Large Margin Nearest Neighbor Embedding for Knowledge Representation

Traditional way of storing facts in triplets ({\it head\_entity, relation, tail\_entity}), abbreviated as ({\it h, r, t}), makes the knowledge intuitively displayed and easily acquired by mankind, but hardly computed or even reasoned by AI machines. Inspired by the success in applying {\it Distributed Representations} to AI-related fields, recent studies expect to represent each entity and relation with a unique low-dimensional embedding, which is different from the symbolic and atomic framework of displaying knowledge in triplets. In this way, the knowledge computing and reasoning can be essentially facilitated by means of a simple {\it vector calculation}, i.e. ${\bf h} + {\bf r} \approx {\bf t}$. We thus contribute an effective model to learn better embeddings satisfying the formula by pulling the positive tail entities ${\bf t^{+}}$ to get together and close to {\bf h} + {\bf r} ({\it Nearest Neighbor}), and simultaneously pushing the negatives ${\bf t^{-}}$ away from the positives ${\bf t^{+}}$ via keeping a {\it Large Margin}. We also design a corresponding learning algorithm to efficiently find the optimal solution based on {\it Stochastic Gradient Descent} in iterative fashion. Quantitative experiments illustrate that our approach can achieve the state-of-the-art performance, compared with several latest methods on some benchmark datasets for two classical applications, i.e. {\it Link prediction} and {\it Triplet classification}. Moreover, we analyze the parameter complexities among all the evaluated models, and analytical results indicate that our model needs fewer computational resources on outperforming the other methods.Comment: arXiv admin note: text overlap with arXiv:1503.0815

Complex Embeddings for Simple Link Prediction

In statistical relational learning, the link prediction problem is key to automatically understand the structure of large knowledge bases. As in previous studies, we propose to solve this problem through latent factorization. However, here we make use of complex valued embeddings. The composition of complex embeddings can handle a large variety of binary relations, among them symmetric and antisymmetric relations. Compared to state-of-the-art models such as Neural Tensor Network and Holographic Embeddings, our approach based on complex embeddings is arguably simpler, as it only uses the Hermitian dot product, the complex counterpart of the standard dot product between real vectors. Our approach is scalable to large datasets as it remains linear in both space and time, while consistently outperforming alternative approaches on standard link prediction benchmarks.Comment: 10+2 pages, accepted at ICML 201

Knowledge Graph Completion via Complex Tensor Factorization

In statistical relational learning, knowledge graph completion deals with automatically understanding the structure of large knowledge graphs—labeled directed graphs—and predicting missing relationships—labeled edges. State-of-the-art embedding models propose different trade-offs between modeling expressiveness, and time and space complexity. We reconcile both expressiveness and complexity through the use of complex-valued embeddings and explore the link between such complex-valued embeddings and unitary diagonalization. We corroborate our approach theoretically and show that all real square matrices—thus all possible relation/adjacency matrices—are the real part of some unitarily diagonalizable matrix. This results opens the door to a lot of other applications of square matrices factorization. Our approach based on complex embeddings is arguably simple, as it only involves a Hermitian dot product, the complex counterpart of the standard dot product between real vectors, whereas other methods resort to more and more complicated composition functions to increase their expressiveness. The proposed complex embeddings are scalable to large data sets as it remains linear in both space and time, while consistently outperforming alternative approaches on standard link prediction benchmarks