Change Point Detection refers to identifying moments within a data sequence with abrupt changes in the statistical properties. These changes can occur at multiple points and may involve shifts in the data’s distribution characteristics, such as mean or variance, either individually (marginal distributions) or in relation to one another (joint distributions).

The challenge of change point detection is particularly pronounced in online settings, where data arrives sequentially, and the detection must occur in real-time. The proposed framework, Rio-CPD, addresses these challenges by monitoring the evolution of correlation matrices, using Riemannian geometry to assess how correlations change over time. By employing techniques like the cumulative sum statistic (CUSUM) and enhancing it with geodesic distances, Rio-CPD aims to accurately and efficiently pinpoint where these changes occur, improving existing methodologies in accuracy and computational efficiency.

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Correlation-aware Online Change Point Detection

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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 change 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 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 Fréchet mean of prior observations. With appropriate choices of Riemannian metrics, Rio-CPD offers a simple yet effective and computationally efficient algorithm. We also provide a theoretical analysis on standard metrics for change point detection within Rio-CPD. Experimental results on both synthetic and real-world datasets demonstrate that Rio-CPD outperforms existing methods on detection accuracy, average detection delay, and efficiency.

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

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The objective of change point detection is to identify abrupt changes at potentially multiple points within a data sequence. This task is particularly challenging in the online setting where various types of changes can occur, including shifts in both the marginal and joint distributions of the data. This paper tackles these challenges by sequentially tracking correlation matrices on their Riemannian geometry, where the geodesic distances accurately capture the development of correlations. We propose Rio-CPD, a non-parametric correlation-aware online change point detection framework that combines the Riemannian geometry of the manifold of symmetric positive definite matrices and the cumulative sum statistic (CUSUM) for detecting change points. Rio-CPD enhances CUSUM by computing the geodesic distance from present observations to the Frechet mean of previous observations. With careful choice of metrics equipped to the Riemannian geometry, Rio-CPD is simple and computationally efficient. Experimental results on both synthetic and real-world datasets demonstrate that Rio-CPD outperforms existing methods in detection accuracy and efficiency.

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