Tree-Wasserstein Barycenter for Large-Scale Multilevel Clustering and Scalable Bayes
Abstract
We study in this paper a variant of Wasserstein barycenter problem, which we refer to as tree-Wasserstein barycenter, by leveraging a specific class of ground metrics, namely tree metrics, for Wasserstein distance. Drawing on the tree structure, we propose an efficient algorithmic approach to solve the tree-Wasserstein barycenter and its variants. The proposed approach is not only fast for computation but also efficient for memory usage. Exploiting the tree-Wasserstein barycenter and its variants, we scale up multi-level clustering and scalable Bayes, especially for large-scale applications where the number of supports in probability measures is large. Empirically, we test our proposed approach against other baselines on large-scale synthetic and real datasets.
Keywords
Cite
@article{arxiv.1910.04483,
title = {Tree-Wasserstein Barycenter for Large-Scale Multilevel Clustering and Scalable Bayes},
author = {Tam Le and Viet Huynh and Nhat Ho and Dinh Phung and Makoto Yamada},
journal= {arXiv preprint arXiv:1910.04483},
year = {2020}
}