Probabilistic polyadic factorization and its application to personalized recommendation

Multiple-dimensional, i.e., polyadic, data exist in many applications, such as personalized recommendation and multiple-dimensional data summarization. Analyzing all the dimensions of polyadic data in a principled way is a challenging research problem. Most existing methods separately analyze the marginal relationships among pairwise dimensions and then combine the results afterwards. Motivated by the fact that various dimensions of polyadic data jointly affect each other, we propose a probabilistic polyadic factorization approach to directly model all the dimensions simultaneously in a unified framework. We then show the connection between the probabilistic polyadic factorization and a non-negative version of the Tucker tensor factorization. We provide detailed theoretical analysis of the new modeling framework, discuss implementation techniques for our models, and propose several extensions to the basic framework. We then apply the proposed models to the application of personalized recommendation. Extensive experiments on a social bookmarking dataset, Delicious, and a paper citation dataset, CiteSeer, demonstrate the effectiveness of the proposed models.