document: Relational learning via collective matrix factorization Relational learning is concerned with predicting unknown values of a relation , given a database of entities and observed relations among entities . An example of relational learning is movie rating prediction , where entities could include users , movies , genres , and actors . Relations encode users ' ratings of movies , movies ' genres , and actors ' roles in movies . A common prediction technique given one pairwise relation , for example a #users x #movies ratings matrix , is low-rank matrix factorization . In domains with multiple relations , represented as multiple matrices , we may improve predictive accuracy by exploiting information from one relation while predicting another . To this end , we propose a collective matrix factorization model : we simultaneously factor several matrices , sharing parameters among factors when an entity participates in multiple relations . Each relation can have a different value type and error distribution ; so , we allow nonlinear relationships between the parameters and outputs , using Bregman divergences to measure error . We extend standard alternating projection algorithms to our model , and derive an efficient Newton update for the projection . Furthermore , we propose stochastic optimization methods to deal with large , sparse matrices . Our model generalizes several existing matrix factorization methods , and therefore yields new large-scale optimization algorithms for these problems . Our model can handle any pairwise relational schema and a wide variety of error models . We demonstrate its efficiency , as well as the benefit of sharing parameters among relations .
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