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...

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Bibliographic Details
Published in:arXiv.org 2024-06
Main Authors: Han, Jiangze, Ryan, Christopher Thomas, Tong, Xin T
Format: Article
Language:English
Subjects:
Algorithms
Clustering
Decomposition
Gradient flow
Online Access:Get full text
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Summary: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.
ISSN:2331-8422