Fuzzy clustering of distribution-valued data using adaptive L2 Wasserstein distances
Abstract
Distributional (or distribution-valued) data are a new type of data arising from several sources and are considered as realizations of distributional variables. A new set of fuzzy c-means algorithms for data described by distributional variables is proposed. The algorithms use the Wasserstein distance between distributions as dissimilarity measures. Beside the extension of the fuzzy c-means algorithm for distributional data, and considering a decomposition of the squared Wasserstein distance, we propose a set of algorithms using different automatic way to compute the weights associated with the variables as well as with their components, globally or cluster-wise. The relevance weights are computed in the clustering process introducing product-to-one constraints. The relevance weights induce adaptive distances expressing the importance of each variable or of each component in the clustering process, acting also as a variable selection method in clustering. We have tested the proposed algorithms on artificial and real-world data. Results confirm that the proposed methods are able to better take into account the cluster structure of the data with respect to the standard fuzzy c-means, with non-adaptive distances.
Cite
@article{arxiv.1605.00513,
title = {Fuzzy clustering of distribution-valued data using adaptive L2 Wasserstein distances},
author = {Antonio Irpino and Francisco De Carvalho and Rosanna Verde},
journal= {arXiv preprint arXiv:1605.00513},
year = {2016}
}