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

TL;DR

This paper introduces a greedy and optimistic clustering algorithm that accounts for element-specific uncertainty in covariates, improving cluster compactness and effectively identifying sibling stars in simulated galactic datasets.

Contribution

The paper proposes a novel GOC clustering algorithm that incorporates empirical uncertainty sets after non-linear transformation of covariates, enhancing clustering performance.

Findings

GOC outperforms traditional methods in clustering accuracy.

Effective identification of sibling stars in simulated Milky Way data.

Public availability of the synthetic datasets used for validation.

Abstract

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.