Multilevel Clustering via Wasserstein Means

TL;DR

This paper introduces a new multilevel clustering method using Wasserstein distances, enabling simultaneous local and global data grouping with proven consistency and scalable algorithms.

Contribution

It presents a novel Wasserstein-based multilevel clustering framework with efficient algorithms and theoretical guarantees, applicable to large hierarchical datasets.

Findings

Demonstrates scalability on synthetic and real data

Establishes consistency of clustering estimates

Offers flexible variants of the clustering problem

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.