On the use of Wasserstein metric in topological clustering of distributional data

TL;DR

This paper introduces a clustering method for histogram data using Self-Organizing Maps with the Wasserstein distance, automatically determining the number of clusters based on local data density, validated on synthetic and real datasets.

Contribution

It combines SOM-based dimension reduction with Wasserstein distance for distributional data clustering, and automatically estimates the optimal number of clusters.

Findings

Effective clustering on synthetic data

Successful application to real datasets

Automatic determination of cluster number

Abstract

This paper deals with a clustering algorithm for histogram data based on a Self-Organizing Map (SOM) learning. It combines a dimension reduction by SOM and the clustering of the data in a reduced space. Related to the kind of data, a suitable dissimilarity measure between distributions is introduced: the $L_2$ Wasserstein distance. Moreover, the number of clusters is not fixed in advance but it is automatically found according to a local data density estimation in the original space. Applications on synthetic and real data sets corroborate the proposed strategy.