# Online Knowledge Learning Model Based on Gravitational Field Theory  
[PERSON]  
1 The Xinjiang Technical Institute of Physics & Chemistry, Chinese Academy of Sciences, Urumqi 830011, China University of Chinese Academy of Sciences, Beijing 100049, China  
The translation-based models inspired by word2 vec are easy to train and effective with good performances. These are usually given \"triple\" (head, relation, tail), often named \(h\), \(r\), and \(t\); TransE learns the vectors for \(h\), \(r\), and \(t\) by \(h+r\approx t\), which indicates that the vector \(t\) is obtained by translating vector \(r\) from vector \(h\). Its loss function is \(loss_{r}(h,t)=\parallel h+r-t\parallel_{L1/L2}\). TransE is good with 1-to-1 relations, but when handling complex relations, such as N-to-N, 1-to-N, and N-to-1 relations, TransE shows poor performance because of its simple loss function [3]. TransH [15] uses projection of the entity to the plane of the corresponding relation to adapt complex relation problems in TransE. The vector of entities is projected to the hyperplane of relation \(r\) to get \(h_{r}=h-w_{r}^{T}hw_{r}\) and \(t_{r}=t-w_{r}^{T}tw_{r}\). TransR and CTransR [16] set a transfer matrix \(M_{r}\) to make the sub-vector space, to which the method maps the embedded entity for each relation \(r\), as different relations should have different semantic spaces. In TransA [10], the distance measure of the loss function is changed to Mahalanobis distance, which was proposed in order to learn the different weights for each dimension of the entities and relations. Its loss function is \(loss_{r}(h,t)=(h+r-t)^{T}W_{r}(h+r-t)\). TansAH [17] employs Mahalanobis distances in TransH and sets the weight matrix \(W_{r}\) to the diagonal matrix, and has achieved good results. TransD considers the transfer matrix \(M_{r}\) in TransR as \(M_{rh}\) and \(M_{tt}\), which are related to both entities and relations. TranSparse [18] uses sparse matrices instead of dense matrices in TransR, while TransG [19] considers that the different semantics of relation \(r\) obey multiple Gaussian distributions. KG2E [20] uses Gaussian distribution to represent entities and relationships. Multiplicative models define product-based functions over embedded vectors. In LFM, the second order relationship between entities and relations is depicted by relation-based bilinear transformation, which defines the score function of every existing triple (\(h\), \(r\), \(t\)) as \(score_{r}(h,t)=l_{h}^{T}M_{r}t_{t}\), where \(l\) is the embedding vector for head or tail, \(M_{r}\in R^{d\times d}\) is the transformation matrix of the relation \(r\), and \(d\) is the dimension of the embedding vector. This model is simple but good at cooperative and low-complexity computation. RESCAL [21], which is similar to LFM in relation-based bilinear transformation, has the benefit of optimizing the parameter if the triples do not exist. DISTMULT [22], using the same bilinear function as RESCAL, simplifies the transformation matrix \(M_{r}\) to the diagonal matrix. This simplification gives better performance. Holographic Embeddings(HolE) [23] represents entities and relations as vectors \(l_{h}\), \(l_{t}\), and \(l_{r}\) in \(R^{d}\) and performs cycle-related operations between both entities as \(\left[l_{h}*l_{t}\right]_{k}=\sum\limits_{i=0}^{d-1}l_{h_{i}}*l_{t(i+k)\times d}\). HolE keeps the simplicity of DISTMULT and expressive power of RESCAL. To model asymmetric relations, Complex Embeddings(ComplEx) [24] introduces complex-valued embedding among DISTMULT. SimplE [13] improves the expressive ability and performance by simplifying the tensor decomposition model and considering the inverse relation. ManifoldE [25] introduces manifold to solve the problem of a multi-solution of an ill-posed algebraic system in knowledge representation learning to improve the accuracy of link prediction. TuckER [26] is a relatively simple but powerful model based on Tucker decomposition of the binary tensor representation of knowledge graph triples.