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# Cross-Graph Learning of Multi-Relational Associations

*Proceedings of The 33rd International Conference on Machine Learning*, PMLR 48:2235-2243, 2016.

#### Abstract

Cross-graph Relational Learning (CGRL) refers to the problem of predicting the strengths or labels of multi-relational tuples of heterogeneous object types, through the joint inference over multiple graphs which specify the internal connections among each type of objects. CGRL is an open challenge in machine learning due to the daunting number of all possible tuples to deal with when the numbers of nodes in multiple graphs are large, and because the labeled training instances are extremely sparse as typical. Existing methods such as tensor factorization or tensor-kernel machines do not work well because of the lack of convex formulation for the optimization of CGRL models, the poor scalability of the algorithms in handling combinatorial numbers of tuples, and/or the non-transductive nature of the learning methods which limits their ability to leverage unlabeled data in training. This paper proposes a novel framework which formulates CGRL as a convex optimization problem, enables transductive learning using both labeled and unlabeled tuples, and offers a scalable algorithm that guarantees the optimal solution and enjoys a constant time complexity with respect to the sizes of input graphs. In our experiments with a subset of DBLP publication records and an Enzyme multi-source dataset, the proposed method successfully scaled to the large cross-graph inference problem, and outperformed other representative approaches significantly.