  Star-galaxy separation is a crucial step in creating target catalogues for
extragalactic spectroscopic surveys. A classifier biased towards inclusivity
risks including spurious stars, wasting fibre hours, while a more conservative
classifier might overlook galaxies, compromising completeness and hence survey
objectives. To avoid bias introduced by a training set in supervised methods,
we employ an unsupervised machine learning approach. Using photometry from the
Wide Area VISTA Extragalactic Survey (WAVES)-Wide catalogue comprising 9-band
$u-K_s$ data, we create a feature space with colours, fluxes, and apparent size
information extracted by ${\rm P{\scriptsize RO} F{\scriptsize OUND}}$. We
apply the non-linear dimensionality reduction method UMAP (Uniform Manifold
Approximation and Projection) combined with the classifier ${\rm{\scriptsize
HDBSCAN}}$ to classify stars and galaxies. Our method is verified against a
baseline colour and morphological method using a truth catalogue from Gaia,
SDSS, GAMA, and DESI. We correctly identify 99.72% of galaxies within the AB
magnitude limit of $Z = 21.2$, with an F1 score of 0.9970 across the entire
ground truth sample, compared to 0.9871 from the baseline method. Our method's
higher purity (0.9966) compared to the baseline (0.9780) increases efficiency,
identifying 11% fewer galaxy or ambiguous sources, saving approximately 70,000
fibre hours on the 4MOST instrument. We achieve reliable classification
statistics for challenging sources including quasars, compact galaxies, and low
surface brightness galaxies, retrieving 95.1%, 84.6%, and 99.5% of them
respectively. Angular clustering analysis validates our classifications,
showing consistency with expected galaxy clustering, regardless of the baseline
classification.
