Intrinsic Gaussian Process on Unknown Manifolds with Probabilistic Metrics

This article presents a novel approach to construct Intrinsic Gaussian Processes for regression on unknown manifolds with probabilistic metrics (GPUM) in point clouds. In many real world applications, one often encounters high dimensional data (e.g.‘point cloud data’) centered around some lower dimensional unknown manifolds. The geometry of manifold is in general different from the usual Euclidean geometry. Naively applying traditional smoothing methods such as Euclidean Gaussian Processes (GPs) to manifold-valued data and so ignoring the geometry of the space can …

applications article cloud cloud data construct data embedded gaussian processes general geometry gps intrinsic manifold metrics novel predictions process processes regression space world