  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
the 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 Fr\'echet 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.
