Multiple Stellar Populations in NGC 2808: a Case Study for Cluster Analysis

In the massive globular cluster NGC 2808, RGB stars form at least five distinct groups in the so-called chromosome map photometric plane, arguably corresponding to different stellar populations. While a human expert can separate the groups by eye relatively easily, algorithmic approaches are desirable for reproducibility and for handling a larger sample of globular clusters. Unfortunately, cluster analysis algorithms often produced unsatisfactory results. Here we apply a range of non-parametric clustering algorithms to the NGC 2808 RGB dataset: partitioning (k-means, Partitioning Around Medoids - PAM), hierarchical (AGglomerative NESting - AGNES, DIvisive ANAlysis - DIANA), and density based (Density-Based Spatial Clustering of Applications with Noise - DBSCAN, Ordering Points To Identify the Clustering Struture - OPTICS). For each algorithm we discuss different choices of the relevant hyperparameters and their impact on the resulting clustering. We find that AGNES produces results that are most similar to the expectations of a human expert, depending on the prescription used for joining adjacent groups - linkage. Among the linkage prescriptions we tested, Ward's method performs best, and average linkage obtains comparable results only if outliers are removed beforehand. We recommend using AGNES with Ward's method or similar linkages in future studies to automatically identify stellar populations in the chromosome map plane.