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| Format: | Preprint |
| Publié: |
2025
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2506.19837 |
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| _version_ | 1866912968018493440 |
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| author | Pal, Susovan |
| author_facet | Pal, Susovan |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_19837 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Convergence and clustering analysis for Mean Shift with radially symmetric, positive definite kernels Pal, Susovan Machine Learning 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. |
| title | Convergence and clustering analysis for Mean Shift with radially symmetric, positive definite kernels |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2506.19837 |