Support Vector Machine (SVM) Theoretical Foundation: Statistical Learning Theory and SVM Principles

In this paper, we provide a detailed overview of the application research status in load forecasting, with emphasis on summarizing the characteristics and influencing factors of load forecasting, along with common methods for short-term load forecasting and analysis of their advantages and limitations. Subsequently, we introduce the theoretical foundation and working principles of Support Vector Machines (SVM), deriving the SVM regression model through mathematical formulation. Our implementation utilizes the Least Squares Support Vector Machine (LSSVM) model, where we analyze historical load data and meteorological data to identify patterns in load variations. The data preprocessing phase includes crucial steps such as anomaly detection and correction for "abnormal data" in historical records, along with normalization of relevant factors considered in load forecasting. We pay particular attention to two parameters in the LSSVM model that significantly impact performance, which are currently addressed using empirical methods. To overcome this limitation, we implement a Particle Swarm Optimization (PSO) algorithm for parameter optimization, where the test set error serves as the decision criterion for optimal parameter selection. This approach enables systematic parameter tuning through iterative swarm intelligence, where particles represent potential parameter solutions and update their positions based on personal and global best experiences. The optimization process enhances prediction accuracy by finding parameter combinations that minimize prediction error on validation datasets. Our practical case studies demonstrate that the proposed forecasting method exhibits excellent convergence properties, high prediction accuracy, and fast training speed. The LSSVM implementation benefits from solving linear equations instead of quadratic programming problems, significantly reducing computational complexity while maintaining generalization performance. Therefore, we conclude that the proposed method shows promising application prospects and can provide valuable references for research in related fields. Furthermore, we believe there remains substantial space for further research and exploration in this domain, and we hope this paper can offer beneficial insights and references for researchers in this field. The accompanying source code provides complete implementation of the LSSVM model with PSO optimization, including data preprocessing modules, kernel function implementations, and parameter optimization routines for practical application.