# Double-Bounded Optimal Transport for Advanced Clustering and Classification

arXiv: https://arxiv.org/abs/2401.11418 · HTML: https://mlsanity.com/paper/2401.11418/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 47 references that are in the map.
- First posted on arXiv 21 Jan 2024.

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

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Unsupervised Learning of Visual Features by Contrasting Cluster Assignments](https://mlsanity.com/paper/2006.09882/) (2020)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Open Graph Benchmark: Datasets for Machine Learning on Graphs](https://mlsanity.com/paper/2005.00687/) (2020)
- [Class-Balanced Loss Based on Effective Number of Samples](https://mlsanity.com/paper/1901.05555/) (2019)
- [Learning Imbalanced Datasets with Label-Distribution-Aware Margin Loss](https://mlsanity.com/paper/1906.07413/) (2019)
- [Decoupling Representation and Classifier for Long-Tailed Recognition](https://mlsanity.com/paper/1910.09217/) (2019)
- [Large-Scale Long-Tailed Recognition in an Open World](https://mlsanity.com/paper/1904.05160/) (2019)
- [Wasserstein GAN](https://mlsanity.com/paper/1701.07875/) (2017)
- [Long-tail learning via logit adjustment](https://mlsanity.com/paper/2007.07314/) (2020)
- [Deep Long-Tailed Learning: A Survey](https://mlsanity.com/paper/2110.04596/) (2021)
- [Balanced Meta-Softmax for Long-Tailed Visual Recognition](https://mlsanity.com/paper/2007.10740/) (2020)
- [Understanding the Behaviour of Contrastive Loss](https://mlsanity.com/paper/2012.09740/) (2020)
- [Equalization Loss for Long-Tailed Object Recognition](https://mlsanity.com/paper/2003.05176/) (2020)
- [Optimal Entropy-Transport problems and a new Hellinger-Kantorovich distance between positive measures](https://mlsanity.com/paper/1508.07941/) (2015)
- [M2m: Imbalanced Classification via Major-to-minor Translation](https://mlsanity.com/paper/2004.00431/) (2020)
- [Gromov-Wasserstein Learning for Graph Matching and Node Embedding](https://mlsanity.com/paper/1901.06003/) (2019)
- [Learning Combinatorial Embedding Networks for Deep Graph Matching](https://mlsanity.com/paper/1904.00597/) (2019)
- [Influence-Balanced Loss for Imbalanced Visual Classification](https://mlsanity.com/paper/2110.02444/) (2021)
- [Neural Graph Matching Network: Learning Lawler's Quadratic Assignment Problem with Extension to Hypergraph and Multiple-graph Matching](https://mlsanity.com/paper/1911.11308/) (2019)
- [Adversarial Robustness under Long-Tailed Distribution](https://mlsanity.com/paper/2104.02703/) (2021)
- [Inverse optimal transport](https://mlsanity.com/paper/1905.03950/) (2019)
- [Learning to Match via Inverse Optimal Transport](https://mlsanity.com/paper/1802.03644/) (2018)
- [Discrete Probabilistic Inverse Optimal Transport](https://mlsanity.com/paper/2112.09754/) (2021)
- [Graph Matching via Optimal Transport](https://mlsanity.com/paper/2111.05366/) (2021)

## Built on by (most cited first, 6 of 6)

- [Dynamic Multimodal Prototype Learning in Vision-Language Models](https://mlsanity.com/paper/2507.03657/) (2025)
- [Computing Approximate Graph Edit Distance via Optimal Transport](https://mlsanity.com/paper/2412.18857/) (2024)
- [Riemannian Optimization on Relaxed Indicator Matrix Manifold](https://mlsanity.com/paper/2503.20505/) (2025)
- [PROTOCOL: Partial Optimal Transport-enhanced Contrastive Learning for Imbalanced Multi-view Clustering](https://mlsanity.com/paper/2506.12408/) (2025)
- [Double-Bounded Nonlinear Optimal Transport for Size Constrained Min Cut Clusterin](https://mlsanity.com/paper/2501.18143/) (2025)
- [SE-Merging: A Self-Enhanced Approach for Dynamic Model Merging](https://mlsanity.com/paper/2506.18135/) (2025)

## Abstract (arXiv)

Optimal transport (OT) is attracting increasing attention in machine learning. It aims to transport a source distribution to a target one at minimal cost. In its vanilla form, the source and target distributions are predetermined, which contracts to the real-world case involving undetermined targets. In this paper, we propose Doubly Bounded Optimal Transport (DB-OT), which assumes that the target distribution is restricted within two boundaries instead of a fixed one, thus giving more freedom for the transport to find solutions. Based on the entropic regularization of DB-OT, three scaling-based algorithms are devised for calculating the optimal solution. We also show that our DB-OT is helpful for barycenter-based clustering, which can avoid the excessive concentration of samples in a single cluster. Then we further develop DB-OT techniques for long-tailed classification which is an emerging and open problem. We first propose a connection between OT and classification, that is, in the classification task, training involves optimizing the Inverse OT to learn the representations, while testing involves optimizing the OT for predictions. With this OT perspective, we first apply DB-OT to improve the loss, and the Balanced Softmax is shown as a special case. Then we apply DB-OT for inference in the testing process. Even with vanilla Softmax trained features, our extensive experimental results show that our method can achieve good results with our improved inference scheme in the testing stage.