# Wasserstein k-means with sparse simplex projection

arXiv: https://arxiv.org/abs/2011.12542 · HTML: https://mlsanity.com/paper/2011.12542/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Nov 2020.

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

- [Sparsity-Constrained Optimal Transport](https://mlsanity.com/paper/2209.15466/) (2022)
- [Overlap-guided Gaussian Mixture Models for Point Cloud Registration](https://mlsanity.com/paper/2210.09836/) (2022)
- [Block-coordinate Frank-Wolfe algorithm and convergence analysis for semi-relaxed optimal transport problem](https://mlsanity.com/paper/2205.13766/) (2022)
- [Fast block-coordinate Frank-Wolfe algorithm for semi-relaxed optimal transport](https://mlsanity.com/paper/2103.05857/) (2021)
- [On the Convergence of Semi-Relaxed Sinkhorn with Marginal Constraint and OT Distance Gaps](https://mlsanity.com/paper/2205.13846/) (2022)
- [Anchor Space Optimal Transport as a Fast Solution to Multiple Optimal Transport Problems](https://mlsanity.com/paper/2310.16123/) (2023)

## Abstract (arXiv)

This paper presents a proposal of a faster Wasserstein k-means algorithm for histogram data by reducing Wasserstein distance computations and exploiting sparse simplex projection. We shrink data samples, centroids, and the ground cost matrix, which leads to considerable reduction of the computations used to solve optimal transport problems without loss of clustering quality. Furthermore, we dynamically reduced the computational complexity by removing lower-valued data samples and harnessing sparse simplex projection while keeping the degradation of clustering quality lower. We designate this proposed algorithm as sparse simplex projection based Wasserstein k-means, or SSPW k-means. Numerical evaluations conducted with comparison to results obtained using Wasserstein k-means algorithm demonstrate the effectiveness of the proposed SSPW k-means for real-world datasets