# CrossE

Interaction Embeddings for Prediction and Explanation in Knowledge Graphs

## Abstract

Crossover interactions — bi-directional effects between entities and relations help select related information when predicting a new triple, but haven’t been formally discussed before
In this paper, we propose CrossE, a novel knowledge graph embedding which explicitly simulates crossover interactions.
Furthermore, we evaluate embeddings from a
new perspective — giving explanations for predicted triples, which is important for real applications.

## Contribution

In summary, our contributions in this paper are the following:
• We propose CrossE, a new KGE which models crossover interactions of entities and relations by learning an interaction matrix.
• We propose a newevaluation scheme for embeddings—searching explanations for predictions, and show that CrossE is able to generate more reliable explanations than other methods. This suggests that interaction embeddings are better at capturing similarities between entities and relations in different contexts of triples.

## Model Description

Our model simulates crossover interactions between entities and relations by learning an interaction matrix to generate multiple specific interaction embeddings.
In our method, each entity and relation is represented by multiple embeddings: (a) a general embedding, which preserves high-level properties, and (b) multiple interaction embeddings, which preserve specific properties as results of crossover interactions

## 基于距离的模型

Model ScoreFunction relation
TransE $$f_r(h,r)= ||h+r-t||^2_2$$ inversion、 composition
TransH $$f_r(h,r) = ||(h-w_r^Thw_r) +d_r -(t-w_r^Ttw_r) ||^2_2$$
TransR $$f_r(h,r) = ||w_rh +r -w_rt ||^2_2$$
PTransE $$G(h,r,t)=E(h,r,t)+E(h,p,t)$$ antisymmetry、 composition
ManifoldE $$f_r(h,t)=||M(h,r,t)-D_r^2||^2$$ inversion、 composition
RotatE $$f_r(h,t)=||h \circ r - t ||^2$$ symmetry、antisymmetry、inversion、 composition