Localized, High-resolution Geographic Representations with Slepian Functions

TL;DR

This paper introduces Slepian function-based geographic encoders that focus representational capacity on specific regions, improving local resolution and efficiency in geographic machine learning tasks.

Contribution

It presents a novel Slepian-based encoding method for geographic data that enhances local resolution and computational efficiency, with a hybrid approach for global context.

Findings

Slepian encodings outperform baselines in multiple tasks

High-resolution localized representations improve model performance

Hybrid encoders balance local detail and global context

Abstract

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.