Disjunctive and Conjunctive Normal Form Explanations of Clusters Using Auxiliary Information
Robert F. Downey, S. S. Ravi
TL;DR
The paper tackles explainability for clustering by introducing tag-based post-hoc descriptors, namely disjunctive descriptors and two-clause CNF descriptors, and shows how these can be computed with ILP or efficient heuristics. It formalizes the problem as a hitting-set optimization and provides exact and approximate solutions, along with a CNF extension that offers richer explanations. Through experiments on College Majors, Movies, Divorce Predictors, and Census datasets, the work demonstrates how meaningful, human-interpretable patterns emerge and discusses scalability with synthetic data. The findings suggest that tag-based CNF explanations can complement simple disjunctive descriptors, enabling more nuanced understanding of cluster composition, while also highlighting practical limitations and avenues for future enhancement in explainable clustering pipelines.
Abstract
We consider generating post-hoc explanations of clusters generated from various datasets using auxiliary information which was not used by clustering algorithms. Following terminology used in previous work, we refer to the auxiliary information as tags. Our focus is on two forms of explanations, namely disjunctive form (where the explanation for a cluster consists of a set of tags) and a two-clause conjunctive normal form (CNF) explanation (where the explanation consists of two sets of tags, combined through the AND operator). We use integer linear programming (ILP) as well as heuristic methods to generate these explanations. We experiment with a variety of datasets and discuss the insights obtained from our explanations. We also present experimental results regarding the scalability of our explanation methods.