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

Guénaël Cabanes; Younès Bennani; Rosanna Verde; Antonio Irpino

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arXiv · 2109.04301

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

Guénaël Cabanes·Younès Bennani·Rosanna Verde·Antonio Irpino

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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.

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Guénaël Cabanes, Younès Bennani, Rosanna Verde, Antonio Irpino. 2021-09-09. On the use of Wasserstein metric in topological clustering of distributional data. https://arxiv.org/abs/2109.04301

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