  Matrix factorization has found incredible success and widespread application
as a collaborative filtering based approach to recommendations. Unfortunately,
incorporating additional sources of evidence, especially ones that are
incomplete and noisy, is quite difficult to achieve in such models, however, is
often crucial for obtaining further gains in accuracy. For example, additional
information about businesses from reviews, categories, and attributes should be
leveraged for predicting user preferences, even though this information is
often inaccurate and partially-observed. Instead of creating customized methods
that are specific to each type of evidences, in this paper we present a generic
approach to factorization of relational data that collectively models all the
relations in the database. By learning a set of embeddings that are shared
across all the relations, the model is able to incorporate observed information
from all the relations, while also predicting all the relations of interest.
Our evaluation on multiple Amazon and Yelp datasets demonstrates effective
utilization of additional information for held-out preference prediction, but
further, we present accurate models even for the cold-starting businesses and
products for which we do not observe any ratings or reviews. We also illustrate
the capability of the model in imputing missing information and jointly
visualizing words, categories, and attribute factors.
