# Entropic Wasserstein Component Analysis

arXiv: https://arxiv.org/abs/2303.05119 · HTML: https://mlsanity.com/paper/2303.05119/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 15 references that are in the map.
- First posted on arXiv 9 Mar 2023.

## Builds on (most cited first, 4 of 4)

- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Wasserstein Discriminant Analysis](https://mlsanity.com/paper/1608.08063/) (2016)
- [Fast, Robust and Non-convex Subspace Recovery](https://mlsanity.com/paper/1406.6145/) (2014)

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

- [A dimensionality reduction technique based on the Gromov-Wasserstein distance](https://mlsanity.com/paper/2501.13732/) (2025)
- [Manifold learning in metric spaces](https://mlsanity.com/paper/2503.16187/) (2025)

## Abstract (arXiv)

Dimension reduction (DR) methods provide systematic approaches for analyzing high-dimensional data. A key requirement for DR is to incorporate global dependencies among original and embedded samples while preserving clusters in the embedding space. To achieve this, we combine the principles of optimal transport (OT) and principal component analysis (PCA). Our method seeks the best linear subspace that minimizes reconstruction error using entropic OT, which naturally encodes the neighborhood information of the samples. From an algorithmic standpoint, we propose an efficient block-majorization-minimization solver over the Stiefel manifold. Our experimental results demonstrate that our approach can effectively preserve high-dimensional clusters, leading to more interpretable and effective embeddings. Python code of the algorithms and experiments is available online.