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arXiv · 1910.04483

Tree-Wasserstein Barycenter for Large-Scale Multilevel Clustering and Scalable Bayes

Tam Le·Viet Huynh·Nhat Ho·Dinh Phung·Makoto Yamada
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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.

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Tam Le, Viet Huynh, Nhat Ho, Dinh Phung, Makoto Yamada. 2019-10-10. Tree-Wasserstein Barycenter for Large-Scale Multilevel Clustering and Scalable Bayes. https://arxiv.org/abs/1910.04483

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