Wasserstein gradient flow for optimal probability measure decomposition
<|reference_start|>Wasserstein gradient flow for optimal probability measure decomposition: 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.<|reference_end|>
@article{han2024wasserstein,
    title={Wasserstein gradient flow for optimal probability measure decomposition},
    author={Jiangze Han, Christopher Thomas Ryan, Xin T. Tong},
    journal={arXiv preprint arXiv:2406.00914},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.00914},
    primaryClass={math.OC cs.AI}
}