用鲁棒中心点检测流数据中的突变，提升稳定性。
Riemannian Change Point Detection on Manifolds with Robust Centroid Estimation
- 引入基于Huber函数的鲁棒中心点，对抗异常值影响。
- 对比经典Karcher均值与鲁棒中心点，设计不敏感的检验统计量。
- 适用于流式数据的曼达托空间变化点检测，尤其适合有噪声场景。
流式时间序列中的非参数变化点检测是信号处理中的长期挑战。近年来，统计与机器学习方法逐步扩展到定义在黎曼流形上的数据。一种主流策略是监测时间序列质心的突变。然而，该方法在流式实现中需精细调整更新步长。本文提出利用来自M-估计理论的流形鲁棒中心点来解决此问题。通过比较经典的Karcher均值（对突变敏感）与基于Huber函数定义的鲁棒中心点（抗突变），构建了对估计方法不敏感的检验统计量。我们还提出一种随机黎曼优化算法，高效估计两个中心点。在模拟数据及两类代表性流形的真实数据上进行的实验表明，所提方法性能更优。
原文摘要 · Abstract (English)
Non-parametric change-point detection in streaming time series data is a long-standing challenge in signal processing. Recent advancements in statistics and machine learning have increasingly addressed this problem for data residing on Riemannian manifolds. One prominent strategy involves monitoring abrupt changes in the center of mass of the time series. Implemented in a streaming fashion, this strategy, however, requires careful step size tuning when computing the updates of the center of mass. In this paper, we propose to leverage robust centroid on manifolds from M-estimation theory to address this issue. Our proposal consists of comparing two centroid estimates: the classical Karcher mean (sensitive to change) versus one defined from Huber's function (robust to change). This comparison leads to the definition of a test statistic whose performance is less sensitive to the underlying estimation method. We propose a stochastic Riemannian optimization algorithm to estimate both robust centroids efficiently. Experiments conducted on both simulated and real-world data across two representative manifolds demonstrate the superior performance of our proposed method.
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