## 2 Related Works
### The Translation Models  
Inspired by the word-embedding vector translation invariance of the word2 vec model, [PERSON] et al. proposed the first translation model, TransE [19]. The model treats relations as translation operations from the head entities to the tail entities. TransE expects the positive triplet to satisfy _h+r-t=0_. However, in triplets, this assumption leads to N-terminal entity embedding vectors approximately identical in the complex relationships, such as 1-to-N, N-to-1, and N-to-N, as shown in Figure 2. In addition, if the relationship is self-reflexive, such as the classmate relationship, there will be cases where _h+r-t=0_ and _t+r-l=0_ exist at the same time, leading to the embedding vectors _l=t_ or _r=0_. Thus, TransE can only offer great results when modeling simple 1-to-1 relationships, and finds it more difficult to solve complex relationships.  
Figure 1: Embedding space.  
To solve the complex relationships between entities, researchers have made a series of improvements to TransE, proposing some classical translation models, where the TransH [21] model projects the head entity vectors and the tail entity vectors to the hyperplane of the relation located through the unit matrices, and completes the translation process on the hyperplane. It allows the entity to have different representations when it is on different relational hyperplanes.  
The TransH model better solves the shortcomings of TransE in handling complex relationships poorly. However, the model still maps entities and relations to the same semantic space, which causes it to be inadequate in representing entities and relations in the knowledge graph. The TransR [22] model establishes an entity space and a relation space, and completes the process of translation in the relation semantic space where the entity vectors are translated through the relationship mapping matrix. Compared to the TransH model, the TransR model has a better generalization performance because it takes into account that entities may have multiple aspects and that the various relations focus on different aspects of the entity. Due to TransR creating a mapping matrix for each relation, it brings more parameters and increases the computational complexity of the model. TransR is difficult to apply to large-scale knowledge graphs. The TransD [23] model replaces the fixed relation-mapping matrices of the TransR model with dynamically determined vectors of entity-relation pairs. The TransD model uses two vectors to represent each entity and relation, where the first one represents the meaning of the entity or relation, and the other one is used as a projection vector to construct the mapping matrix to project the entity into the vector space of the relation. It changes the matrix multiplication in TransR to vector multiplication, which greatly reduces the computational effort and thus increases the speed of operations. The TransM [24] model is different from the way TransE treats each triplet equally. It calculates the weights of the triplets based on the complexity of relations, and the more complex the relation, the lower the weight of the triplet. However, the TransM model focuses only on the type of relations, with triplets that have the same relation having the same weight. It does not take into account the mapping properties of each triplet. TranSparse [25] is designed to address the heterogeneity (the number of entity nodes corresponding to each relation is different) and imbalance (the same relation corresponds to a different number of head and tail entity nodes) of entities and relations. It proposes a self-adaptive construction of sparse matrices [36; 37] for the projection of entities according to the complexity of the relations, which prevents the occurrence of over-fitting of simple relations and the under-fitting of complex relations.