Online change point detection on Riemannian manifolds with karcher mean estimates

Online detection of abrupt changes in streaming time series is a challenging problem with many applications, in particular when little prior knowledge of the statistics of the data is available and computation resources are scarce. While many algorithms have been developed for Euclidean spaces, there is a wealth of data that belongs to Riemannian manifolds. Taking the geometry of the data space into account is however paramount in designing effective change point detection algorithms. In this paper, we propose a non-parametric online algorithm to detect abrupt changes in manifold-valued data streams. The proposed method monitors abrupt changes in the Karcher mean of the data using a stochastic Riemannian optimization algorithm. Experiments with both synthetic and real data illustrate the performance of the proposed method.