够广泛应用至各种有限制或高维等复杂条件中,且对聚类算法的抽样算法框架有显著提升试验点的价值属性。

In view of the fact that simplex in the sampling algorithm design scheme cannot be applied to the conditional distribution under complex constraints and meet the requirements of high-dimensional situations,it is necessary to propose an effective sampling algorithm,namely Gibbs sampling algorithm,to provide a reliable algorithm framework for the restricted simplex uniform random sampling.At the same time,in order to obtain the representative points of the uniform distribution on the restricted simplex,this study introduces three clustering algorithms.From the numerical simulation results,it can be seen that the proposed sampling method can obtain relatively uniform samples,and can be widely applied to various complex conditions such as limited or high-dimensional conditions.It also significantly improves the value attribute of the sampling algorithm framework for clustering algorithms.