# Uncertainty-Aware Probabilistic Constrained Clustering from Entangled Pairwise Supervision

arXiv: https://arxiv.org/abs/2608.12027 · HTML: https://mlsanity.com/paper/2608.12027/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 55 references that are in the map.
- First posted on arXiv 12 Aug 2026.

## Builds on (most cited first, 21 of 21)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [Unsupervised Deep Embedding for Clustering Analysis](https://mlsanity.com/paper/1511.06335/) (2015)
- [Contrastive Clustering](https://mlsanity.com/paper/2009.09687/) (2020)
- [Deep learning from crowds](https://mlsanity.com/paper/1709.01779/) (2017)
- [Multi-class Classification without Multi-class Labels](https://mlsanity.com/paper/1901.00544/) (2019)
- [A Framework for Deep Constrained Clustering -- Algorithms and Advances](https://mlsanity.com/paper/1901.10061/) (2019)
- [A Framework for Deep Constrained Clustering](https://mlsanity.com/paper/2101.02792/) (2021)
- [Deep Conditional Gaussian Mixture Model for Constrained Clustering](https://mlsanity.com/paper/2106.06385/) (2021)
- [Clustering-driven Deep Embedding with Pairwise Constraints](https://mlsanity.com/paper/1803.08457/) (2018)
- [A Classification-Based Approach to Semi-Supervised Clustering with Pairwise Constraints](https://mlsanity.com/paper/2001.06720/) (2020)
- [AutoEmbedder: A semi-supervised DNN embedding system for clustering](https://mlsanity.com/paper/2007.05830/) (2020)
- [Semi-Supervised Constrained Clustering: An In-Depth Overview, Ranked Taxonomy and Future Research Directions](https://mlsanity.com/paper/2303.00522/) (2023)
- [Semi-crowdsourced Clustering with Deep Generative Models](https://mlsanity.com/paper/1810.11971/) (2018)
- [Deep Clustering with Incomplete Noisy Pairwise Annotations: A Geometric Regularization Approach](https://mlsanity.com/paper/2305.19391/) (2023)
- [Efficient Multi-View Graph Clustering with Local and Global Structure Preservation](https://mlsanity.com/paper/2309.00024/) (2023)
- [A probabilistic constrained clustering for transfer learning and image category discovery](https://mlsanity.com/paper/1806.11078/) (2018)
- [Fuzzy Discriminant Clustering with Fuzzy Pairwise Constraints](https://mlsanity.com/paper/2104.08546/) (2021)
- [ConstraintMatch for Semi-constrained Clustering](https://mlsanity.com/paper/2311.15395/) (2023)
- [Angular Constraint Embedding via SpherePair Loss for Constrained Clustering](https://mlsanity.com/paper/2510.06907/) (2025)

## Abstract (arXiv)

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 relation 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.