Optimal Decision Trees For Interpretable Clustering with Constraints (Extended Version)

TL;DR

This paper introduces a SAT-based framework for interpretable constrained clustering that guarantees solution quality and supports domain-specific constraints, addressing limitations of previous methods.

Contribution

It presents the first approach combining interpretability, constraints, and theoretical guarantees in clustering, using a novel SAT-based method.

Findings

Produces high-quality, interpretable clustering solutions

Supports domain-specific clustering constraints

Provides strong theoretical guarantees on solution quality

Abstract

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.