Segmented Continuous Optimization

Abstract

Segmented curve fitting remains an essential approach for the comprehensive analysis of local patterns in non-stationary time-series data. However, traditional regression algorithms primarily focus on linear or polynomial functions, which can be insufficient for analyzing raw signals with oscillatory or transcendental behavior. In this paper, we propose Segmented Continuous Optimization (SCO), a framework that performs piecewise continuous curve fitting on various non-linear models, including trigonometric, polynomial, and exponential. SCO presents a novel signal representation by optimizing a user-defined model in segments with $C^1$ continuity to properly analyze the data's local and global trends. The framework is tested for accuracy and efficiency across all included models. Finally, we provide examples using velocity and EEG datasets to demonstrate the algorithm's practical usage in examining signal patterns, optimized parameters, derivatives, and integrals of the final fit.