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<p>The mean shift (MS) is a nonparametric, 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 <i>sufficiently large bandwidth</i> convergence is guaranteed in any dimension with <i>any radially symmetric and strictly positive definite kernels</i>. Although the author acknowledges that our result is partially more restrictive than that of Yamasaki and Tanaka (IEEE Trans Pattern Anal Mach Intell 46(10):6688–6698, 2024) due to the lower limit of the bandwidth, our kernel class is not covered by the kernel class in Yamasaki and Tanaka (2024), and the proof technique is different. Moreover, we show theoretically and experimentally that while for Gaussian kernel, accurate clustering at <i>large bandwidths</i> is generally impossible, it may still be possible for other radially symmetric, strictly positive definite kernels.</p>

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Convergence and clustering analysis for mean shift with radially symmetric, positive definite kernels

  • 期刊论文

  • 发表日期：

    2026年4月20日

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  • Susovan Pal

摘要

The mean shift (MS) is a nonparametric, 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 sufficiently large bandwidth convergence is guaranteed in any dimension with any radially symmetric and strictly positive definite kernels. Although the author acknowledges that our result is partially more restrictive than that of Yamasaki and Tanaka (IEEE Trans Pattern Anal Mach Intell 46(10):6688–6698, 2024) due to the lower limit of the bandwidth, our kernel class is not covered by the kernel class in Yamasaki and Tanaka (2024), and the proof technique is different. Moreover, we show theoretically and experimentally that while for Gaussian kernel, accurate clustering at large bandwidths is generally impossible, it may still be possible for other radially symmetric, strictly positive definite kernels.