Near-infrared high-angular resolution imaging observations of the Milky Way's nuclear star cluster have revealed all luminous members of the existing stellar population within the central parsec. Generally, these stars are either evolved late-type giants or massive young, early-type stars. We revisit the problem of stellar classification based on intermediate-band photometry in the K band, with the primary aim of identifying faint early-type candidate stars in the extended vicinity of the central massive black hole. A random forest classifier, trained on a subsample of spectroscopically identified stars, performs similarly well as competitive methods (F1 = 0.85), without involving any model of stellar spectral energy distributions. Advantages of using such a machine-trained classifier are a minimum of required calibration effort, a predictive accuracy expected to improve as more training data become available, and the ease of application to future, larger data sets. By applying this classifier to archive data, we are also able to reproduce the results of previous studies of the spatial distribution and the K-band luminosity function of both the early- and late-type stars.