We present a star/galaxy classification for the Southern Photometric Local Universe Survey (S-PLUS), based on a Machine Learning approach: the Random Forest algorithm. We train the algorithm using the S-PLUS optical photometry up to $r$=21, matched to SDSS/DR13, and morphological parameters. The metric of importance is defined as the relative decrease of the initial accuracy when all correlations related to a certain feature is vanished. In general, the broad photometric bands presented higher importance when compared to narrow ones. The influence of the morphological parameters has been evaluated training the RF with and without the inclusion of morphological parameters, presenting accuracy values of 95.0% and 88.1%, respectively. Particularly, the morphological parameter {rm FWHM/PSF} performed the highest importance over all features to distinguish between stars and galaxies, indicating that it is crucial to classify objects into stars and galaxies. We investigate the misclassification of stars and galaxies in the broad-band colour-colour diagram $(g-r)$ versus $(r-i)$. The morphology can notably improve the classification of objects at regions in the diagram where the misclassification was relatively high. Consequently, it provides cleaner samples for statistical studies. The expected contamination rate of red galaxies as a function of the redshift is estimated, providing corrections for red galaxy samples. The classification of QSOs as extragalactic objects is slightly better using photometric-only case. An extragalactic point-source catalogue is provided using the classification without any morphology feature (only the SED information) with additional constraints on photometric redshifts and {rm FWHM/PSF} values.
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