Identifying breakpoints in piecewise regression is critical in enhancing the reliability and interpretability of data fitting. In this paper, we propose novel algorithms based on the greedy algorithm to accurately and efficiently identify breakpoints in piecewise polynomial regression. The algorithm updates the breakpoints to minimize the error by exploring the neighborhood of each breakpoint. It has a fast convergence rate and stability to find optimal breakpoints. Moreover, it can determine the optimal number of breakpoints. The computational results for real and synthetic data show that its accuracy is better than any existing methods. The real-world datasets demonstrate that breakpoints through the proposed algorithm provide valuable data information.

翻译：分段回归中识别断点对于增强数据拟合的可靠性和可解释性至关重要。本文提出了基于贪心算法的新算法，能够准确高效地识别分段多项式回归中的断点。该算法通过探索每个断点邻域来更新断点位置以最小化误差，具有快速收敛性和稳定性，能够找到最优断点集合。此外，该算法还能自动确定最优的断点数量。在真实数据和合成数据上的计算结果表明，该算法的准确性优于现有所有方法。真实世界数据集验证了通过该算法识别的断点能够提供有价值的数据信息。