Knowledge graph embedding (KGE) models have been proposed to improve the performance of knowledge graph reasoning. However, there is a general phenomenon in most of KGEs, as the training progresses, the symmetric relations tend to zero vector, if the symmetric triples ratio is high enough in the dataset. This phenomenon causes subsequent tasks, e.g. link prediction etc., of symmetric relations to fail. The root cause of the problem is that KGEs do not utilize the semantic information of symmetric relations. We propose KGE bi-vector models, which represent the symmetric relations as vector pair, significantly increasing the processing capability of the symmetry relations. We generate the benchmark datasets based on FB15k and WN18 by completing the symmetric relation triples to verify models. The experiment results of our models clearly affirm the effectiveness and superiority of our models against baseline.
. @cite_0 adopts a relation-specific diagonal matrix @math to represents the characteristics of a relation. The score function @math is a bilinear function, which score of positive triples should be higher than negative triples. @cite_2 employs circular correlations by holographic to create compositional representations, and has advantages of computation efficiency and representing scalability. @cite_8 adopt tensor factorization to estimate relation axis. @cite_3 embed the entities and relation to complex space, then computes loss vaule. . @cite_6 defines two relation-specific matrices for @math , i.e. @math , and defines the score function as @math . There are many other KGE models try to try to use various embedding methods, such as @cite_4 , @cite_10 , , , , etc.
@cite_4 @cite_8 @cite_6 @cite_3 @cite_0 @cite_2 @cite_10
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The representation of a knowledge graph (KG) in a latent space recently has attracted more and more attention. To this end, some proposed models (e.g., TransE) embed entities and relations of a KG into a "point" vector space by optimizing a global loss function which ensures the scores of positive triplets are higher than negative ones. We notice that these models always regard all entities and relations in a same manner and ignore their (un)certainties. In fact, different entities and relations may contain different certainties, which makes identical certainty insufficient for modeling. Therefore, this paper switches to density-based embedding and propose KG2E for explicitly modeling the certainty of entities and relations, which learn the representations of KGs in the space of multi-dimensional Gaussian distributions. Each entity relation is represented by a Gaussian distribution, where the mean denotes its position and the covariance (currently with diagonal covariance) can properly represent its certainty. In addition, compared with the symmetric measures used in point-based methods, we employ the KL-divergence for scoring triplets, which is a natural asymmetry function for effectively modeling multiple types of relations. We have conducted extensive experiments on link prediction and triplet classification with multiple benchmark datasets (WordNet and Freebase). Our experimental results demonstrate that our method can effectively model the (un)certainties of entities and relations in a KG, and it significantly outperforms state-of-the-art methods (including TransH and TransR). We introduce a novel embedding method for knowledge base completion task. Our approach advances state-of-the-art (SOTA) by employing a convolutional neural network (CNN) for the task which can capture global relationships and transitional characteristics. We represent each triple (head entity, relation, tail entity) as a 3-column matrix which is the input for the convolution layer. Different filters having a same shape of 1x3 are operated over the input matrix to produce different feature maps which are then concatenated into a single feature vector. This vector is used to return a score for the triple via a dot product. The returned score is used to predict whether the triple is valid or not. Experiments show that ConvKB achieves better link prediction results than previous SOTA models on two current benchmark datasets WN18RR and FB15k-237. We design a new distribution over poly(r e-1) x n matrices S so that for any fixed n x d matrix A of rank r, with probability at least 9 10, SAx2 = (1 pm e)Ax2 simultaneously for all x ∈ Rd. Such a matrix S is called a subspace embedding. Furthermore, SA can be computed in O(nnz(A)) + O(r2e-2) time, where nnz(A) is the number of non-zero entries of A. This improves over all previous subspace embeddings, which required at least Ω(nd log d) time to achieve this property. We call our matrices S sparse embedding matrices. Using our sparse embedding matrices, we obtain the fastest known algorithms for overconstrained least-squares regression, low-rank approximation, approximating all leverage scores, and lp-regression: to output an x' for which Ax'-b2 ≤ (1+e)minx Ax-b2 for an n x d matrix A and an n x 1 column vector b, we obtain an algorithm running in O(nnz(A)) + O(d3e-2) time, and another in O(nnz(A)log(1 e)) + O(d3log(1 e)) time. (Here O(f) = f ⋅ logO(1)(f).) to obtain a decomposition of an n x n matrix A into a product of an n x k matrix L, a k x k diagonal matrix D, and a n x k matrix W, for which F A - L D W ≤ (1+e)F A-Ak , where Ak is the best rank-k approximation, our algorithm runs in O(nnz(A)) + O(nk2 e-4log n + k3e-5log2n) time. to output an approximation to all leverage scores of an n x d input matrix A simultaneously, with constant relative error, our algorithms run in O(nnz(A) log n) + O(r3) time. to output an x' for which Ax'-bp ≤ (1+e)minx Ax-bp for an n x d matrix A and an n x 1 column vector b, we obtain an algorithm running in O(nnz(A) log n) + poly(r e-1) time, for any constant 1 ≤ p We present a Bayesian tensor factorization model for inferring latent group structures from dynamic pairwise interaction patterns. For decades, political scientists have collected and analyzed records of the form "country @math took action @math toward country @math at time @math "---known as dyadic events---in order to form and test theories of international relations. We represent these event data as a tensor of counts and develop Bayesian Poisson tensor factorization to infer a low-dimensional, interpretable representation of their salient patterns. We demonstrate that our model's predictive performance is better than that of standard non-negative tensor factorization methods. We also provide a comparison of our variational updates to their maximum likelihood counterparts. In doing so, we identify a better way to form point estimates of the latent factors than that typically used in Bayesian Poisson matrix factorization. Finally, we showcase our model as an exploratory analysis tool for political scientists. We show that the inferred latent factor matrices capture interpretable multilateral relations that both conform to and inform our knowledge of international affairs.