  A direct approach to studying the galaxy-halo connection is the analysis of
observed groups and clusters of galaxies that trace the underlying dark matter
halos, making identifying galaxy clusters and their associated brightest
cluster galaxies (BCGs) crucial. We test and propose a robust density-based
clustering algorithm that outperforms the traditional Friends-of-Friends (FoF)
algorithm in the currently available galaxy group/cluster catalogs. Our new
approach is a modified version of the Ordering Points To Identify the
Clustering Structure (OPTICS) algorithm, which accounts for line-of-sight
positional uncertainties due to redshift space distortions by incorporating a
scaling factor, and is thereby referred to as sOPTICS. When tested on both a
galaxy group catalog based on semi-analytic galaxy formation simulations and
observational data, our algorithm demonstrated robustness to outliers and
relative insensitivity to hyperparameter choices. In total, we compared the
results of eight clustering algorithms. The proposed density-based clustering
method, sOPTICS, outperforms FoF in accurately identifying giant galaxy
clusters and their associated BCGs in various environments with higher purity
and recovery rate, also successfully recovering 115 BCGs out of 118 reliable
BCGs from a large galaxy sample.
