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Communication Dans Un Congrès Année : 2024

Non-parametric online change point detection on Riemannian manifolds

Résumé

Non-parametric detection of change points in streaming time series data that belong to Euclidean spaces has been extensively studied in the literature. Nevertheless, when the data belongs to a Riemannian manifold, existing approaches are no longer applicable as they fail to account for the structure and geometry of the manifold. In this paper, we introduce a non-parametric algorithm for online change point detection in manifold-valued data streams. This algorithm monitors the generalized Karcher mean of the data, computed using stochastic Riemannian optimization. We provide theoretical bounds on the detection and false alarm rate performances of the algorithm, using a new result on the non-asymptotic convergence of the stochastic Riemannian gradient descent. We apply our algorithm to two different Riemannian manifolds. Experimental results with both synthetic and real data illustrate the performance of the proposed method.
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Dates et versions

hal-04632586 , version 1 (02-07-2024)

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  • HAL Id : hal-04632586 , version 1

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Xiuheng Wang, Ricardo Augusto Borsoi, Cédric Richard. Non-parametric online change point detection on Riemannian manifolds. 41st International Conference on Machine Learning, ICML 2024, Jul 2024, Vienne, Austria. ⟨hal-04632586⟩
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