This paper considers the problem of embedding Knowledge Graphs (KGs) consisting of entities and relations into low-dimensional vector spaces. Most of the existing methods perform this task based solely on observed facts. The only requirement is that the learned embeddings should be compatible within each individual fact. In this paper, aiming at further discovering the intrinsic geometric structure of the embedding space, we propose  Semantically Smooth Embedding  (SSE). The key idea of SSE is to take full advantage of additional semantic information and enforce the embedding space to be semantically smooth, i.e., entities belonging to the same semantic category will lie close to each other in the embedding space. Two manifold learning algorithms Laplacian Eigenmaps and Locally Linear Embedding are used to model the smoothness assumption. Both are formulated as geometrically based regularization terms to constrain the embedding task. Two lines of embedding strategies are tested, i.e., strategies based on latent distance models and strategies based on tensor factorization techniques. We empirically evaluate SSE on two benchmark tasks of link prediction and triple classification, and achieve significant and consistent improvements over state-of-the-art methods. The results demonstrate the superiority and generality of SSE.
['Shu Guo', 'Quan Wang', 'Bin Wang', 'Lihong V. Wang', 'Li Guo']
SSE: Semantically Smooth Embedding for Knowledge Graphs