Knowledge graphs are graphical representations of large databases of facts, which typically suffer from incompleteness. Inferring missing relations (links) between entities (nodes) is the task of link prediction. A recent state-of-the-art approach to link prediction, ConvE, implements a convolutional neural network to extract features from concatenated subject and relation vectors. Whilst results are impressive, the method is unintuitive and poorly understood. We propose a hypernetwork architecture that generates simplified relation-specific convolutional filters that (i) outperforms ConvE and all previous approaches across standard datasets; and (ii) can be framed as tensor factorization and thus set within a well established family of factorization models for link prediction. We thus demonstrate that convolution simply offers a convenient computational means of introducing sparsity and parameter tying to find an effective trade-off between non-linear expressiveness and the number of parameters to learn.
Numerous matrix factorization approaches to link prediction have been proposed. An early model, RESCAL @cite_10 , tackles the link prediction task by optimizing a scoring function containing a bilinear product between vectors for each of the subject and object entities and a full rank matrix for each relation. DistMult @cite_9 can be viewed as a special case of RESCAL with a diagonal matrix per relation type, which limits the linear transformation performed on entity vectors to a stretch. ComplEx @cite_0 extends DistMult to the complex domain. TransE @cite_23 is an affine model that represents a relation as a translation operation between subject and object entity vectors.
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We model knowledge graphs for their completion by encoding each entity and relation into a numerical space. All previous work including Trans(E, H, R, and D) ignore the heterogeneity (some relations link many entity pairs and others do not) and the imbalance (the number of head entities and that of tail entities in a relation could be different) of knowledge graphs. In this paper, we propose a novel approach TranSparse to deal with the two issues. In TranSparse, transfer matrices are replaced by adaptive sparse matrices, whose sparse degrees are determined by the number of entities (or entity pairs) linked by relations. In experiments, we design structured and unstructured sparse patterns for transfer matrices and analyze their advantages and disadvantages. We evaluate our approach on triplet classification and link prediction tasks. Experimental results show that TranSparse outperforms Trans(E, H, R, and D) significantly, and achieves state-of-the-art performance. We consider learning representations of entities and relations in KBs using the neural-embedding approach. We show that most existing models, including NTN (, 2013) and TransE (, 2013b), can be generalized under a unified learning framework, where entities are low-dimensional vectors learned from a neural network and relations are bilinear and or linear mapping functions. Under this framework, we compare a variety of embedding models on the link prediction task. We show that a simple bilinear formulation achieves new state-of-the-art results for the task (achieving a top-10 accuracy of 73.2 vs. 54.7 by TransE on Freebase). Furthermore, we introduce a novel approach that utilizes the learned relation embeddings to mine logical rules such as "BornInCity(a,b) and CityInCountry(b,c) => Nationality(a,c)". We find that embeddings learned from the bilinear objective are particularly good at capturing relational semantics and that the composition of relations is characterized by matrix multiplication. More interestingly, we demonstrate that our embedding-based rule extraction approach successfully outperforms a state-of-the-art confidence-based rule mining approach in mining Horn rules that involve compositional reasoning. Knowledge graphs are useful resources for numerous AI applications, but they are far from completeness. Previous work such as TransE, TransH and TransR CTransR regard a relation as translation from head entity to tail entity and the CTransR achieves state-of-the-art performance. In this paper, we propose a more fine-grained model named TransD, which is an improvement of TransR CTransR. In TransD, we use two vectors to represent a named symbol object (entity and relation). The first one represents the meaning of a(n) entity (relation), the other one is used to construct mapping matrix dynamically. Compared with TransR CTransR, TransD not only considers the diversity of relations, but also entities. TransD has less parameters and has no matrix-vector multiplication operations, which makes it can be applied on large scale graphs. In Experiments, we evaluate our model on two typical tasks including triplets classification and link prediction. Evaluation results show that our approach outperforms stateof-the-art methods. 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 between 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 (which we call SimplE) of CP 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 in terms of logical rules 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.