Relation chaining in binary positive-only recommender systems

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Recommender systems typically work on user-item preference relation data. Recommendations can be improved by including side relations that are indirectly linked to the target relation. Data fusion by matrix co-factorization is one such method that can integrate heterogeneous representations of objects of different types. A shared latent matrix factor model is inferred, which is then used to approximate and thus predict multiple data matrices at the same time. The factor model can also be used to infer indirect relations among objects, by multiplying the corresponding factor matrices on a chain of relations that link those objects (i.e., relation chaining). We show that recommendation in binary positive-only data can be improved by relation chaining. We can filter out less reliable relations by using the number of supporting intermediate paths as an additional parameter in a multi-objective Pareto optimization. Our method outperforms other state-of-the-art chaining methods. To speed-up the computation of relation chaining, we propose a chain matrix multiplication-based approach for chaining.To evaluate our method, we have created synthetic data on transitive relations among objects, for a varying degree of noise. Results on synthetic data show that chaining indeed works on chains containing transitive relations. Results on three real datasets show that the inclusion of the number of intermediate paths improves relation chaining predictions. Compared to the full data matrix multiplication approach, the proposed relation chaining method achieved two-fold speed-up.