Weak semantic techniques rely on the integration of Semantic Web techniques with social annotations, and aim to embrace the strengths of both of them. In this paper, we propose a novel weak semantic technique for query expansion. Traditional query expansion techniques are based on the computation of two-dimensional co-occurrence matrices. Our approach proposes the use of three-dimensional matrices, where the added dimension is represented by semantic classes, (i.e., categories comprising all the terms that share a semantic property) related to the folksonomy extracted from social bookmarking services such as delicious and StumbleUpon. The results of an in-depth experimental evaluation performed on both artificial datasets and real users show that our approach outperforms traditional techniques, such as relevance feedback and per- sonalized PageRank, so confirming the validity and usefulness of the categorization of the user needs and preferences in semantic classes. We also present the results of a questionnaire aimed to know the users opinion regarding the system. As one drawback of several query expansion techniques is their high compu- tational costs, we also provide a complexity analysis of our system, in order to show its capability to operate in real time.