# Knowledge-Graph-Based Integrated Line Loss Evaluation Management System
## 2 Constructing a Knowledge Graph for Comprehensive Line Loss Evaluation Management
### Building a Line Loss Indicator Model Based on Kernel Principal Component Analysis  
The loss of electric energy can be attributed to a number of factors, including transmission, transformation, distribution, and electricity consumption. However, the complex topology and diverse forms of anomalous line losses give rise to ambiguity regarding line loss indicators. Consequently, it is of paramount importance to minimize the burden of data collection, enhance the independence of the selected indicators, and augment the data information embedded in the individual indicators. In light of the aforementioned requirements, this paper proposes the selection of line loss feature indicators based on kernel principal component analysis (KPCA). This approach maps the line loss feature quantities from a low-dimensional state space to a high-dimensional space, thereby facilitating a more comprehensive exploration of the relationships that exist between the feature quantities. In the process of knowledge extraction and knowledge fusion within the knowledge graph, an analysis of the factors affecting the line loss rate for each indicator is conducted on the basis of the aforementioned analysis in the text. The kernel principal component analysis method is employed for the reduction of the dimensionality of the indicators [20]. Subsequently, a composite evaluation method is adopted for the construction of the evaluation process, which subsequently calculates the classification evaluation prediction accuracy of the evaluation indicator system in the evaluation. This enables the influence coefficients of each indicator under this method to be obtained. Principal component analysis (PCA) is a significant statistical method that can be employed to transform a multi-indicator problem into a smaller number of composite indicators [21]. For a sample space of order \(N\times P\) containing \(N\) samples, each containing \(P\)-dimensional indicators, the matrix is represented as  
\[X= \begin{pmatrix}x_{11}&x_{12}&\cdots&x_{1p}\\ x_{21}&x_{22}&\cdots&x_{2p}\\ \vdots&\vdots&&\vdots\\ x_{N1}&x_{N2}&\ldots&x_{Np}\end{pmatrix} \]  
The cumulative variance contribution of the first \(n\) principal components is  
\[\rho=\sum_{i=1}^{n}\lambda_{i}/\sum_{j=1}^{P}\lambda_{j} \tag{4}\]  
When \(\rho\geq 0.70\), it can be assumed that the first \(n\) principal components cover most of the information in the original data, and the contribution rate of each principal component is used as the weight, which constitutes the comprehensive evaluation index as  
\[f=\alpha_{1}y_{1}+\alpha_{2}y_{2}+\cdots+\alpha_{n}y_{n} \tag{5}\]  
where \(n\) is the number of adopted principal components; \(a_{j}\) is the contribution rate of the \(j\)th principal component. The higher the comprehensive line loss index, the higher the base line loss rate in the urban area due to various objective factors, such as the grid structure, equipment condition, load level, etc., which should be taken into account when evaluating the level of line loss management. Figure 2 illustrates the construction of the line loss indicator system based on principal component analysis. This method transforms multiple indicators into multiple multivariate statistical composite indicators, while ensuring that the line loss information is screened less. Once screening has been completed, the comprehensive indicators are referred to as principal components. Each principal component is a linear combination of the original variables, and each principal component is uncorrelated with the others. This makes the principal components perform better than the original variables. In addressing problems that are not linear in nature, the use of PCA, which employs linear transformations, often results in suboptimal outcomes. Consequently, scholars have proposed a nonlinear dimensionality reduction method that involves projecting data into a higher-dimensional space before performing PCA operations, which is known as Kernel Principal Component Analysis (KPCA).