Wasserstein gradient flow for optimal probability measure decomposition
Optimization and Control
2024-06-04 v1 Artificial Intelligence
Abstract
We examine the infinite-dimensional optimization problem of finding a decomposition of a probability measure into K probability sub-measures to minimize specific loss functions inspired by applications in clustering and user grouping. We analytically explore the structures of the support of optimal sub-measures and introduce algorithms based on Wasserstein gradient flow, demonstrating their convergence. Numerical results illustrate the implementability of our algorithms and provide further insights.
Cite
@article{arxiv.2406.00914,
title = {Wasserstein gradient flow for optimal probability measure decomposition},
author = {Jiangze Han and Christopher Thomas Ryan and Xin T. Tong},
journal= {arXiv preprint arXiv:2406.00914},
year = {2024}
}