Analytical parameter selection with critical computational resources

Nowadays, Support Vector Machines (SVMs) are fundamental for classification tasks in machine learning, yet their performance is highly sensitive to the selection of Gaussian Kernel hyperparameters. Traditional selection methods, such as cross-validation and heuristic optimization, often incur high computational time complexity, which is impractical for real-time decision-making in high-pressure environments. This study addresses these limitations by proposing a geometric-differentiable method for analytical parameter selection, based on the concept of class separability. By optimizing a specific objective function through direct and inverse variation criteria, the proposed method reduces the searching time for the Gaussian Kernel parameter without compromising predictive accuracy. The robustness of the algorithm was validated using the German Credit Data dataset, adapted to simulate credit capacity assessments within humanitarian logistics. Results demonstrate that our analytical approach achieves accuracy rates of up to 98.8% in testing sets, effectively generalizing previous methods while maintaining a significantly lower computational footprint. In the context of disaster management and humanitarian crisis reconstruction, this optimized efficiency enables government and private entities to rapidly classify victims and distribute financial support according to specific needs. Ultimately, this research establishes a mathematical framework for deploying efficient machine learning models, enhancing decision support systems even when computational resources are critically constrained