Generating learning-friendly representations for points in space is a
fundamental and long-standing problem in ML. Recently, multi-scale encoding
schemes (such as Space2Vec and NeRF) were proposed to directly encode any point
in 2D/3D Euclidean space as a high-dimensional vector, and has been
successfully applied to various geospatial prediction and generative tasks.
However, all current 2D and 3D location encoders are designed to model point
distances in Euclidean space. So when applied to large-scale real-world GPS
coordinate datasets, which require distance metric learning on the spherical
surface, both types of models can fail due to the map projection distortion
problem (2D) and the spherical-to-Euclidean distance approximation error (3D).
To solve these problems, we propose a multi-scale location encoder called
Sphere2Vec which can preserve spherical distances when encoding point
coordinates on a spherical surface. We developed a unified view of
distance-reserving encoding on spheres based on the DFS. We also provide
theoretical proof that the Sphere2Vec preserves the spherical surface distance
between any two points, while existing encoding schemes do not. Experiments on
20 synthetic datasets show that Sphere2Vec can outperform all baseline models
on all these datasets with up to 30.8% error rate reduction. We then apply
Sphere2Vec to three geo-aware image classification tasks - fine-grained species
recognition, Flickr image recognition, and remote sensing image classification.
Results on 7 real-world datasets show the superiority of Sphere2Vec over
multiple location encoders on all three tasks. Further analysis shows that
Sphere2Vec outperforms other location encoder models, especially in the polar
regions and data-sparse areas because of its nature for spherical surface
distance preservation. Code and data are available at
this https URL

该研究提出了一种名为 Sphere2Vec 的多尺度位置编码器，可在编码球面上点坐标时保留球面距离，与现有编码方案相比具有更优异的分类效果。