Global explainable clustering via equivalence relation

Clustering is a fundamental task in unsupervised learning, yet explaining clustering results remains challenging. Most existing interpretable clustering methods provide local explanations for individual clusters or their pairwise differences. However, as the number of clusters grows, these methods often become difficult to interpret. To address this issue, we introduce a global explainable clustering framework based on the mathematical concepts of equivalence relations and equivalence classes. Two specific global explainable models are proposed: ER-MST, derived from graph connectivity in the minimum spanning tree, and ER-DBSCAN, based on the density-connected property in DBSCAN. We also propose an evaluation metric called the Explanation Accuracy of Equivalence Relations (ExpAcc), which measures how well an equivalence relation explains a given clustering result. Experiments on 20 datasets show that both ER-MST and ER-DBSCAN achieve ExpAcc values that are highly consistent with the Rand Index (RI), suggesting effectiveness on explaining clustering outcome in a global manner.