  Identification of chemically similar stars using elemental abundances is core
to many pursuits within Galactic archaeology. However, measuring the chemical
likeness of stars using abundances directly is limited by systematic imprints
of imperfect synthetic spectra in abundance derivation. We present a novel
data-driven model that is capable of identifying chemically similar stars from
spectra alone. We call this Relevant Scaled Component Analysis (RSCA). RSCA
finds a mapping from stellar spectra to a representation that optimizes
recovery of known open clusters. By design, RSCA amplifies factors of chemical
abundance variation and minimizes those of non-chemical parameters, such as
instrument systematics. The resultant representation of stellar spectra can
therefore be used for precise measurements of chemical similarity between
stars. We validate RSCA using 185 cluster stars in 22 open clusters in the
APOGEE survey. We quantify our performance in measuring chemical similarity
using a reference set of 151,145 field stars. We find that our representation
identifies known stellar siblings more effectively than stellar abundance
measurements. Using RSCA, 1.8% of pairs of field stars are as similar as birth
siblings, compared to 2.3% when using stellar abundance labels. We find that
almost all of the information within spectra leveraged by RSCA fits into a
two-dimensional basis, which we link to [Fe/H] and alpha-element abundances. We
conclude that chemical tagging of stars to their birth clusters remains
prohibitive. However, using the spectra has noticeable gain, and our approach
is poised to benefit from larger datasets and improved algorithm designs.
