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Covariance-based soft clustering of functional data based on the Wasserstein-Procrustes metric

V. MasarottoG. Masarotto
Dec 2022
摘要
We consider the problem of clustering functional data according to theircovariance structure. We contribute a soft clustering methodology based on theWasserstein-Procrustes distance, where the in-between cluster variability ispenalised by a term proportional to the entropy of the partition matrix. Inthis way, each covariance operator can be partially classified into more thanone group. Such soft classification allows for clusters to overlap, and arisesnaturally in situations where the separation between all or some of theclusters is not well-defined. We also discuss how to estimate the number ofgroups and to test for the presence of any cluster structure. The algorithm isillustrated using simulated and real data. An R implementation is available inthe Supplementary materials.
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