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In this study, we examine a clustering problem in which the covariates ofeach individual element in a dataset are associated with an uncertaintyspecific to that element. More specifically, we consider a clustering approachin which a pre-processing applying a non-linear transformation to thecovariates is used to capture the hidden data structure. To this end, weapproximate the sets representing the propagated uncertainty for thepre-processed features empirically. To exploit the empirical uncertainty sets,we propose a greedy and optimistic clustering (GOC) algorithm that finds betterfeature candidates over such sets, yielding more condensed clusters. As animportant application, we apply the GOC algorithm to synthetic datasets of theorbital properties of stars generated through our numerical simulationmimicking the formation process of the Milky Way. The GOC algorithmdemonstrates an improved performance in finding sibling stars originating fromthe same dwarf galaxy. These realistic datasets have also been made publiclyavailable.

A Greedy and Optimistic Approach to Clustering with a Specified Uncertainty of Covariates