Abstract: Over the past decade, knowledge graphs became popular for capturing structured domain knowledge. Relational learning models enable the prediction of missing links inside knowledge graphs. More specifically, latent distance approaches model the relationships among entities via a distance between latent representations. Translating embedding models (e.g., TransE) are among the most popular latent distance approaches which use one distance function to learn multiple relation patterns. However, they are not capable of capturing symmetric relations. They also force relations with reflexive patterns to become symmetric and transitive. In order to improve distance based embedding, we propose multi-distance embeddings (MDE). Our solution is based on the idea that by learning independent embedding vectors for each entity and relation one can aggregate contrasting distance functions. Benefiting from MDE, we also develop supplementary distances resolving the above-mentioned limitations of TransE. We further propose an extended loss function for distance based embeddings and show that MDE and TransE are fully expressive using this loss function. Furthermore, we obtain a bound on the size of their embeddings for full expressivity. Our empirical results show that MDE significantly improves the translating embeddings and outperforms several state-of-the-art embedding models on benchmark datasets.

Introduction: While machine learning methods conventionally model functions given sample inputs and outputs, a subset of statistical relational learning(SRL) BIBREF0 , BIBREF1 approaches specifically aim to model “things” (entities) and relations between them. These methods usually model human knowledge which is structured in the form of multi-relational Knowledge Graphs(KG). KGs allow semantically rich queries in search engines, natural language processing (NLP) and question answering. However, they usually miss a substantial portion of true relations, i.e. they are incomplete. Therefore, the prediction of missing links/relations in KGs is a crucial challenge for SRL approaches. A KG usually consists of a set of facts. A fact is a triple (head, relation, tail) where head and tail are called entities. Among the SRL models, distance based knowledge graph embeddings are popular because of their simplicity, their low number of parameters, and their efficiency on large scale datasets. Specifically, their simplicity allows integrating them into many models. Previous studies have integrated them with logical rule embeddings BIBREF2 , have adopted them to encode temporal information BIBREF3 and have applied them to find equivalent entities between multi-language datasets BIBREF4 . Since the introduction of the first multi-relational distance based method BIBREF5 many variations were published (e.g., TransH BIBREF6 , TransR BIBREF7 , TransD BIBREF8 , STransE BIBREF9 ) that – despite their improvement in the accuracy of the model – suffer from several inherent limitations of TransE that restrict their expressiveness. As BIBREF10 , BIBREF11 noted, within the family of distance based embeddings, usually reflexive relations are forced to be symmetric and transitive. In addition, those approaches are unable to learn symmetric relations. In this work, we put forward a distance based approach that addresses the limitations of these distance based models. Since our approach consists of several distances as objectives, we dubbed it multi-distance embeddings (MDE). We show that 1. TransE and MDE are fully expressive, 2. MDE is able to learn several relational patterns, 3. It is extendable, 4. It shows competitive performance in the empirical evaluations and 5. We also develop an algorithm to find the limits for the limit-based loss function to use in embedding models.

Question: What are the domains covered in the dataset?
Answer: Alarm
Bank
Bus
Calendar
Event
Flight
Home
Hotel
Media
Movie
Music
RentalCar
Restaurant
RideShare
Service
Travel
Weather