# PROTOCOL: Partial Optimal Transport-enhanced Contrastive Learning for Imbalanced Multi-view Clustering

arXiv: https://arxiv.org/abs/2506.12408 · HTML: https://mlsanity.com/paper/2506.12408/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 50 references that are in the map.
- First posted on arXiv 14 Jun 2025.

## Builds on (most cited first, 27 of 27)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Fashion-MNIST: a Novel Image Dataset for Benchmarking Machine Learning Algorithms](https://mlsanity.com/paper/1708.07747/) (2017)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Contrastive Multiview Coding](https://mlsanity.com/paper/1906.05849/) (2019)
- [Temporal Ensembling for Semi-Supervised Learning](https://mlsanity.com/paper/1610.02242/) (2016)
- [Self-labelling via simultaneous clustering and representation learning](https://mlsanity.com/paper/1911.05371/) (2019)
- [Deep Long-Tailed Learning: A Survey](https://mlsanity.com/paper/2110.04596/) (2021)
- [Parametric Contrastive Learning](https://mlsanity.com/paper/2107.12028/) (2021)
- [Fast Computation of Wasserstein Barycenters](https://mlsanity.com/paper/1310.4375/) (2013)
- [A Survey on Multi-view Learning](https://mlsanity.com/paper/1304.5634/) (2013)
- [Multi-level Feature Learning for Contrastive Multi-view Clustering](https://mlsanity.com/paper/2106.11193/) (2021)
- [Twin Contrastive Learning for Online Clustering](https://mlsanity.com/paper/2210.11680/) (2022)
- [Reconsidering Representation Alignment for Multi-view Clustering](https://mlsanity.com/paper/2103.07738/) (2021)
- [Generalized Parametric Contrastive Learning](https://mlsanity.com/paper/2209.12400/) (2022)
- [Scaling Algorithms for Unbalanced Transport Problems](https://mlsanity.com/paper/1607.05816/) (2016)
- [Sinkhorn Label Allocation: Semi-Supervised Classification via Annealed Self-Training](https://mlsanity.com/paper/2102.08622/) (2021)
- [Unbalanced Incomplete Multi-view Clustering via the Scheme of View Evolution: Weak Views are Meat; Strong Views do Eat](https://mlsanity.com/paper/2011.10254/) (2020)
- [GCFAgg: Global and Cross-view Feature Aggregation for Multi-view Clustering](https://mlsanity.com/paper/2305.06799/) (2023)
- [A Unified Perspective for Loss-Oriented Imbalanced Learning via Localization](https://mlsanity.com/paper/2310.04752/) (2023)
- [Long-Tailed Recognition by Mutual Information Maximization between Latent Features and Ground-Truth Labels](https://mlsanity.com/paper/2305.01160/) (2023)
- [Masked Unsupervised Self-training for Label-free Image Classification](https://mlsanity.com/paper/2206.02967/) (2022)
- [Provably Learning Diverse Features in Multi-View Data with Midpoint Mixup](https://mlsanity.com/paper/2210.13512/) (2022)
- [P2OT: Progressive Partial Optimal Transport for Deep Imbalanced Clustering](https://mlsanity.com/paper/2401.09266/) (2024)
- [Wrapped Cauchy Distributed Angular Softmax for Long-Tailed Visual Recognition](https://mlsanity.com/paper/2305.18732/) (2023)
- [On the Effects of Self-supervision and Contrastive Alignment in Deep Multi-view Clustering](https://mlsanity.com/paper/2303.09877/) (2023)
- [Double-Bounded Optimal Transport for Advanced Clustering and Classification](https://mlsanity.com/paper/2401.11418/) (2024)
- [SP2OT: Semantic-Regularized Progressive Partial Optimal Transport for Imbalanced Clustering](https://mlsanity.com/paper/2404.03446/) (2024)

## Built on by (most cited first, 2 of 2)

- [EGA: Adapting Frozen Encoders for Vector Search with Bounded Out-of-Distribution Degradation](https://mlsanity.com/paper/2605.05674/) (2026)
- [Multi-Marginal Inverse Optimal Transport for Contrastive Learning Via Explicit Anchor-Positive-Negative Coupling](https://mlsanity.com/paper/2609.33741/) (2026)

## Abstract (arXiv)

While contrastive multi-view clustering has achieved remarkable success, it implicitly assumes balanced class distribution. However, real-world multi-view data primarily exhibits class imbalance distribution. Consequently, existing methods suffer performance degradation due to their inability to perceive and model such imbalance. To address this challenge, we present the first systematic study of imbalanced multi-view clustering, focusing on two fundamental problems: i. perceiving class imbalance distribution, and ii. mitigating representation degradation of minority samples. We propose PROTOCOL, a novel PaRtial Optimal TranspOrt-enhanced COntrastive Learning framework for imbalanced multi-view clustering. First, for class imbalance perception, we map multi-view features into a consensus space and reformulate the imbalanced clustering as a partial optimal transport (POT) problem, augmented with progressive mass constraints and weighted KL divergence for class distributions. Second, we develop a POT-enhanced class-rebalanced contrastive learning at both feature and class levels, incorporating logit adjustment and class-sensitive learning to enhance minority sample representations. Extensive experiments demonstrate that PROTOCOL significantly improves clustering performance on imbalanced multi-view data, filling a critical research gap in this field.