Uncovering the structure of hypergraphs through tensor decomposition: an application to folksonomy analysis

Folksonomies shared vocabularies generated by users through collective annotation (tagging) of web-based content, which are formally hypergraphs connecting users, tags and objects, are beginning to play an increasingly important role in social media. Effective use of folksonomies for organizing and locating web content, discovering and organizing user communities in order to facilitate the contact and collaboration between users who share parts of their interests and attitudes calls for effective methods for discovering coherent groupings of users, objects, and tags. We empirically compare the results of several folksonomy clustering methods using tensor decompositions such as PARAFAC, Tucker3 and HOSVD which are generalizations of principal component analysis and singular value decomposition with standard methods that use 2-dimensional projections of the original 3-way relationships. Our results suggest that the proposed methods overcome some of the limitations of 2-way decomposition methods in clustering folksonomies.