On Efficient Multilevel Clustering via Wasserstein Distances
This addresses hierarchical data analysis for researchers, but it appears incremental as it builds on existing Wasserstein barycenter methods.
The authors tackled multilevel clustering by jointly optimizing over discrete probability measures using Wasserstein distances, achieving consistency in local and global cluster estimates and demonstrating flexibility and scalability in experiments.
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 several 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, experimental results with both synthetic and real data are presented to demonstrate the flexibility and scalability of the proposed approach.