Uncertainty-Aware Probabilistic Constrained Clustering from Entangled Pairwise Supervision

2026-08-12

AI Summary

This work addresses the challenge of soft pairwise constraint clustering in real-world scenarios, where constraints are often fuzzy, stochastic, and uncertain. Moving beyond the limitations of traditional hard must-link/cannot-link labels, the paper introduces UPCC, an uncertainty-aware probabilistic constrained clustering framework. UPCC formally characterizes the conditional identifiability problem under soft pairwise constraints for the first time and proposes a novel angular pairwise objective function, termed ProbPair. It further unifies belief estimation, correction, and reliability-aware weighting within a cohesive ECI-PP framework. By integrating probabilistic modeling, angular similarity measurement, and a deep constrained clustering architecture, UPCC consistently outperforms existing methods across diverse probabilistic supervision settings and demonstrates strong robustness under default configurations.

Abstract

Pairwise constrained clustering typically relies on hard must-link/cannot-link labels, whereas realistic pairwise supervision may be real-valued and entangle intrinsic ambiguity, expert judgment, and stochastic corruption. Existing deep constrained clustering (DCC) methods mainly target hard, expert-agnostic constraints, treating soft labels mostly numerically rather than semantically. We formalize this setting as uncertainty-aware probabilistic constrained clustering (UPCC), defining a canonical aleatoric target through a heterogeneous observation process and analyzing its conditional identifiability. We introduce ProbPair, an angular pairwise objective for probabilistic relations, and build ECI-PP, an estimator--corrector--integrator framework that refines imperfect supervision via belief estimation, correction, and reliability-aware integration. Across challenging probabilistic supervision settings, experiments on diverse benchmarks show that ECI-PP outperforms state-of-the-art DCC methods and remains robust with a shared default configuration.

Problem

• constrained clustering
• pairwise supervision
• uncertainty-aware
• probabilistic constraints
• aleatoric uncertainty

Innovation

• uncertainty-aware clustering
• probabilistic constraints
• pairwise supervision
• deep constrained clustering
• belief correction