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The two currently largest all-sky photometric datasets, WISE and SuperCOSMOS, were cross-matched by Bilicki et al. (2016) (B16) to construct a novel photometric redshift catalogue on 70% of the sky. Galaxies were therein separated from stars and quasars through colour cuts, which may leave imperfections because of mixing different source types which overlap in colour space. The aim of the present work is to identify galaxies in the WISExSuperCOSMOS catalogue through an alternative approach of machine learning. This allows us to define more complex separations in the multi-colour space than possible with simple colour cuts, and should provide more reliable source classification. For the automatised classification we use the support vector machines learning algorithm, employing SDSS spectroscopic sources cross-matched with WISExSuperCOSMOS as the training and verification set. We perform a number of tests to examine the behaviour of the classifier (completeness, purity and accuracy) as a function of source apparent magnitude and Galactic latitude. We then apply the classifier to the full-sky data and analyse the resulting catalogue of candidate galaxies. We also compare thus produced dataset with the one presented in B16. The tests indicate very high accuracy, completeness and purity (>95%) of the classifier at the bright end, deteriorating for the faintest sources, but still retaining acceptable levels of 85%. No significant variation of classification quality with Galactic latitude is observed. Application of the classifier to all-sky WISExSuperCOSMOS data gives 15 million galaxies after masking problematic areas. The resulting sample is purer than the one in B16, at a price of lower completeness over the sky. The automatic classification gives a successful alternative approach to defining a reliable galaxy sample as compared to colour cuts.