统计与管理学院2016年学术报告13期
【主 题】Convergence and Stability Analysis of Dynamic Clustering Algorithm
【报告人】 Wang Xiaogang
York University
【时 间】 2016年4月22日（星期五）15:00－16:00
【地 点】 上海财经大学统计与管理学院大楼1208室
【摘 要】 A theoretical framework is derived to investigate the convergence and stability of dynamic clustering methods which transform data according to different laws of attraction to achieve autonomous par- titions. On applying the conservation law, we establish partial dif- ferential equations to prescribe the successive transformations of the underlying probability densities in dynamic clustering. These par- tial differential equations correspond to anti-diffusion processes and are solved analytically. We show that a broad class of unsupervised shrinking or clustering methods including the mean-shift algorithm are intrinsically unstable except for independent normal densities. Theoretical results of the supervised dynamic clustering processes indicate that an effective supervision must be chosen judiciously to ensure a correct convergence since a universally optimal supervising function does not exist.
【邀请人】 冯兴东
