标题： 均值漂移方法的收敛性和抗扩散性 显示英文标题

标题： Convergent and Anti-diffusive Properties of Mean-Shift Method

摘要： 基于偏微分方程的分析框架被推导出来，用于某些动态聚类方法。 所提出的数学框架基于物理学中守恒定律的应用，以表征底层概率密度函数的连续变换。 然后将其应用于分析均值漂移型动态聚类算法的收敛性和稳定性。 理论分析表明，无监督的均值漂移型算法本质上是不稳定的。 证明了无监督均值漂移型算法正确收敛的唯一可能性是将原始概率密度转换为没有依赖结构的多元正态分布。 我们的分析结果表明，通过采用精心选择的监督机制，可能实现更稳定和收敛的均值漂移算法。 显示英文摘要

摘要： An analytic framework based on partial differential equations is derived for certain dynamic clustering methods. The proposed mathematical framework is based on the application of the conservation law in physics to characterize successive transformations of the underlying probability density function. It is then applied to analyze the convergence and stability of mean shift type of dynamic clustering algorithms. Theoretical analysis shows that un-supervised mean-shift type of algorithm is intrinsically unstable. It is proved that the only possibility of a correct convergence for unsupervised mean shift type of algorithm is to transform the original probability density into a multivariate normal distribution with no dependence struture. Our analytical results suggest that a more stable and convergent mean shift algorithm might be achieved by adopting a judiciously chosen supervision mechanism.