非线性Mean Shift收敛性分析

Convergence analysis of nonlinear Mean Shift algorithm

作为一种有效的迭代算法,非线性Mean Shift收敛性的研究是应用的基础。虽然Raghav等给出了理论分析,但忽略了对流形上迭代点列收敛性的讨论,对于密度函数收敛性的证明也不够充分。运用黎曼流形的相关知识,指出了算法收敛到局部稳定点的条件,并给出了密度函数和迭代点列收敛的详细证明,为非线性Mean Shift算法的深入研究及应用奠定了理论基础。

Nonlinear Mean Shift is an efficient iterative algorithm. The research for its convergence is the basis of applications. Although some theoretical properties are proposed, the convergence of data on manifolds isn＇t dis- cussed. Besides, the proof of the convergence of density function sequence isn＇ t sufficient. With knowledge of Rie- mann manifolds, the condition of convergence to the local stable point is offered and the convergence of density function sequence and iterative data is proved in details, which contribute to further development of the algorithm and extension of its applications.