[1]唐益明,刘子龙,高健玮.全局数据驱动的模糊聚类有效性评价指标[J].智能系统学报,2026,21(3):598-616.[doi:10.11992/tis.202507010]
TANG Yiming,LIU Zilong,GAO Jianwei.Global data-driven fuzzy cluster validity index[J].CAAI Transactions on Intelligent Systems,2026,21(3):598-616.[doi:10.11992/tis.202507010]
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TANG Yiming,LIU Zilong,GAO Jianwei.Global data-driven fuzzy cluster validity index[J].CAAI Transactions on Intelligent Systems,2026,21(3):598-616.[doi:10.11992/tis.202507010]
全局数据驱动的模糊聚类有效性评价指标
《智能系统学报》[ISSN 1673-4785/CN 23-1538/TP] 卷:
21
期数:
2026年第3期
页码:
598-616
栏目:
学术论文—机器学习
出版日期:
2026-05-05
- Title:
- Global data-driven fuzzy cluster validity index
- Keywords:
- clustering algorithms; fuzzy clustering; clustering validity index; fuzzy C-means algorithms; weighted compactness; weighted separation; robustness; noise robustness
- 分类号:
- TP181；TN99
- 文献标志码:
- 2025-12-23
- 摘要:
- 现有模糊聚类有效性指标(cluster validity index, CVI)在处理具有噪声干扰以及簇规模差异较大的数据集时，往往难以保持准确的评估性能。为此，本文提出了一个全局数据驱动指标(global data driven index, GDD)，该指标针对聚类结果中各簇规模的差异，设计了一套针对簇内紧致度与簇间分离度的基于簇规模的加权机制，以此来应对该差异对指标结果的影响。GDD指标设计时采用簇内紧致度与簇间分离度比值的形式，对于可能会出现的CVI结果根据聚类结果数目单调递增的情况进行遏制；在考虑模糊隶属度的簇内点的平均距离的基础上，基于不同规模的簇占数据集中的比重不同，对于较大的簇给予其更高的权重，在计算单个簇内紧致度的基础上引入了该簇样本数占总样本的比值，该加权机制将直接影响该簇紧致度结果对于加和过后的总紧致度的贡献，从而构建了更客观的簇内紧致度的表达；综合考虑了所有类中心之间的均值与不同规模的簇占数据集的比重，对于较大的簇给予更高的权重，在计算每个聚类中心到聚类中心均值的距离的基础上加入了该簇样本数占总样本的比值，从而锚定了上述距离结果占所有簇加和的距离结果的比重，这种加权机制构建了更合理的簇间分离度的表达。实验结果显示，GDD能够很好地适应各种模糊聚类算法，而且在面对复杂结构和噪声时表现出较强的鲁棒性。本文提出的GDD指标可以在复杂结构与噪声环境下较好地完成对各类模糊聚类算法的评价。
- Abstract:
- Existing cluster validity index(CVI) for fuzzy clustering often struggle to maintain accurate evaluation performance when handling datasets containing noise interference or exhibiting significant differences in cluster sizes. To address these limitations, this study proposes a global data-driven(GDD) index. The GDD index incorporates a scale-aware weighting mechanism for intra-cluster compactness and inter-cluster separation to mitigate the adverse impact of imbalanced cluster sizes on validity assessment. First, the GDD index adopts a ratio-based formulation of intra-cluster compactness to inter-cluster separation. This design prevents the undesirable monotonic increase of the index value as the number of clusters grows. Second, to obtain a more objective measure of intra-cluster compactness, the index computes the average distance among data points within each cluster, incorporating fuzzy membership degrees. Crucially, recognizing that clusters of different scales contribute unequally to the overall dataset structure, larger clusters are assigned higher weights. Specifically, the ratio of the number of samples in each cluster to the total number of samples is introduced into the compactness calculation. This weighting scheme directly influences each cluster’s contribution to the overall compactness, thereby enhancing representational fairness and accuracy. Third, for inter-cluster separation, the index comprehensively considers both the centroid distribution and the relative sizes of different clusters. Rather than treating all centroids equally, the index assigns higher weights to centroids of larger clusters. When computing the distance from each cluster centroid to the mean of all centroids, the sample-size ratio of the corresponding cluster is incorporated. This adjustment anchors the contribution of each centroid’s distance to the total separation measure, resulting in a more reasonable and balanced expression of inter-cluster separation. To evaluate the effectiveness and robustness of the GDD index, extensive experiments were conducted using three representative fuzzy clustering algorithms. Experimental results demonstrate that the GDD index consistently identifies the optimal number of clusters with high accuracy, adapts well across various fuzzy clustering frameworks, and demonstrates strong robustness in challenging scenarios with noise and highly imbalanced cluster sizes. The proposed index provides a more comprehensive and reliable evaluation of fuzzy clustering algorithms in complex, noisy environments.
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备注/Memo
收稿日期:2025-7-7。
基金项目:国家自然科学基金项目(62576130, 62176083).
作者简介:唐益明，教授，博士，主要研究方向为聚类、模糊逻辑与推理、情感计算和图像处理。主持国家自然科学基金项目4项。发表学术论文100余篇，获国家发明专利授权8项。E-mail：tym608@163.com。;刘子龙，硕士研究生，主要研究方向为聚类和聚类有效性指标。E-mail：2024170934@mail.hfut.edu.cn。;高健玮，博士研究生，主要研究方向为聚类、粒计算和模糊推理。E-mail：jwgao810@163.com。
通讯作者:高健玮. E-mail：jwgao810@163.com
更新日期/Last Update:
1900-01-01