Detecting multiple structural breaks in high-dimensional data remains a challenge, particularly when changes occur in higher-order moments or within complex manifold structures. In this paper, we propose REAMP (Resonance-Enhanced Analysis of Multi-change Points), a novel framework that integrates optimal transport theory with the physical principles of stochastic resonance. By utilizing a two-stage dimension reduction via the Earth Movers Distance (EMD) and Shortest Hamiltonian Paths (SHP), we map high-dimensional observations onto a graph-based count statistic. To overcome the locality constraints of traditional search algorithms, we implement a stochastic resonance system that utilizes randomized Beta-density priors to vibrate the objective function. This process allows multiple change points to resonate as global minima across iterative simulations, generating a candidate point cloud. A double-sharpening procedure is then applied to these candidates to pinpoint precise change point locations. We establish the asymptotic consistency of the resonance estimator and demonstrate through simulations that REAMP outperforms state-of-the-art methods, especially in scenarios involving simultaneous mean and variance shifts. The practical utility of the method is further validated through an application to time-lapse embryo monitoring, where REAMP provides both accurate detection and intuitive visualization of cell division stages.

翻译：在高维数据中检测多重结构突变仍是一个挑战，尤其是在高阶矩或复杂流形结构内发生变化的场景下。本文提出REAMP（共振增强的多变化点分析），这是一种将最优传输理论与随机共振物理原理相结合的新框架。通过基于地球移动距离和最短哈密顿路径的两阶段降维，我们将高维观测映射到基于图的计数统计量上。为克服传统搜索算法的局部性限制，我们实现了一个随机共振系统，该系统利用随机化的Beta密度先验使目标函数产生振动。这一过程使得多个变化点在迭代模拟中作为全局极小值产生共振，从而生成候选点云。随后对这些候选点应用双重锐化程序以精确定位变化点位置。我们建立了共振估计量的渐近一致性，并通过仿真证明REAMP在涉及均值与方差同时偏移的场景中优于现有先进方法。该方法的实用价值进一步通过延时胚胎监测应用得到验证，其中REAMP不仅实现了细胞分裂阶段的精确检测，还提供了直观的可视化结果。