Title: Riemannian TransE: Multi-relational Graph Embedding in Non-Euclidean Space. Abstract: Multi-relational graph embedding which aims at achieving effective representations with reduced low-dimensional parameters, has been widely used in knowledge base completion. Although knowledge base data usually contains tree-like or cyclic structure, none of existing approaches can embed these data into a compatible space that in line with the structure. To overcome this problem, a novel framework, called Riemannian TransE, is proposed in this paper to embed the entities in a Riemannian manifold. Riemannian TransE models each relation as a move to a point and defines specific novel distance dissimilarity for each relation, so that all the relations are naturally embedded in correspondence to the structure of data. Experiments on several knowledge base completion tasks have shown that, based on an appropriate choice of manifold, Riemannian TransE achieves good performance even with a significantly reduced parameters.