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Title: Random domain decomposition for spatial prediction of manifold-valued data Authors:  Davide Pigoli - King\'s College London (United Kingdom) [presenting]
Alessandra Menafoglio - Politecnico di Milano (Italy)
Piercesare Secchi - Politecnico di Milano (Italy)
Abstract: Data taking value on a Riemannian manifold and observed over a complex spatial domain are becoming more and more frequent in applications, e.g. in environmental sciences and in geoscience. The analysis of these data needs to rely on local models to account for the non stationarity of the generating random process, the non linearity of the manifold and the complex topology of the domain. A method is illustrated to predict a spatial field taking value on a smooth Riemannian manifold. A Random Domain Decomposition of the spatial domain will be used to estimate an ensemble of local models which will be eventually aggregated through Fr\'{e}chet averaging. The proposed algorithm will be first described in complete generality and then applied to the case of positive definite matrices. As an illustrative case study, we will report the analysis of covariance matrices for an environmental dataset observed over the Chesapeake Bay (USA).