Constrained clustering is a semi-supervised task that employs a limited amount of labelled data, formulated as constraints, to incorporate domain-specific knowledge and to significantly improve clustering accuracy. Previous work has considered exact optimization formulations that can guarantee optimal clustering while satisfying all constraints, however these approaches lack interpretability. Recently, decision-trees have been used to produce inherently interpretable clustering solutions, however existing approaches do not support clustering constraints and do not provide strong theoretical guarantees on solution quality. In this work, we present a novel SAT-based framework for interpretable clustering that supports clustering constraints and that also provides strong theoretical guarantees on solution quality. We also present new insight into the trade-off between interpretability and satisfaction of such user-provided constraints. Our framework is the first approach for interpretable and constrained clustering. Experiments with a range of real-world and synthetic datasets demonstrate that our approach can produce high-quality and interpretable constrained clustering solutions.

翻译：约束聚类是一种半监督任务，利用少量标记数据（以约束形式表示）融入领域知识，从而显著提升聚类准确率。已有研究提出了能确保在满足所有约束条件下实现最优聚类的精确优化模型，但这类方法缺乏可解释性。近期，决策树被用于生成具有内在可解释性的聚类解，但现有方法不支持聚类约束，也无法为解的质量提供强理论保证。本文提出一种新颖的基于SAT的可解释聚类框架，该框架既支持聚类约束，又能为解的质量提供强理论保证。我们进一步揭示了可解释性与用户提供约束满足度之间的权衡关系。该框架是首个兼顾可解释性与约束性的聚类方法。在多种真实与合成数据集上的实验表明，本方法可生成高质量且可解释的约束聚类解。