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arXiv · 2406.00914

Wasserstein gradient flow for optimal probability measure decomposition

Jiangze Han·Christopher Thomas Ryan·Xin T. Tong
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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.

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Jiangze Han, Christopher Thomas Ryan, Xin T. Tong. 2024-06-03. Wasserstein gradient flow for optimal probability measure decomposition. https://arxiv.org/abs/2406.00914

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