We propose a novel method for detecting optional arguments of Hungarian verbs using only positive data. We introduce a custom variant of collexeme analysis that explicitly models the noise in verb frames. Our method is, for the most part, unsupervised: we use the spectral clustering algorithm described in Brew and Schulte in Walde (2002) to build a noise model from a short, manually verified seed list of verbs. We experimented with both raw count- and context-based clusterings and found their performance almost identical. The code for our algorithm and the frame list are freely available at http://hlt.bme.hu/en/resources/tade.