Knowledge graphs have recently become the state-of-the-art tool for representing the diverse and complex knowledge of the world. Examples include the proprietary knowledge graphs of companies such as Google, Facebook, IBM, or Microsoft, but also freely available ones such as YAGO, DBpedia, and Wikidata. A distinguishing feature of Wikidata is that the knowledge is collaboratively edited and curated. While this greatly enhances the scope of Wikidata, it also makes it impossible for a single individual to grasp complex connections between properties or understand the global impact of edits in the graph. We apply Formal Concept Analysis to efficiently identify comprehensible implications that are implicitly present in the data. Although the complex structure of data modelling in Wikidata is not amenable to a direct approach, we overcome this limitation by extracting contextual representations of parts of Wikidata in a systematic fashion. We demonstrate the practical feasibility of our approach through several experiments and show that the results may lead to the discovery of interesting implicational knowledge.

We have previously delved into detail about concept, conceptualization, and relations to build a knowledge graph. In this, we shall see how domain expertise can contribute to these vital components of the graph and its building exercise. Current knowledge engineering methodologies are analogous to software engineering approaches. Knowledge Engineers drive the knowledge graph authoring process. They are the people who know how to create formal conceptualizations of a domain but do not know the domain to be modeled.

Taxonomies are semantic hierarchies of concepts. One limitation of current taxonomy learning systems is that they define concepts as single words. This position paper argues that contextualized word representations, which recently achieved state-of-the-art results on many competitive NLP tasks, are a promising method to address this limitation. We outline a novel approach for taxonomy learning that (1) defines concepts as synsets, (2) learns density-based approximations of contextualized word representations, and (3) can measure similarity and hypernymy among them.

Knowledge graphs are structured representations of real world facts. However, they typically contain only a small subset of all possible facts. Link prediction is a task of inferring missing facts based on existing ones. We propose TuckER, a relatively simple but powerful linear model based on Tucker decomposition of the binary tensor representation of knowledge graph triples. TuckER outperforms all previous state-of-the-art models across standard link prediction datasets. We prove that TuckER is a fully expressive model, deriving the bound on its entity and relation embedding dimensionality for full expressiveness which is several orders of magnitude smaller than the bound of previous state-of-the-art models ComplEx and SimplE. We further show that several previously introduced linear models can be viewed as special cases of TuckER.

Collaborative filtering often suffers from sparsity and cold start problems in real recommendation scenarios, therefore, researchers and engineers usually use side information to address the issues and improve the performance of recommender systems. In this paper, we consider knowledge graphs as the source of side information. We propose MKR, a Multi-task feature learning approach for Knowledge graph enhanced Recommendation. MKR is a deep end-to-end framework that utilizes knowledge graph embedding task to assist recommendation task. The two tasks are associated by cross&compress units, which automatically share latent features and learn high-order interactions between items in recommender systems and entities in the knowledge graph. We prove that cross&compress units have sufficient capability of polynomial approximation, and show that MKR is a generalized framework over several representative methods of recommender systems and multi-task learning. Through extensive experiments on real-world datasets, we demonstrate that MKR achieves substantial gains in movie, book, music, and news recommendation, over state-of-the-art baselines. MKR is also shown to be able to maintain a decent performance even if user-item interactions are sparse.

Word representations are created using analogy context-based statistics and lexical relations on words. Word representations are inputs for the learning models in Natural Language Understanding (NLU) tasks. However, to understand language, knowing only the context is not sufficient. Reading between the lines is a key component of NLU. Embedding deeper word relationships which are not represented in the context enhances the word representation. This paper presents a word embedding which combines an analogy, context-based statistics using Word2Vec, and deeper word relationships using Conceptnet, to create an expanded word representation. In order to fine-tune the word representation, Self-Organizing Map is used to optimize it. The proposed word representation is compared with semantic word representations using Simlex 999. Furthermore, the use of 3D visual representations has shown to be capable of representing the similarity and association between words. The proposed word representation shows a Spearman correlation score of 0.886 and provided the best results when compared to the current state-of-the-art methods, and exceed the human performance of 0.78.

