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。

Sphere2Vec：一个通用的球面位置表示学习模型，用于大规模地理空间预测

Sphere2Vec: A General-Purpose Location Representation Learning over a  Spherical Surface for Large-Scale Geospatial Predictions

Generating learning-friendly representations for points in a 2D space is a
fundamental and long-standing problem in machine learning. Recently,
multi-scale encoding schemes (such as Space2Vec) were proposed to directly
encode any point in 2D space as a high-dimensional vector, and has been
successfully applied to various (geo)spatial prediction tasks. However, a map
projection distortion problem rises when applying location encoding models to
large-scale real-world GPS coordinate datasets (e.g., species images taken all
over the world) - all current location encoding models are designed for
encoding points in a 2D (Euclidean) space but not on a spherical surface, e.g.,
earth surface. To solve this problem, we propose a multi-scale location
encoding model called Sphere2V ec which directly encodes point coordinates on a
spherical surface while avoiding the mapprojection distortion problem. We
provide theoretical proof that the Sphere2Vec encoding preserves the spherical
surface distance between any two points. We also developed a unified view of
distance-reserving encoding on spheres based on the Double Fourier Sphere
(DFS). We apply Sphere2V ec to the geo-aware image classification task. Our
analysis shows that Sphere2V ec outperforms other 2D space location encoder
models especially on the polar regions and data-sparse areas for image
classification tasks because of its nature for spherical surface distance
preservation.

提出了一种新的多尺度定位编码模型 Sphere2Vec，可以直接编码球形表面上的点坐标，避免地图投影扭曲问题。通过应用于地理感知图像分类任务的实验，证明了该模型在极地和数据稀疏区域的图像分类任务中性能优于其他二维定位编码模型。