We present a novel technique for ranking the relative importance of galaxy properties in the process of quenching star formation. Specifically, we develop an artificial neural network (ANN) approach for pattern recognition and apply it to a population of over 400,000 central galaxies taken from the Sloan Digital Sky Survey Data Release 7. We utilise a variety of physical galaxy properties for training the pattern recognition algorithm to recognise star forming and passive systems, for a 'training set' of ∼100,000 galaxies. We then apply the ANN model to a 'verification set' of ∼100,000 different galaxies, randomly chosen from the remaining sample. The success rate of each parameter singly, and in conjunction with other parameters, is taken as an indication of how important the parameters are to the process(es) of central galaxy quenching. We find that central velocity dispersion, bulge mass and B/T are excellent predictors of the passive state of the system, indicating that properties related to the central mass of the galaxy are most closely linked to the cessation of star formation. Larger scale galaxy properties (total or disk stellar masses), or those linked to environment (halo masses or δ 5 ) perform significantly less well. Our results are plausibly explained by AGN feedback driving the quenching of central galaxies, although we discuss other possibilities as well.