A BFGS-Optimized Approach with Polynomial Smooth Support Vector Machines for Rapid and Effective Classification

Abstract

Data smoothing, which is an essential component in the field of predictive modelling, proves to be a potent tool in extracting subtle variations and enabling the prediction of various trends and patterns. This research undertakes an investigation into the diverse range of uses that smoothing techniques have, with a particular emphasis on their widespread implementation in the resolution of intricate mathematical challenges. The core of this research revolves around the utilisation of smoothing methodologies to define and address Support Vector Machine (SVM), which have been cleverly recast as unrestricted optimisation challenges. The present formulation incorporates a flexible smoothing parameter set and a fourth-order polynomial function, which are referred to collectively as the Polynomial Smooth Support Vector Machine (PSSVM). The complexities and details of the PSSVM method are systematically examined and enhanced via optimization applying the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. The BFGS method, which is well-known for its ability to rapidly converge, plays a critical role in providing the effectiveness and accuracy of the PSSVM technique. PSSVM is distinguished in this regard by its exceptional capacity for generalization. The remarkable capability of generalization is conferred upon PSSVM through the coordinated interaction of the fine-tuned smoothing parameters and the fourth-order polynomial function. The aforementioned attribute establishes PSSVM as an essential implement within the framework of predictive analytics. This study presents an innovative methodology for predictive modelling, demonstrating how the BFGS method optimizes Polynomial Smooth Support Vector Machines to achieve an outstanding effect. The outcomes highlight the efficacy, accuracy, and ability to generalization of PSSVM, establishing it as a leading solution in the field of SVM problem-solving. This study introduces novel opportunities for predictive analytics and agile data smoothing, thereby altering the mathematical problem-solving domain within the framework of Support Vector Machines. Several experiments are performed and from the numerical results it is concluded that PSSVM is better classifier. It is more effective and faster than the previous methods for solving SVM with better generalization ability