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Multilevel Clustering via Wasserstein Means
Nhat Ho · XuanLong Nguyen · Mikhail Yurochkin · Hung Bui · Viet Huynh · Dinh Phung

Tue Aug 08 01:30 AM -- 05:00 AM (PDT) @ Gallery #69

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.

Author Information

Nhat Ho (University of Michigan)
XuanLong Nguyen (University of Michigan)
Mikhail Yurochkin (University of Michigan)
Hung Bui (Adobe Research)
Viet Huynh (Deakin University)
Dinh Phung (Deakin University)

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