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Data fields sampled on irregularly spaced points arise in many applications in the sciences and engineering. For regular grids, Convolutional Neural Networks (CNNs) have been successfully used to gaining benefits from weight sharing and invariances. We generalize CNNs by introducing methods for data on unstructured point clouds based on Generalized Moving Least Squares (GMLS). GMLS is a non-parametric technique for estimating linear bounded functionals from scattered data, and has recently beenarXiv:1909.05371v2 fatcat:4qwq3u3rx5axnf5qyrdrje2lb4