基于知识度量的模糊粗糙c-均值算法

Fuzzy rough c-means based on the knowledge measure

摘要

提出基于知识度量的模糊粗糙c-均值聚类(fuzzy rough c-means based on the knowledge measure, KFRCM)算法。传统聚类算法在处理具有模糊边界的数据时存在一定的局限性,表现为对初始聚类中心较为敏感且在高维空间中效率较低。为解决上述问题,引入特征加权的知识度量,结合模糊隶属度函数与粗糙集近似算子,采用高斯核相似度以增强边界特性。实验采用14个数据集,实验结果表明,KFRCM算法的聚类准确性、稳定性和计算效率均优于6种主流聚类算法。该研究首次将知识度量与模糊粗糙聚类相结合,为开发更为可靠和适应性更强的聚类算法提供了新的思路和算法。

Abstract

A knowledge-based fuzzy rough c-means clustering method (KFRCM) is introduced. Traditional clustering methods have limitations in handling data with fuzzy boundaries, which are sensitive to the initial cluster centers, and exhibit low efficiency in high-dimensional spaces. To address these issues, the KFRCM is proposed. a feature-weighted knowledge measure is incorporated, fuzzy membership functions are integrated with rough set approximation operators, and Gaussian kernel similarity is utilized to enhance boundary characterization. Experimental results on 14 datasets demonstrate that the proposed KFRCM algorithm outperforms 6 mainstream clustering algorithms in terms of accuracy, stability, and computational efficiency. This study is recognized as the first integration of knowledge measurement with fuzzy rough clustering, offering a new perspective and an advanced algorithmic framework for developing more reliable and adaptable clustering techniques.

关键词

模糊粗糙集 / 知识度量 / 聚类分析 / 高斯核函数 / 上下近似集

Key words

fuzzy rough sets / knowledge measurement / clustering analysis / gaussian kernel function / upper and lower approximation sets

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基金资助

唐山市基础研究项目(24130202C)