  The chemical composition of a star's atmosphere reflects the chemical
composition of its birth environment. Therefore, it should be feasible to
recognize stars born together that have scattered throughout the galaxy, solely
based on their chemistry. This concept, known as "strong chemical tagging", is
a major objective of spectroscopic studies, but has yet to yield the
anticipated results. We assess the existence and the robustness of the relation
between chemical abundances and birth place using known member stars of open
clusters. We followed a supervised machine learning approach, using chemical
abundances obtained from APOGEE DR17, observed open clusters as labels and
different data preprocessing techniques. We found that open clusters can be
recovered with any classifier and on data whose features are not carefully
selected. In the sample with no field stars, we obtain an average accuracy of
$75.2\%$ and we find that the prediction accuracy depends mostly on the
uncertainties of the chemical abundances. When field stars outnumber the
cluster members, the performance degrades. Our results show the difficulty of
recovering birth clusters using chemistry alone, even in a supervised scenario.
This clearly challenges the feasibility of strong chemical tagging.
Nevertheless, including information about ages could potentially enhance the
possibility of recovering birth clusters.
