Localized, High-resolution Geographic Representations with Slepian Functions
This addresses localized geographic data challenges for applications like disease tracking and ecology, but it is incremental as it builds on existing spherical harmonic methods.
The authors tackled the problem of machine learning models struggling with fine-grained geographic resolution by proposing a geographic location encoder using spherical Slepian functions to concentrate representational capacity in regions-of-interest, achieving performance advantages across five tasks including classification and regression.
Geographic data is fundamentally local. Disease outbreaks cluster in population centers, ecological patterns emerge along coastlines, and economic activity concentrates within country borders. Machine learning models that encode geographic location, however, distribute representational capacity uniformly across the globe, struggling at the fine-grained resolutions that localized applications require. We propose a geographic location encoder built from spherical Slepian functions that concentrate representational capacity inside a region-of-interest and scale to high resolutions without extensive computational demands. For settings requiring global context, we present a hybrid Slepian-Spherical Harmonic encoder that efficiently bridges the tradeoff between local-global performance, while retaining desirable properties such as pole-safety and spherical-surface-distance preservation. Across five tasks spanning classification, regression, and image-augmented prediction, Slepian encodings outperform baselines and retain performance advantages across a wide range of neural network architectures.