Collaborative tagging services (folksonomies) have been among the stars of the Web 2.0 era. They allow their users to label diverse resources with freely chosen keywords (tags). Our studies of two real-world folksonomies unveil that individual users develop highly personalized vocabularies of tags. While these meet individual needs and preferences, the considerable differences between personal tag vocabularies (personomies) impede services such as social search or customized tag recommendation. In this paper, we introduce a novel user-centric tag model that allows us to derive mappings between personal tag vocabularies and the corresponding folksonomies. Using these mappings, we can infer the meaning of user-assigned tags and can predict choices of tags a user may want to assign to new items. Furthermore, our translational approach helps in reducing common problems related to tag ambiguity, synonymous tags, or multilingualism. We evaluate the applicability of our method in tag recommendation and tag-based social search. Extensive experiments show that our translational model improves the prediction accuracy in both scenarios.