Knowledge Graph Fact Prediction Via KnowledgeEnriched Tensor Factorization Abstract   We present a family of novel methods for embedding knowledge graphs into realvalued tensors. These tensorbased embeddings capture the ordered relations that are typical in the knowledge graphs represented by semantic web languages like RDF. Unlike many previous models, our methods can easily use prior background knowledge provided by users or extracted automatically from existing knowledge graphs. In addition to providing more robust methods for knowledge graph embedding, we provide a provablyconvergent, linear tensor factorization algorithm. We demonstrate the efficacy of our models for the task of predicting new facts across eight different knowledge graphs, achieving between 5% and 50% relative improvement over existing stateoftheart knowledge graph embedding techniques. Our empirical evaluation shows that all of the tensor decomposition models perform well when the average degree of an entity in a graph is high, with constraintbased models doing better on graphs with a small number of highly similar relations and regularizationbased models dominating for graphs with relations of varying degrees of similarity.

A Physical Embedding Model for Knowledge Graphs. Knowledge graph embedding methods learn continuous vector representations for entities in knowledge graphs and have been used successfully in a large number of applications. We present a novel and scalable paradigm for the computation of knowledge graph embeddings, which we dub PYKE . Our approach combines a physical model based on Hookeu0027s law and its inverse with ideas from simulated annealing to compute embeddings for knowledge graphs efficiently. We prove that PYKE achieves a linear space complexity. While the time complexity for the initialization of our approach is quadratic, the time complexity of each of its iterations is linear in the size of the input knowledge graph. Hence, PYKEu0027s overall runtime is close to linear. Consequently, our approach easily scales up to knowledge graphs containing millions of triples. We evaluate our approach against six stateoftheart embedding approaches on the DrugBank and DBpedia datasets in two series of experiments. The first series shows that the cluster purity achieved by PYKE is up to 26% (absolute) better than that of the state of art. In addition, PYKE is more than 22 times faster than existing embedding solutions in the best case. The results of our second series of experiments show that PYKE is up to 23% (absolute) better than the state of art on the task of type prediction while maintaining its superior scalability. Our implementation and results are opensource and are available at this http URL.