We are entering an era of unprecedented quantities of data from current and planned survey telescopes. To maximize the potential of such surveys, automated data analysis techniques are required. Here we implement a new methodology for variable star classification, through the combination of Kohonen Self-Organizing Maps (SOMs, an unsupervised machine learning algorithm) and the more common Random Forest (RF) supervised machine learning technique. We apply this method to data from the K2 mission fields 0-4, finding 154 ab-type RR Lyraes (10 newly discovered), 377 {delta} Scuti pulsators, 133 {gamma} Doradus pulsators, 183 detached eclipsing binaries, 290 semidetached or contact eclipsing binaries and 9399 other periodic (mostly spot-modulated) sources, once class significance cuts are taken into account. We present light-curve features for all K2 stellar targets, including their three strongest detected frequencies, which can be used to study stellar rotation periods where the observed variability arises from spot modulation. The resulting catalogue of variable stars, classes, and associated data features are made available online. We publish our SOM code in python as part of the open source pymvpa package, which in combination with already available RF modules can be easily used to recreate the method.