Visual Intelligence Seminar: Beyond the (Point) Clouds: Domain-Aware Dimensionality Reduction with Neural Operators

Abstract

Many real-world datasets represent continuous processes over time, space, or other domains, yet standard dimensionality-reduction methods typically treat observations as discrete point clouds, disregarding the relationships induced by the underlying domain. This loss of structural information can exaggerate apparent clustering and violate the continuous structure of the data in the reduced space.

We present Neural Operator Function Embedding (NOFE), a domain-aware approach that learns function-to-function embeddings using a Graph Kernel Operator and can be evaluated independently of the original sampling grid. NOFE is designed to preserve local structure while remaining consistent across varying sample densities and disconnected spatial patches.