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.
With the first embedding models, asymmetry of relations was quickly seen as a problem and asymmetric extensions of tensors were studied, mostly by either considering independent embeddings @cite_20 or considering relations as matrices instead of vectors in the RESCAL model @cite_22 , or both @cite_29 . Direct extensions were based on uni-,bi- and trigram latent factors for triple data @cite_4 , as well as a low-rank relation matrix @cite_21 . propose a two-layer model where subject and object embeddings are first separately combined with the relation embedding, then each intermediate representation is combined into the final score.
@cite_4 @cite_22 @cite_29 @cite_21 @cite_20
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This paper tackles the problem of endogenous link prediction for knowledge base completion. Knowledge bases can be represented as directed graphs whose nodes correspond to entities and edges to relationships. Previous attempts either consist of powerful systems with high capacity to model complex connectivity patterns, which unfortunately usually end up overfitting on rare relationships, or in approaches that trade capacity for simplicity in order to fairly model all relationships, frequent or not. In this paper, we propose TATEC, a happy medium obtained by complementing a high-capacity model with a simpler one, both pre-trained separately and then combined. We present several variants of this model with different kinds of regularization and combination strategies and show that this approach outperforms existing methods on different types of relationships by achieving state-of-the-art results on four benchmarks of the literature. Relational learning is becoming increasingly important in many areas of application. Here, we present a novel approach to relational learning based on the factorization of a three-way tensor. We show that unlike other tensor approaches, our method is able to perform collective learning via the latent components of the model and provide an efficient algorithm to compute the factorization. We substantiate our theoretical considerations regarding the collective learning capabilities of our model by the means of experiments on both a new dataset and a dataset commonly used in entity resolution. Furthermore, we show on common benchmark datasets that our approach achieves better or on-par results, if compared to current state-of-the-art relational learning solutions, while it is significantly faster to compute. We consider the problem of learning probabilistic models for complex relational structures between various types of objects. A model can help us "understand" a dataset of relational facts in at least two ways, by finding interpretable structure in the data, and by supporting predictions, or inferences about whether particular unobserved relations are likely to be true. Often there is a tradeoff between these two aims: cluster-based models yield more easily interpretable representations, while factorization-based approaches have given better predictive performance on large data sets. We introduce the Bayesian Clustered Tensor Factorization (BCTF) model, which embeds a factorized representation of relations in a nonparametric Bayesian clustering framework. Inference is fully Bayesian but scales well to large data sets. The model simultaneously discovers interpretable clusters and yields predictive performance that matches or beats previous probabilistic models for relational data. Many data such as social networks, movie preferences or knowledge bases are multi-relational, in that they describe multiple relations between entities. While there is a large body of work focused on modeling these data, modeling these multiple types of relations jointly remains challenging. Further, existing approaches tend to breakdown when the number of these types grows. In this paper, we propose a method for modeling large multi-relational datasets, with possibly thousands of relations. Our model is based on a bilinear structure, which captures various orders of interaction of the data, and also shares sparse latent factors across different relations. We illustrate the performance of our approach on standard tensor-factorization datasets where we attain, or outperform, state-of-the-art results. Finally, a NLP application demonstrates our scalability and the ability of our model to learn efficient and semantically meaningful verb representations. The Semantic Web fosters novel applications targeting a more efficient and satisfying exploitation of the data available on the web, e.g. faceted browsing of linked open data. Large amounts and high diversity of knowledge in the Semantic Web pose the challenging question of appropriate relevance ranking for producing fine-grained and rich descriptions of the available data, e.g. to guide the user along most promising knowledge aspects. Existing methods for graph-based authority ranking lack support for fine-grained latent coherence between resources and predicates (i.e. support for link semantics in the linked data model). In this paper, we present TripleRank, a novel approach for faceted authority ranking in the context of RDF knowledge bases. TripleRank captures the additional latent semantics of Semantic Web data by means of statistical methods in order to produce richer descriptions of the available data. We model the Semantic Web by a 3-dimensional tensor that enables the seamless representation of arbitrary semantic links. For the analysis of that model, we apply the PARAFAC decomposition, which can be seen as a multi-modal counterpart to Web authority ranking with HITS. The result are groupings of resources and predicates that characterize their authority and navigational (hub) properties with respect to identified topics. We have applied TripleRank to multiple data sets from the linked open data community and gathered encouraging feedback in a user evaluation where TripleRank results have been exploited in a faceted browsing scenario.