Disjunctive and Conjunctive Normal Form Explanations of Clusters Using Auxiliary Information

2025-04-29

AI Summary

This paper addresses the problem of post-hoc interpretability for clustering: generating concise, semantically coherent logical explanations for precomputed clusterings using auxiliary labels not involved in the clustering process. We propose two explanation forms—disjunctive (OR-of-labels) and a novel conjunctive normal form (CNF) termed AND-of-two-label-sets, the first structured CNF explanation for clustering that balances fidelity and human comprehensibility. Our method employs integer linear programming (ILP) and an efficient heuristic algorithm to perform label-driven logical modeling and optimization. Extensive evaluation across multi-source datasets demonstrates substantial improvements in explanation quality and semantic consistency. Both the ILP formulation and the heuristic scale effectively, enabling real-time explanation generation for clustering results involving thousands of samples.

Technology Category

• Machine Learning: Clustering
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Knowledge Representation and Reasoning: Description Logics

Application Category

• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Web Mining and Content Analysis: Normalization, clustering, classification, and summarization of Web text
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

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.

Problem

• Generate post-hoc explanations for clusters using auxiliary tags
• Develop disjunctive and CNF explanations via ILP and heuristics
• Evaluate explanation methods on scalability and dataset insights

Innovation

• Using auxiliary tags for cluster explanations
• Employing ILP and heuristic methods
• Generating disjunctive and CNF explanations