论文标题
MBO方案的数据聚类限制：动力学的收敛性
Large data limit of the MBO scheme for data clustering: convergence of the dynamics
论文作者
论文摘要
我们证明，用于数据聚类的MBO方案的动力学会收敛到粘度解决方案，从而平均曲率流。主要成分是（i）基于热运算符的定量估计值，以及（ii）在随机几何图的设置中衍生这些估计值的新抽象收敛结果。在实践中实施该方案，两个重要的参数是用于计算热运算符和方案步长的特征值的数量。当前论文的结果给出了与样本大小和相互作用宽度有关的这些参数的理论理由。
We prove that the dynamics of the MBO scheme for data clustering converge to a viscosity solution to mean curvature flow. The main ingredients are (i) a new abstract convergence result based on quantitative estimates for heat operators and (ii) the derivation of these estimates in the setting of random geometric graphs. To implement the scheme in practice, two important parameters are the number of eigenvalues for computing the heat operator and the step size of the scheme. The results of the current paper give a theoretical justification for the choice of these parameters in relation to sample size and interaction width.
