# RIO-CPD: A Riemannian Geometric Method for Correlation-aware Online Change Point Detection

arXiv: https://arxiv.org/abs/2407.09698 · HTML: https://mlsanity.com/paper/2407.09698/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 17 of its 70 references that are in the map.
- First posted on arXiv 12 Jul 2024.

## Builds on (most cited first, 17 of 17)

- [Geometric Deep Learning on Molecular Representations](https://mlsanity.com/paper/2107.12375/) (2021)
- [An Evaluation of Change Point Detection Algorithms](https://mlsanity.com/paper/2003.06222/) (2020)
- [Kernel Change-point Detection with Auxiliary Deep Generative Models](https://mlsanity.com/paper/1901.06077/) (2019)
- [Scan B-Statistic for Kernel Change-Point Detection](https://mlsanity.com/paper/1507.01279/) (2015)
- [Hierarchical Graph Neural Networks for Causal Discovery and Root Cause Localization](https://mlsanity.com/paper/2302.01987/) (2023)
- [Neural Tangent Kernel Maximum Mean Discrepancy](https://mlsanity.com/paper/2106.03227/) (2021)
- [Spatio-temporal Bayesian On-line Changepoint Detection with Model Selection](https://mlsanity.com/paper/1805.05383/) (2018)
- [NEWMA: a new method for scalable model-free online change-point detection](https://mlsanity.com/paper/1805.08061/) (2018)
- [Change Detection with the Kernel Cumulative Sum Algorithm](https://mlsanity.com/paper/1903.01661/) (2019)
- [Automatic Change-Point Detection in Time Series via Deep Learning](https://mlsanity.com/paper/2211.03860/) (2022)
- [Fast Online Changepoint Detection via Functional Pruning CUSUM statistics](https://mlsanity.com/paper/2110.08205/) (2021)
- [LEMMA-RCA: A Large Multi-modal Multi-domain Dataset for Root Cause Analysis](https://mlsanity.com/paper/2406.05375/) (2024)
- [Online Kernel CUSUM for Change-Point Detection](https://mlsanity.com/paper/2211.15070/) (2022)
- [Change Point Detection in Correlation Networks](https://mlsanity.com/paper/1410.0761/) (2014)
- [Multi-modal Causal Structure Learning and Root Cause Analysis](https://mlsanity.com/paper/2402.02357/) (2024)
- [Real-time financial surveillance via quickest change-point detection methods](https://mlsanity.com/paper/1509.01570/) (2015)
- [Fr'echet Change Point Detection](https://mlsanity.com/paper/1911.11864/) (2019)

## Abstract (arXiv)

Change point detection aims to identify abrupt shifts occurring at multiple points within a data sequence. This task becomes particularly challenging in the online setting, where different types of changes can occur, including shifts in both the marginal and joint distributions of the data. In this paper, we address these challenges by tracking the Riemannian geometry of correlation matrices, allowing Riemannian metrics to compute the geodesic distance as an accurate measure of correlation dynamics. We introduce Rio-CPD, a non-parametric, correlation-aware online change point detection framework that integrates the Riemannian geometry of the manifold of symmetric positive definite matrices with the cumulative sum (CUSUM) statistic for detecting change points. Rio-CPD employs a novel CUSUM design by computing the geodesic distance between current observations and the Fr'echet mean of prior observations. With appropriate choices of Riemannian metrics, Rio-CPD offers a simple yet effective and computationally efficient algorithm. Experimental results on both synthetic and real-world datasets demonstrate that Rio-CPD outperforms existing methods on detection accuracy, average detection delay and efficiency.