@inproceedings{d16d05ca9c41497e9f62f82d6b643e03,
title = "Entropic Wasserstein Component Analysis",
abstract = "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 1.1https://github.com/antoinecollas/Entropic\_Wasserstein\_Component\_Analysis",
keywords = "Dimension reduction, Optimal Transport, PCA, block-majorization-minimization, entropy",
author = "Antoine Collas and Titouan Vayer and Remi Flamary and Arnaud Breloy",
note = "Publisher Copyright: {\textcopyright} 2023 IEEE.; 33rd IEEE International Workshop on Machine Learning for Signal Processing, MLSP 2023 ; Conference date: 17-09-2023 Through 20-09-2023",
year = "2023",
month = jan,
day = "1",
doi = "10.1109/MLSP55844.2023.10285975",
language = "English",
series = "IEEE International Workshop on Machine Learning for Signal Processing, MLSP",
publisher = "IEEE Computer Society",
editor = "Danilo Comminiello and Michele Scarpiniti",
booktitle = "Proceedings of the 2023 IEEE 33rd International Workshop on Machine Learning for Signal Processing, MLSP 2023",
}