Mathematics Colloquia and Seminars

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Description

In this talk, we first introduce standard diffusion wavelets and the geometric scattering transform for graphs, and discuss their applications to graph neural networks. For vector-valued signals, we introduce vector diffusion wavelets (VDWs), a novel family of wavelets inspired by the vector diffusion maps algorithm that was introduced to analyze data lying in the tangent bundle of a Riemannian manifold. We show that these wavelets may be effectively incorporated into a family of geometric graph neural networks, which we refer to as VDW-GNNs. We demonstrate that such networks are effective on synthetic point cloud data, as well as on real-world data derived from wind-field measurements and neural activity data. We also discuss useful frame-theoretic and equivariance properties.