On Efficient Multilevel Clustering via Wasserstein Distances

TL;DR

This paper introduces a scalable multilevel clustering method using Wasserstein distances, enabling simultaneous data partitioning and pattern discovery in hierarchical datasets with proven consistency and demonstrated effectiveness.

Contribution

It presents a novel joint optimization framework over Wasserstein spaces for multilevel clustering, with fast algorithms and theoretical consistency guarantees.

Findings

Effective clustering on synthetic and real datasets

Fast optimization algorithms developed

Proven consistency of clustering estimates

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 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.