A Greedy and Optimistic Approach to Clustering with a Specified Uncertainty of Covariates
This work addresses clustering challenges in astronomy for identifying stellar origins, but it appears incremental as it builds on existing methods with specific adaptations.
The paper tackles clustering with element-specific covariate uncertainty by proposing a greedy and optimistic algorithm (GOC) that uses non-linear transformations and empirical uncertainty sets to find better feature candidates, resulting in more condensed clusters. It demonstrates improved performance in identifying sibling stars from the same dwarf galaxy in synthetic datasets mimicking Milky Way formation.
In this study, we examine a clustering problem in which the covariates of each individual element in a dataset are associated with an uncertainty specific to that element. More specifically, we consider a clustering approach in which a pre-processing applying a non-linear transformation to the covariates is used to capture the hidden data structure. To this end, we approximate the sets representing the propagated uncertainty for the pre-processed features empirically. To exploit the empirical uncertainty sets, we propose a greedy and optimistic clustering (GOC) algorithm that finds better feature candidates over such sets, yielding more condensed clusters. As an important application, we apply the GOC algorithm to synthetic datasets of the orbital properties of stars generated through our numerical simulation mimicking the formation process of the Milky Way. The GOC algorithm demonstrates an improved performance in finding sibling stars originating from the same dwarf galaxy. These realistic datasets have also been made publicly available.