  The vast volume of data generated by modern astronomical surveys offers test
beds for the application of machine-learning. It is important to evaluate
potential existing tools and determine those that are optimal for extracting
scientific knowledge from the available observations. We explore the
possibility of using clustering algorithms to separate stellar populations with
distinct chemical patterns. Star clusters are likely the most chemically
homogeneous populations in the Galaxy, and therefore any practical approach to
identifying distinct stellar populations should at least be able to separate
clusters from each other. We applied eight clustering algorithms combined with
four dimensionality reduction strategies to automatically distinguish stellar
clusters using chemical abundances of 13 elements. Our sample includes 18
stellar clusters with a total of 453 stars. We use statistical tests showing
that some pairs of clusters are indistinguishable from each other when chemical
abundances from the Apache Point Galactic Evolution Experiment (APOGEE) are
used. However, for most clusters we are able to automatically assign membership
with metric scores similar to previous works. The confusion level of the
automatically selected clusters is consistent with statistical tests that
demonstrate the impossibility of perfectly distinguishing all the clusters from
each other. These statistical tests and confusion levels establish a limit for
the prospect of blindly identifying stars born in the same cluster based solely
on chemical abundances. We find that some of the algorithms we explored are
capable of blindly identify stellar populations with similar ages and chemical
distributions in the APOGEE data. Because some stellar clusters are chemically
indistinguishable, our study supports the notion of extending weak chemical
tagging that involves families of clusters instead of individual clusters