Knowledge graphs contain knowledge about the world and provide a structured representation of this knowledge. Current knowledge graphs contain only a small subset of what is true in the world. Link prediction approaches aim at predicting new links for a knowledge graph given the existing links among the entities. Tensor factorization approaches have proved promising for such link prediction problems. Proposed in 1927, Canonical Polyadic (CP) decomposition is among the first tensor factorization approaches. CP generally performs poorly for link prediction as it learns two independent embedding vectors for each entity, whereas they are really tied. We present a simple enhancement of CP (which we call SimplE) to allow the two embeddings of each entity to be learned dependently. The complexity of SimplE grows linearly with the size of embeddings. The embeddings learned through SimplE are interpretable, and certain types of background knowledge can be incorporated into these embeddings through weight tying. We prove SimplE is fully expressive and derive a bound on the size of its embeddings for full expressivity. We show empirically that, despite its simplicity, SimplE outperforms several state-of-the-art tensor factorization techniques. SimplE's code is available on GitHub at https://github.com/Mehran-k/SimplE.

Learning low-dimensional embeddings of knowledge graphs is a powerful approach used to predict unobserved or missing edges between entities. However, an open challenge in this area is developing techniques that can go beyond simple edge prediction and handle more complex logical queries, which might involve multiple unobserved edges, entities, and variables. For instance, given an incomplete biological knowledge graph, we might want to predict "em what drugs are likely to target proteins involved with both diseases X and Y?" -- a query that requires reasoning about all possible proteins that might interact with diseases X and Y. Here we introduce a framework to efficiently make predictions about conjunctive logical queries -- a flexible but tractable subset of first-order logic -- on incomplete knowledge graphs. In our approach, we embed graph nodes in a low-dimensional space and represent logical operators as learned geometric operations (e.g., translation, rotation) in this embedding space. By performing logical operations within a low-dimensional embedding space, our approach achieves a time complexity that is linear in the number of query variables, compared to the exponential complexity required by a naive enumeration-based approach. We demonstrate the utility of this framework in two application studies on real-world datasets with millions of relations: predicting logical relationships in a network of drug-gene-disease interactions and in a graph-based representation of social interactions derived from a popular web forum.

Neural models operating over structured spaces such as knowledge graphs require a continuous embedding of the discrete elements of this space (such as entities) as well as the relationships between them. Relational embeddings with high expressivity, however, have high model complexity, making them computationally difficult to train. We propose a new family of embeddings for knowledge graphs that interpolate between a method with high model complexity and one, namely Holographic embeddings (HolE), with low dimensionality and high training efficiency. This interpolation, termed HolEx, is achieved by concatenating several linearly perturbed copies of original HolE. We formally characterize the number of perturbed copies needed to provably recover the full entity-entity or entity-relation interaction matrix, leveraging ideas from Haar wavelets and compressed sensing. In practice, using just a handful of Haar-based or random perturbation vectors results in a much stronger knowledge completion system. On the Freebase FB15K dataset, HolEx outperforms originally reported HolE by 14.7\% on the HITS@10 metric, and the current path-based state-of-the-art method, PTransE, by 4\% (absolute).

Neural models operating over structured spaces such as knowledge graphs require a continuous embedding of the discrete elements of this space (such as entities) as well as the relationships between them. Relational embeddings with high expressivity, however, have high model complexity, making them computationally difficult to train. We propose a new family of embeddings for knowledge graphs that interpolate between a method with high model complexity and one, namely Holographic embeddings (HolE), with low dimensionality and high training efficiency. This interpolation, termed HolEx, is achieved by concatenating several linearly perturbed copies of original HolE. We formally characterize the number of perturbed copies needed to provably recover the full entity-entity or entity-relation interaction matrix, leveraging ideas from Haar wavelets and compressed sensing. In practice, using just a handful of Haar-based or random perturbation vectors results in a much stronger knowledge completion system. On the Freebase FB15K dataset, HolEx outperforms originally reported HolE by 14.7\% on the HITS@10 metric, and the current path-based state-of-the-art method, PTransE, by 4\% (absolute).