# Knowledge Graph Extrapolation Network with Transductive Learning for Recommendation
## 1 Introduction  
The personalized recommendation algorithm has a strong effect in assisting users to find items useful to them in a limited time. This method effectively alleviates the data explosion [1] problem brought on by the information age. Therefore, recommendation algorithms are widely used in many scenarios [2; 3], such as online shopping, search engines, movie recommendation websites and so on. Collaborative filtering (CF) [4; 5], a traditional recommendation algorithm, has attracted much attention due to its effectiveness and universality. The main idea of CF is to predict the user's personal preference by mining the user's historical behavior information and then recommend similar products to users with similar preferences. However, the recommendation algorithm of collaborative filtering ignores side information, such as users' attributes, items' attributes and so on. Thus, the CF method suffers from data sparsity and cold start problem, where the user has a few interactions or no interactions. In order to exploit side information, some recommendation algorithms integrate deep learning methods [6; 7] to obtain feature vectors of users and items, and calculate the probability of users' preference for items. It is worth noting that users, items and their attribute information are related, instead of independent. Knowledge Graphs (KGs) are the multi-relational graphs which represent structured data. KGs consist of nodes and edges, where nodes represent entities and edges represent relations of entities. So, KGs are able to capture high-order structure information. Therefore, KGs [8; 9; 10] are introduced into the recommendation algorithmbecause of their powerful ability to represent structured data. [PERSON] et al. [11] proposed a deep knowledge-aware network, which combines knowledge graph representation and news recommendation and fuses semantic-level and knowledge-level representations of news. For the sequential recommendation, [PERSON] et al. [12] proposed an explainable interaction-driven user modeling, recommended interpretability is provided by extracting paths between user-item pairs. Graph theory [13] is the study of graphs, which has been widely used in non-European graph data learning. Therefore, knowledge graph recommendations based on the graph neural network has become a popular solution, which utilizes embedding propagation of entities to aggregate higher-order neighborhood information. For example, [PERSON] et al. [10] proposed a description-enhanced machine learning knowledge graph-based method, that combined the knowledge graph-based and text-based methods, which aggregates neighbors information by a graph neural network with attention. In the real recommendation scenarios, there is a long tail effect [14], that is, a large amount of data has few interactions, and only a small portion of data has a large amount of interaction information. This is a challenge for recommendation because only a small amount of data can be used for training. Furthermore, the KG is dynamic, not static. The general methods based on KG are to make recommendations on the existing knowledge graph, and predict unknown entities through known entities, while ignoring the association between unknown entities, which also limits the accuracy of recommendations. To address the limitations of existing methods, an end-to-end model, Knowledge Graph Extrapolation Network with Transductive Learning for Recommendation (KGET) is introduced. Specifically, KGET is equipped with two designs to tackle the challenges: (1) Embedding propagation learns the features of unknown entities by a knowledge propagation combined collaborative signal, and learns the weights of neighbor nodes to distill useful knowledge. It is able to capture collaborative and high-order structural information and long-distance interest. (2) Transductive learning is able to obtain more accurate and informative items representations, which models the relationships between unknown entities to enrich representations of items and realize extrapolate KG.