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<p>The performance of spectral clustering relies greatly on the similarity relationship of the data. Gaussian kernel function is a typical and popularly adopted metric function to reflect sample similarity. However, since its kernel parameter is globally fixed, it faces challenges when dealing with complex data of heterogeneous densities. To overcome the problem, a novel local density-weighted adaptive Gaussian kernel function is proposed, named SC-LD, to establish similarity relationships in data applied to spectral clustering. The function adjusts the width of the kernel using local scale parameters and assigns different weights to the data points based on the relative local density. In experiments, we verify the validity of the proposed algorithm on six synthetic datasets and eleven real-world datasets. Results present that SC-LD has strong competitiveness in NMI, ACC, and F-measure metrics. Especially on the Haves_roth dataset, the SC-LD algorithm achieves significantly higher ACC and F-measure compared to the second-best algorithm by 37.94% and 33.54%, respectively. The NMI is nearly four times higher than that of the second-best algorithm.</p>

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Spectral clustering based on weighted Gaussian kernel function with local density

  • 期刊论文

  • 发表日期：

    2025年7月11日

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  • Huan Ren,
  • Peng Zhou,
  • Zekun Wang,
  • Jiawen Chen

摘要

The performance of spectral clustering relies greatly on the similarity relationship of the data. Gaussian kernel function is a typical and popularly adopted metric function to reflect sample similarity. However, since its kernel parameter is globally fixed, it faces challenges when dealing with complex data of heterogeneous densities. To overcome the problem, a novel local density-weighted adaptive Gaussian kernel function is proposed, named SC-LD, to establish similarity relationships in data applied to spectral clustering. The function adjusts the width of the kernel using local scale parameters and assigns different weights to the data points based on the relative local density. In experiments, we verify the validity of the proposed algorithm on six synthetic datasets and eleven real-world datasets. Results present that SC-LD has strong competitiveness in NMI, ACC, and F-measure metrics. Especially on the Haves_roth dataset, the SC-LD algorithm achieves significantly higher ACC and F-measure compared to the second-best algorithm by 37.94% and 33.54%, respectively. The NMI is nearly four times higher than that of the second-best algorithm.