Topic
Binary relation
About: Binary relation is a research topic. Over the lifetime, 2377 publications have been published within this topic receiving 44323 citations. The topic is also known as: 2-place relation & dyadic relation.
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TL;DR: The original rough set approach proved to be very useful in dealing with inconsistency problems following from information granulation, but is failing when preference-orders of attribute domains (criteria) are to be taken into account and it cannot handle inconsistencies following from violation of the dominance principle.
1,544 citations
TL;DR: Constraints are treated algebraically, and the solution of a system of linear equations in this algebra provides an approximation of the minimal network, and this solution is proved exact in special cases, e.g., for tree-like and series-parallel networks and for classes of relations for which a distributive property holds.
1,468 citations
Proceedings Article•
19 Jun 2016TL;DR: This work makes use of complex valued embeddings to solve the link prediction problem through latent factorization, and uses the Hermitian dot product, the complex counterpart of the standard dot product between real vectors.
Abstract: 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.
1,113 citations
Posted Content•
TL;DR: In this article, the authors make use of complex valued embeddings to handle a large variety of binary relations, among them symmetric and antisymmetric relations, and their approach is scalable to large datasets as it remains linear in both space and time.
Abstract: 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.
1,100 citations
TL;DR: This paper presents a framework for the formulation, interpretation, and comparison of neighborhood systems and rough set approximations using the more familiar notion of binary relations, and introduces a special class of neighborhood system, called 1-neighborhood systems.
967 citations