Probabilistic Multilevel Clustering via Composite Transportation Distance

Nhat Ho, Viet Huynh, Dinh Phung, Michael Jordan
Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, PMLR 89:3149-3157, 2019.

Abstract

We propose a novel probabilistic approach to multilevel clustering problems based on composite transportation distance, which is a variant of transportation distance where the underlying metric is Kullback-Leibler divergence. Our method involves solving a joint optimization problem over spaces of probability measures to simultaneously discover grouping structures within groups and among groups. By exploiting the connection of our method to the problem of finding composite transportation barycenters, we develop fast and efficient optimization algorithms even for potentially large-scale multilevel datasets. Finally, we present experimental results with both synthetic and real data to demonstrate the efficiency and scalability of the proposed approach.

Cite this Paper

BibTeX
@InProceedings{pmlr-v89-ho19a, title = {Probabilistic Multilevel Clustering via Composite Transportation Distance}, author = {Ho, Nhat and Huynh, Viet and Phung, Dinh and Jordan, Michael}, booktitle = {Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics}, pages = {3149--3157}, year = {2019}, editor = {Chaudhuri, Kamalika and Sugiyama, Masashi}, volume = {89}, series = {Proceedings of Machine Learning Research}, month = {16--18 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v89/ho19a/ho19a.pdf}, url = {https://proceedings.mlr.press/v89/ho19a.html}, abstract = {We propose a novel probabilistic approach to multilevel clustering problems based on composite transportation distance, which is a variant of transportation distance where the underlying metric is Kullback-Leibler divergence. Our method involves solving a joint optimization problem over spaces of probability measures to simultaneously discover grouping structures within groups and among groups. By exploiting the connection of our method to the problem of finding composite transportation barycenters, we develop fast and efficient optimization algorithms even for potentially large-scale multilevel datasets. Finally, we present experimental results with both synthetic and real data to demonstrate the efficiency and scalability of the proposed approach.} }
Endnote
%0 Conference Paper %T Probabilistic Multilevel Clustering via Composite Transportation Distance %A Nhat Ho %A Viet Huynh %A Dinh Phung %A Michael Jordan %B Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Masashi Sugiyama %F pmlr-v89-ho19a %I PMLR %P 3149--3157 %U https://proceedings.mlr.press/v89/ho19a.html %V 89 %X We propose a novel probabilistic approach to multilevel clustering problems based on composite transportation distance, which is a variant of transportation distance where the underlying metric is Kullback-Leibler divergence. Our method involves solving a joint optimization problem over spaces of probability measures to simultaneously discover grouping structures within groups and among groups. By exploiting the connection of our method to the problem of finding composite transportation barycenters, we develop fast and efficient optimization algorithms even for potentially large-scale multilevel datasets. Finally, we present experimental results with both synthetic and real data to demonstrate the efficiency and scalability of the proposed approach.
APA
Ho, N., Huynh, V., Phung, D. & Jordan, M.. (2019). Probabilistic Multilevel Clustering via Composite Transportation Distance. Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 89:3149-3157 Available from https://proceedings.mlr.press/v89/ho19a.html.

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