Clustering clusters: unsupervised machine learning on globular cluster
  structural parameters
  Globular Clusters (GCs) have historically been subdivided in either two
(disk/halo) or three (disk/inner-halo/outer-halo) groups based on their
orbital, chemical and internal physical properties. The qualitative nature of
this subdivision makes it impossible to determine whether the natural number of
groups is actually two, three, or more. In this paper we use cluster analysis
on the $(\log M, \log \sigma_0, \log R_e, [Fe/H], \log | Z |)$ space to show
that the intrinsic number of GC groups is actually either $k=2$ or $k=3$, with
the latter being favored albeit non-significantly. In the $k=2$ case, the
Partitioning Around Medoids (PAM) clustering algorithm recovers a metal-poor
halo GC group and a metal-rich disk GC group. With $k=3$ the three groups can
be interpreted as disk/inner-halo/outer-halo families. For each group we obtain
a medoid, i.e. a representative element (NGC $6352$, NGC $5986$, and NGC $5466$
for the disk, inner halo, and outer halo respectively), and a measure of how
strongly each GC is associated to its group, the so-called silhouette width.
Using the latter, we find a correlation with age for both disk and outer halo
GCs where the stronger the association of a GC with the disk (outer halo)
group, the younger (older) it is.
