Constrained Centroid Clustering: A Novel Approach for Compact and Structured Partitioning

TL;DR

This paper introduces Constrained Centroid Clustering (CCC), a new clustering method that enforces maximum distance constraints to produce more compact and structured clusters, validated through synthetic data experiments.

Contribution

The paper proposes a novel CCC method with a closed-form solution that controls cluster spread while maintaining interpretability, extending classical centroid clustering techniques.

Findings

CCC produces more compact clusters than K-means and GMM.

CCC effectively preserves angular structure in synthetic data.

Experimental results demonstrate improved cluster spread control.

Abstract

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.