Multilevel Clustering via Wasserstein Means

Nhat Ho, XuanLong Nguyen, Mikhail Yurochkin, Hung Hai Bui, Viet Huynh, Dinh Phung
Proceedings of the 34th International Conference on Machine Learning, PMLR 70:1501-1509, 2017.

Abstract

We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our method involves a joint optimization formulation over several spaces of discrete probability measures, which are endowed with Wasserstein distance metrics. We propose a number of variants of this problem, which admit fast optimization algorithms, by exploiting the connection to the problem of finding Wasserstein barycenters. Consistency properties are established for the estimates of both local and global clusters. Finally, experiment results with both synthetic and real data are presented to demonstrate the flexibility and scalability of the proposed approach.

Cite this Paper

BibTeX
@InProceedings{pmlr-v70-ho17a, title = {Multilevel Clustering via {W}asserstein Means}, author = {Nhat Ho and XuanLong Nguyen and Mikhail Yurochkin and Hung Hai Bui and Viet Huynh and Dinh Phung}, booktitle = {Proceedings of the 34th International Conference on Machine Learning}, pages = {1501--1509}, year = {2017}, editor = {Precup, Doina and Teh, Yee Whye}, volume = {70}, series = {Proceedings of Machine Learning Research}, month = {06--11 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v70/ho17a/ho17a.pdf}, url = {https://proceedings.mlr.press/v70/ho17a.html}, abstract = {We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our method involves a joint optimization formulation over several spaces of discrete probability measures, which are endowed with Wasserstein distance metrics. We propose a number of variants of this problem, which admit fast optimization algorithms, by exploiting the connection to the problem of finding Wasserstein barycenters. Consistency properties are established for the estimates of both local and global clusters. Finally, experiment results with both synthetic and real data are presented to demonstrate the flexibility and scalability of the proposed approach.} }
Endnote
%0 Conference Paper %T Multilevel Clustering via Wasserstein Means %A Nhat Ho %A XuanLong Nguyen %A Mikhail Yurochkin %A Hung Hai Bui %A Viet Huynh %A Dinh Phung %B Proceedings of the 34th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2017 %E Doina Precup %E Yee Whye Teh %F pmlr-v70-ho17a %I PMLR %P 1501--1509 %U https://proceedings.mlr.press/v70/ho17a.html %V 70 %X We propose a novel approach to the problem of multilevel clustering, which aims to simultaneously partition data in each group and discover grouping patterns among groups in a potentially large hierarchically structured corpus of data. Our method involves a joint optimization formulation over several spaces of discrete probability measures, which are endowed with Wasserstein distance metrics. We propose a number of variants of this problem, which admit fast optimization algorithms, by exploiting the connection to the problem of finding Wasserstein barycenters. Consistency properties are established for the estimates of both local and global clusters. Finally, experiment results with both synthetic and real data are presented to demonstrate the flexibility and scalability of the proposed approach.
APA
Ho, N., Nguyen, X., Yurochkin, M., Bui, H.H., Huynh, V. & Phung, D.. (2017). Multilevel Clustering via Wasserstein Means. Proceedings of the 34th International Conference on Machine Learning, in Proceedings of Machine Learning Research 70:1501-1509 Available from https://proceedings.mlr.press/v70/ho17a.html.

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