通过约束簇中心到最远点距离，实现紧凑且结构化的聚类。
Constrained Centroid Clustering: A Novel Approach for Compact and Structured Partitioning
- 基于拉格朗日法推导出闭式解，控制簇内扩散。
- 在环形数据上减少径向扩散，熵指标优于K均值与GMM。
- 适合需结构化聚类和扩散控制的场景，如机器人协作。
本文提出约束中心聚类（Constrained Centroid Clustering, CCC），通过在簇中心与簇内最远点间施加最大距离约束，扩展经典中心聚类方法。利用拉格朗日公式推导出闭式解，在保持可解释性的同时控制簇的展开程度。在具有径向对称性和均匀角分布的合成环形数据上进行实验，采用环状、扇区及联合熵作为评估指标，结果表明CCC能有效减小径向扩散，同时保留角结构，优于K均值与高斯混合模型（GMM）。该方法适用于需结构化聚类并控制簇扩散的应用，如传感器网络、协同机器人与可解释模式分析。
原文摘要 · Abstract (English)
This paper presents Constrained Centroid Clustering (CCC), a method that extends classical centroid-based clustering by enforcing a constraint on the maximum distance between the cluster center and the farthest point in the cluster. Using a Lagrangian formulation, we derive a closed-form solution that maintains interpretability while controlling cluster spread. To evaluate CCC, we conduct experiments on synthetic circular data with radial symmetry and uniform angular distribution. Using ring-wise, sector-wise, and joint entropy as evaluation metrics, we show that CCC achieves more compact clusters by reducing radial spread while preserving angular structure, outperforming standard methods such as K-means and GMM. The proposed approach is suitable for applications requiring structured clustering with spread control, including sensor networks, collaborative robotics, and interpretable pattern analysis.
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