# Co-clustering through Optimal Transport

arXiv: https://arxiv.org/abs/1705.06189 · HTML: https://mlsanity.com/paper/1705.06189/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 May 2017.

## Built on by (most cited first, 13 of 13)

- [Recent Advances in Optimal Transport for Machine Learning](https://mlsanity.com/paper/2306.16156/) (2023)
- [PLOT: Prompt Learning with Optimal Transport for Vision-Language Models](https://mlsanity.com/paper/2210.01253/) (2022)
- [Deep Cut-informed Graph Embedding and Clustering](https://mlsanity.com/paper/2503.06635/) (2025)
- [Interpretable Zero-Shot Learning with Locally-Aligned Vision-Language Model](https://mlsanity.com/paper/2506.23822/) (2025)
- [Label Propagation Through Optimal Transport](https://mlsanity.com/paper/2110.01446/) (2021)
- [Kernel Biclustering algorithm in Hilbert Spaces](https://mlsanity.com/paper/2208.03675/) (2022)
- [Learning representations that are closed-form Monge mapping optimal with application to domain adaptation](https://mlsanity.com/paper/2305.07500/) (2023)
- [Constrained Sliced Wasserstein Embedding](https://mlsanity.com/paper/2506.02203/) (2025)
- [Graph Cuts with Arbitrary Size Constraints Through Optimal Transport](https://mlsanity.com/paper/2402.04732/) (2024)
- [Regularized Optimal Transport for Dynamic Semi-supervised Learning](https://mlsanity.com/paper/2103.11937/) (2021)
- [Estimation of Stationary Optimal Transport Plans](https://mlsanity.com/paper/2107.11858/) (2021)
- [Collaborative Multi-source Domain Adaptation Through Optimal Transport](https://mlsanity.com/paper/2404.06599/) (2024)
- [Beyond Looking Up, Try Looking Around: Harmonizing Global Structure and Local Consistency in Optimal Transport for Short Text Clustering](https://mlsanity.com/paper/2607.10548/) (2026)

## Abstract (arXiv)

In this paper, we present a novel method for co-clustering, an unsupervised learning approach that aims at discovering homogeneous groups of data instances and features by grouping them simultaneously. The proposed method uses the entropy regularized optimal transport between empirical measures defined on data instances and features in order to obtain an estimated joint probability density function represented by the optimal coupling matrix. This matrix is further factorized to obtain the induced row and columns partitions using multiscale representations approach. To justify our method theoretically, we show how the solution of the regularized optimal transport can be seen from the variational inference perspective thus motivating its use for co-clustering. The algorithm derived for the proposed method and its kernelized version based on the notion of Gromov-Wasserstein distance are fast, accurate and can determine automatically the number of both row and column clusters. These features are vividly demonstrated through extensive experimental evaluations.