# Sphere2Vec: Multi-Scale Representation Learning over a Spherical Surface for Geospatial Predictions

arXiv: https://arxiv.org/abs/2201.10489 · HTML: https://mlsanity.com/paper/2201.10489/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 45 references that are in the map.
- First posted on arXiv 25 Jan 2022.

## Builds on (most cited first, 14 of 14)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Rethinking the Inception Architecture for Computer Vision](https://mlsanity.com/paper/1512.00567/) (2015)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [PlaNet - Photo Geolocation with Convolutional Neural Networks](https://mlsanity.com/paper/1602.05314/) (2016)
- [Presence-Only Geographical Priors for Fine-Grained Image Classification](https://mlsanity.com/paper/1906.05272/) (2019)
- [Multi-Scale Representation Learning for Spatial Feature Distributions using Grid Cells](https://mlsanity.com/paper/2003.00824/) (2020)
- [Reconstructing continuous distributions of 3D protein structure from cryo-EM images](https://mlsanity.com/paper/1909.05215/) (2019)
- [A Review of Location Encoding for GeoAI: Methods and Applications](https://mlsanity.com/paper/2111.04006/) (2021)
- [Emergence of grid-like representations by training recurrent neural networks to perform spatial localization](https://mlsanity.com/paper/1803.07770/) (2018)
- [Geo-Aware Networks for Fine-Grained Recognition](https://mlsanity.com/paper/1906.01737/) (2019)
- [Improving Image Classification with Location Context](https://mlsanity.com/paper/1505.03873/) (2015)
- [SE-KGE: A Location-Aware Knowledge Graph Embedding Model for Geographic Question Answering and Spatial Semantic Lifting](https://mlsanity.com/paper/2004.14171/) (2020)
- [Learning Grid Cells as Vector Representation of Self-Position Coupled with Matrix Representation of Self-Motion](https://mlsanity.com/paper/1810.05597/) (2018)

## Built on by (most cited first, 2 of 2)

- [CSP: Self-Supervised Contrastive Spatial Pre-Training for Geospatial-Visual Representations](https://mlsanity.com/paper/2305.01118/) (2023)
- [Learning latent representations for operational nitrogen response rate prediction](https://mlsanity.com/paper/2205.09025/) (2022)

## Abstract (arXiv)

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.