用分段连续优化方法拟合非线性信号，更好捕捉时序数据的局部与全局趋势。
Segmented Continuous Optimization
- 分段优化用户定义的非线性模型，保证一阶连续性
- 在速度和脑电数据上验证了高精度与效率
- 适合需要分析信号局部特征的研究者
分段曲线拟合仍是分析非平稳时间序列中局部模式的重要方法。然而，传统回归算法多聚焦于线性或多项式函数，难以有效处理具有振荡或超越函数特性的原始信号。本文提出分段连续优化（SCO）框架，对三角、多项式、指数等多种非线性模型进行分段连续拟合，并通过在各段上优化用户定义模型，实现 $C^1$ 连续性，从而更准确地刻画数据的局部与全局趋势。该框架在所有包含模型上进行了精度与效率测试。最后，通过速度与脑电数据集实例，展示了算法在信号模式分析、参数优化、导数与积分计算方面的实际应用价值。
原文摘要 · Abstract (English)
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.
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