# Disjunctive and Conjunctive Normal Form Explanations of Clusters Using Auxiliary Information

arXiv: https://arxiv.org/abs/2504.20846 · HTML: https://mlsanity.com/paper/2504.20846/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 29 references that are in the map.
- First posted on arXiv 29 Apr 2025.

## Builds on (most cited first, 6 of 6)

- [Explanation in Artificial Intelligence: Insights from the Social Sciences](https://mlsanity.com/paper/1706.07269/) (2017)
- [Explainable Recommendation: A Survey and New Perspectives](https://mlsanity.com/paper/1804.11192/) (2018)
- [ExKMC: Expanding Explainable k-Means Clustering](https://mlsanity.com/paper/2006.02399/) (2020)
- [Balancing the Tradeoff Between Clustering Value and Interpretability](https://mlsanity.com/paper/1912.07820/) (2019)
- [Efficient Algorithms for Generating Provably Near-Optimal Cluster Descriptors for Explainability](https://mlsanity.com/paper/2002.02487/) (2020)
- [Towards Practical Explainability with Cluster Descriptors](https://mlsanity.com/paper/2210.10662/) (2022)

## Abstract (arXiv)

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.