# 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
Kernel principal component analysis (KPCA) maps the original data into a higher-dimensional space using a kernel function and then performs PCA dimensionality reduction within this space, proving an effective approach for handling nonlinear issues. In this paper, the kernel matrix K represented by N\(\times\)N is defined as follows:  
\[K_{\hat{S}}=\left\langle\varphi(x_{i}),\varphi(x_{i})\right\rangle \tag{6}\]  
By incorporating Equation (6), the inner product can be obtained. Given the high degree of uncertainty and nonlinearity in the management of power grid line losses, this paper selects the Gaussian kernel function as the kernel function for the KPCA algorithm through experimental determination, with the expression given by  
\[K(x,x_{i})=\exp\left(-\frac{\left\|x-x_{i}^{2}\right\|}{2\sigma^{2}}\right) \tag{7}\]  
where \(x\) and \(x_{i}\) are data points in the original space, and \(\sigma\) is the bandwidth parameter of the Gaussian kernel. For a new set of observational data, it is projected into the feature space, and the feature vectors \(v_{j}(j=1,\cdots,p)\) are extracted (where \(p\) represents the number of principal components to be extracted), resulting in the principal components:  
\[t_{j}=\left\langle v_{j},\varphi(x)\right\rangle=\sum_{i=1}^{N}\alpha_{i}^{j} \langle\varphi(x),\varphi(x_{i})\rangle \tag{8}\]  
Kernel principal component analysis (KPCA) is an algorithm that performs dimensionality reduction by solving an eigenvalue problem for a kernel matrix, without the need to explicitly consider the nonlinear mapping relationship \(\varphi\). To validate the superiority of the dimensionality reduction method presented in this paper, traditional principal component analysis (PCA) and kernel principal component analysis (KPCA) were applied to the same  
Figure 2: Construction of line loss index system based on principal component analysis. nature of existing line loss management, this paper proposes a hybrid evaluation approach, drawing upon the knowledge map of line loss indicators [22; 23]. In light of the aforementioned challenges, this paper proposes an integrated approach that combines the single evaluation method of line loss indicators with the evaluation ideas between methods, thereby achieving an \"organic combination\". The integration of this method is evident in various aspects of the evaluation method for local conditions, which may be described as a process of \"re-engineering\". The study of line loss evaluation object indicators can be broadly divided into four dimensions: planning, management, operation, and technical. It is possible that the evaluation results of different dimensions may appear as extreme values and outliers, which could result in a certain degree of deviation in the overall evaluation results of the indicators. Accordingly, the portfolio evaluation presented in this paper is based on the DEMATEL subjective assignment method and the Entropy-Weight and TOPSIS objective assignment method, which collectively serve to construct the basic framework for portfolio evaluation. Figure 5 is the technical roadmap diagram, which illustrates the design of the technical aspects in the actual application of this project.