The mean shift (MS) is a non-parametric, density-based, iterative algorithm with prominent usage in clustering and image segmentation. A rigorous proof for the convergence of its mode estimate sequence in full generality remains unknown. In this paper, we show that for\textit{ sufficiently large bandwidth} convergence is guaranteed in any dimension with \textit{any radially symmetric and strictly positive definite kernels}. Although the author acknowledges that our result is partially more restrictive than that of \cite{YT} due to the lower limit of the bandwidth, our kernel class is not covered by the kernel class in \cite{YT}, and the proof technique is different. Moreover, we show theoretically and experimentally that while for Gaussian kernel, accurate clustering at \textit{large bandwidths} is generally impossible, it may still be possible for other radially symmetric, strictly positive definite kernels.

翻译：均值漂移（MS）是一种非参数、基于密度的迭代算法，在聚类和图像分割领域具有重要应用。其模式估计序列在一般情况下的收敛性尚未得到严格证明。本文证明，对于\textit{足够大的带宽}，在任意维度下使用\textit{任意径向对称且严格正定的核函数}均可保证收敛性。尽管作者承认，由于带宽下限的存在，我们的结果在部分情况下比\cite{YT}的结论更具限制性，但本文所研究的核函数类别未被\cite{YT}中的核函数类所覆盖，且证明方法亦不相同。此外，我们通过理论与实验表明：对于高斯核，在\textit{大带宽}下通常无法实现精确聚类，但对于其他径向对称的严格正定核，精确聚类仍可能实现。