The problem of change point detection can be solved either by online methods, based on a discrepancy measure, or by offline methods. The former tries to detect the change points one by one with a sliding window and leads to a lower computational time but are more sensitive to noise. Conversely, offline methods consider the entire data to detect all the change points which make them more robust against the noise but at a price of higher computational cost. In this paper, we propose an operational search method that combines the benefits of both approaches with the double aim to get higher noise resistance while keeping a blazingly fast time. The search method slides over the edges of the signal to determines their state by considering a global constrained energy. Thanks to the calculus of variation, the computation of this energy is reduced to the estimation of the effective jump for each edge. We study the performance and accuracy of our energy variation method to detect the change points in synthetic and real-world examples. The results compare favorably against state of the art algorithm in terms of speed and accuracy.

变化点检测的问题可以通过基于差异度量的在线方法或离线方法来解决。前者尝试用滑动窗口逐个检测变化点，计算时间较短，但对噪声更敏感。相反，离线方法会考虑整个数据来检测所有变化点，这使它们对噪声更加鲁棒，但代价是计算成本更高。在本文中，我们提出了一种操作搜索方法，该方法结合了两种方法的优点和双重目标，即在保持极快的时间的同时获得更高的抗噪性。搜索方法滑过信号的边缘，通过考虑全局约束能量来确定它们的状态。多亏了变分法，该能量的计算被简化为对每条边的有效跳跃的估计。我们研究了我们的能量变化方法的性能和准确性，以检测合成和现实世界示例中的变化点。结果在速度和准确性方面优于最先进的算法。