Online Learning refers to continuously updating a model or algorithm in real-time as new data becomes available rather than processing the entire dataset simultaneously. For change point detection, the goal is to identify abrupt changes in data sequences as they occur, which requires the algorithm to operate sequentially without access to the entire dataset from the start.

In Rio-CPD, an online learning approach tracks changes in correlation matrices over time. By leveraging Riemannian geometry and cumulative sum statistics (CUSUM), the framework incrementally processes each new observation to detect any significant shifts in the data distributions (marginal or joint) as soon as they occur. This enables real-time detection of change points in evolving data streams.

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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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