  Knowledge graphs contain rich relational structures of the world, and thus
complement data-driven machine learning in heterogeneous data. One of the most
effective methods in representing knowledge graphs is to embed symbolic
relations and entities into continuous spaces, where relations are
approximately linear translation between projected images of entities in the
relation space. However, state-of-the-art relation projection methods such as
TransR, TransD or TransSparse do not model the correlation between relations,
and thus are not scalable to complex knowledge graphs with thousands of
relations, both in computational demand and in statistical robustness. To this
end we introduce TransF, a novel translation-based method which mitigates the
burden of relation projection by explicitly modeling the basis subspaces of
projection matrices. As a result, TransF is far more light weight than the
existing projection methods, and is robust when facing a high number of
relations. Experimental results on the canonical link prediction task show that
our proposed model outperforms competing rivals by a large margin and achieves
state-of-the-art performance. Especially, TransF improves by 9%/5% in the
head/tail entity prediction task for N-to-1/1-to-N relations over the best
performing translation-based method.
