# A Review of Knowledge Graph-Based Reasoning Technology in the Operation of Power Systems
## 2 Knowledge Graph Key Technologies
### Knowledge Reasoning
#### 2.5.2 Inductive-Based Knowledge Reasoning  
Inductive-based knowledge inference no longer requires explicit inference steps but is mainly the learning and summarization of existing data. In addition to the observation of large amounts of data, it also includes rule constraints on a priori knowledge to achieve precise inference.  
The embedding model for knowledge representation learning allows the algorithm to automatically capture and reason about the required features in the process of learning vector representations to accomplish the task of link prediction of multiple relationships. The classical TransE model [72] is designed to train to obtain the representation learningresults of KG using a loss function with a maximum interval between positive and negative samples. The loss function \(L\) is  
\[L=\sum_{(h,r,t)\in S}\sum_{(h^{\prime},r,t^{\prime})\in S^{\prime}_{(h,r,t)}} \left[\gamma+f(h,r,t)-f\big{(}h^{\prime},r^{\prime},t^{\prime}\big{)}\right]_{+} \tag{2}\]  
where \(S\) denotes the set of positive samples in KG; \(S^{\prime}\) denotes the negative samples of \((h,r,t)\), obtained by replacing either the head entity \(h\) or the tail entity \(t\) on-the-fly during training. \(\left[x\right]_{+}\) denotes \(\max(0,x)\). \(\gamma\) denotes the interval in the loss function \(L\), a super parameter greater than zero that needs to be set. \(f(h,r,t)\) takes either the \(L_{1}\) or \(L_{2}\) norm to represent the score function of the TransE model, designed as  
\[f(h,r,t)=\parallel h+r-t\parallel_{L_{1}/L_{2}} \tag{3}\]  
where the degree of approximation between \(h+r\) and \(t\) is measured by vector. To achieve the training objective of the TransE model to make the loss function \(L\) as small as possible, \(f\) for positive sample triples should be as small as possible, and \(f\) for negative sample triples should be as large as possible. We train the function using a gradient-based optimization algorithm until convergence.  
TransE is a simple and efficient method of KG representations but suffers from a lack of expressive power and can only capture one-to-one relationships. In fact, there is not only one-to-one correspondence between entities, but also one-to-many, many-to-one, and many-to-many relationships. To express more complex relationships, TransH [73], TransR [74], and TransD [75] distance transfer models are developed to enhance the expressiveness of the TransE using multiple spaces to perform triad score calculation by projection. The vector space assumptions for the above four distance transfer models are plotted in Table 1.  
\begin{table}
\begin{tabular}{c c} \hline \hline \(f(h,r,t)=\parallel h+r-t\parallel_{L_{1}/L_{2}}\) & \(f(h,r,t)=\parallel h_{\perp}+r-t_{\perp}\parallel_{L_{1}/L_{2}}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Distance Transfer Model Vector Graphs and Score Functions [73; 74; 75].  
Due to the inaccuracy and difficulties of the classical model of TransE, scholars have improved it in the same model framework and proposed new modeling approaches such as TransG [76], TransS [77], and TransAE [78].  
In addition to these, knowledge inference methods based on graph structure can utilize graph neural networks [79,80] to accomplish knowledge base complementation, link prediction, and entity discovery, which effectively improves reasoning efficiency and greatly reduces computer processing costs.