The technique of chemical tagging uses the elemental abundances of stellar atmospheres to `reconstruct chemically homogeneous star clusters that have long since dispersed. The GALAH spectroscopic survey --which aims to observe one million stars using the Anglo-Australian Telescope -- allows us to measure up to 30 elements or dimensions in the stellar chemical abundance space, many of which are not independent. How to find clustering reliably in a noisy high-dimensional space is a difficult problem that remains largely unsolved. Here we explore t-distributed stochastic neighbour embedding (t-SNE) -- which identifies an optimal mapping of a high-dimensional space into fewer dimensions -- whilst conserving the original clustering information. Typically, the projection is made to a 2D space to aid recognition of clusters by eye. We show that this method is a reliable tool for chemical tagging because it can: (i) resolve clustering in chemical space alone, (ii) recover known open and globular clusters with high efficiency and low contamination, and (iii) relate field stars to known clusters. t-SNE also provides a useful visualization of a high-dimensional space. We demonstrate the method on a dataset of 13 abundances measured in the spectra of 187,000 stars by the GALAH survey. We recover 7 of the 9 observed clusters (6 globular and 3 open clusters) in chemical space with minimal contamination from field stars and low numbers of outliers. With chemical tagging, we also identify two Pleiades supercluster members (which we confirm kinematically), one as far as 6$^circ$ -- one tidal radius away from the cluster centre.
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