# Riemannian Change Point Detection on Manifolds with Robust Centroid Estimation

arXiv: https://arxiv.org/abs/2508.18045 · HTML: https://mlsanity.com/paper/2508.18045/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 27 references that are in the map.
- First posted on arXiv 25 Aug 2025.

## Builds on (most cited first, 5 of 5)

- [First-order Methods for Geodesically Convex Optimization](https://mlsanity.com/paper/1602.06053/) (2016)
- [NEWMA: a new method for scalable model-free online change-point detection](https://mlsanity.com/paper/1805.08061/) (2018)
- [Online change-point detection with kernels](https://mlsanity.com/paper/2002.02704/) (2020)
- [Fr'echet Change Point Detection](https://mlsanity.com/paper/1911.11864/) (2019)
- [Online Graph-Based Change Point Detection in Multiband Image Sequences](https://mlsanity.com/paper/2006.14033/) (2020)

## Abstract (arXiv)

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.