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A Review of Location Encoding for GeoAI: Methods and Applications

Gengchen Mai, Krzysztof Janowicz, Yingjie Hu, Song Gao, Bo Yan, Rui Zhu, Ling Cai, Ni Lao

arXiv:2111.04006v2cs.LG

TL;DR

GeoAI needs usable representations for diverse spatial data, while vector data are difficult to incorporate directly into deep-learning models. This paper defines location encoding, surveys and classifies existing approaches, and unifies them in a shared framework. It also identifies applications and continuing challenges, including limited direction-aware research and unresolved fine-grained polygon encoding.

  • Problem

    GeoAI lacks a systematic review of how diverse spatial data, especially difficult vector data, can be encoded for machine-learning models.

  • Method

    The paper formally defines location encoding, classifies encoders by inputs and design characteristics, and reformulates them under unified frameworks.

  • Results

    Existing location encoding models are unified under shared formulations, and location encoding is shown across multiple GeoAI tasks and spatial-data applications.

  • Takeaways & Limitations

    Location encoding provides a general-purpose representation approach for incorporating spatial information into downstream GeoAI models.

  • Takeaways & Limitations

    Direction-aware encoding remains comparatively underexplored, while polygon encoding lacks satisfactory solutions for fine-grained geometries.

Abstract

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A common need for artificial intelligence models in the broader geoscience is to represent and encode various types of spatial data, such as points (e.g., points of interest), polylines (e.g., trajectories), polygons (e.g., administrative regions), graphs (e.g., transportation networks), or rasters (e.g., remote sensing images), in a hidden embedding space so that they can be readily incorporated into deep learning models. One fundamental step is to encode a single point location into an embedding space, such that this embedding is learning-friendly for downstream machine learning models such as support vector machines and neural networks. We call this process location encoding. However, there lacks a systematic review on the concept of location encoding, its potential applications, and key challenges that need to be addressed. This paper aims to fill this gap. We first provide a formal definition of location encoding, and discuss the necessity of location encoding for GeoAI research from a machine learning perspective. Next, we provide a comprehensive survey and discussion about the current landscape of location encoding research. We classify location encoding models into different categories based on their inputs and encoding methods, and compare them based on whether they are parametric, multi-scale, distance preserving, and direction aware. We demonstrate that existing location encoding models can be unified under a shared formulation framework. We also discuss the application of location encoding for different types of spatial data. Finally, we point out several challenges in location encoding research that need to be solved in the future.

1. Introduction and Motivation

GeoAI models must represent diverse spatial data in forms that machine-learning systems can use, but vector data remain difficult to handle directly. The paper motivates location encoding as a learning-friendly representation of point locations and surveys its methods, applications, and challenges.

  • Motivation: GeoAI models need to encode points, polylines, polygons, graphs, and rasters into hidden embeddings usable by machine-learning models.Raster encoding can use regular-grid models such as CNNs, whereas vector-data representation is more complicated.
  • Motivation: Early conversions of vector data into voxels or images can lose information and require difficult spatial-resolution choices.Finer resolutions increase sparsity and computation cost, while coarser resolutions can reduce prediction quality.
  • Location encoding: Location encoding converts a point location into a high-dimensional embedding that downstream neural networks or SVMs can learn from efficiently.The encoding is intended to make complex spatial distributions easier to learn with relatively simple models.
  • Applications: Location encoding has been applied to geo-aware image and POI classification, place annotation, trajectory prediction, privacy protection, geographic question answering, and point-cloud tasks.The cited applications span multiple GeoAI tasks rather than a single application domain.
  • Paper scope: Despite these applications, the field lacked a systematic review, motivating a comparative survey and a unified conceptual framework for existing location encoding methods.The paper also discusses broader spatial-data applications and future research challenges.
  • Paper scope: The paper formally defines location encoding, explains its machine-learning necessity, classifies existing models, and discusses applications across spatial-data types.Its structure includes formal definition, necessity, research landscape, spatial-data applications, and future challenges.

2. Definitions

Location encoding maps coordinates into high-dimensional embeddings that preserve spatial information while remaining suitable for downstream learning. The paper formalizes distance preservation, direction awareness, inductive learning, task independence, and model parametrization as key properties.

  • Formal definition: A location encoder maps an L-dimensional coordinate to a d-dimensional vector, with L < d, producing a location embedding.The encoder may also depend on a set of points and, in some cases, location attributes.
  • Formal definition: Location encoding can represent both global locations and spatial relations such as the affinity vector between two locations.The spatial relation is represented as the coordinate difference between two locations.
  • Spatial properties: Distance preservation requires embedding similarity to decrease monotonically as the distance between locations increases.The distance may be Euclidean, Manhattan, geodesic, or great-circle distance.
  • Spatial properties: Direction awareness requires locations with more similar directions from a reference point to have more similar relative embeddings.The property compares inner products of embeddings for displacement vectors at different angular separations.
  • Spatial properties: Direction-aware encoders are needed when isotropy cannot be assumed, but deliberate direction-aware design remains underdeveloped and lacks theoretical proof in existing work.Prior evidence was mainly empirical, including visualization-based findings for multi-scale and baseline encoders.
  • Generalization properties: Generalizable location encoders should support inductive encoding of unseen locations and remain task-independent across downstream applications.The same architecture should work across tasks without modification, unlike several transductive or task-dependent approaches.
  • Model properties: Parametric encoders use a finite parameter set and bounded complexity, whereas non-parametric models are more flexible but can grow with the data.The review notes that not every surveyed model satisfies distance preservation, direction awareness, or parametrization, while all satisfy the inductive and task-independent properties.

3. The necessity of location encoding for GeoAI

Location encoding is motivated by the need to make geographic representations easier for machine learning models to use. By transforming low-dimensional coordinates into higher-dimensional features, it can make complex spatial distributions more amenable to simpler downstream models.

  • Machine learning perspective: The bias-variance trade-off creates tension between flexible models that require substantial data and simpler models that may lack expressive power.Large hypothesis spaces can approximate nonlinear distributions but require many samples to avoid overfitting.
  • Machine learning perspective: Kernel methods model highly nonlinear low-dimensional inputs with limited complexity but require storing kernels during inference.Neural networks provide another route with established mechanisms for controlling effective model complexity.
  • Role of location encoding: Location encoding decomposes coordinates into higher-dimensional features so distributions such as P(y|x) may become linear and usable by simpler downstream models.The stated downstream models include support vector machines and neural networks.

4. A review of the current landscape of location encoding

The review organizes location encoding methods by encoder inputs and spatial-feature transformations, separating single-point and neighborhood-aggregation approaches. It compares these models using shared criteria including parametrization, scale, distance preservation, and direction awareness.

  • Taxonomy: The survey classifies encoders first by input type into single-point encoders and aggregation encoders that incorporate neighborhood locations.Single-point encoders are further grouped by positional encoder, while aggregation encoders are grouped by neighborhood choice.
  • Comparison criteria: Table 1 compares methods by spatial dimension, parametrization, multi-scale representation, distance preservation, and direction awareness.Distance and direction entries distinguish empirically or theoretically supported properties from unknown cases.
  • Comparison criteria: The review uses shared criteria to summarize location encoding approaches rather than treating each method as an isolated design.The table overview covers both single-point and aggregation encoders and marks multi-scale representations.

4.1. Single point location encoder Encpxq

Single-point location encoders transform coordinates into learning-friendly embeddings through a position-encoding function and a neural network. The reviewed families differ in how they normalize or decompose locations, with recurring limitations involving discretization, scale, density, and spherical geometry.

  • General formulation: Single-point encoders commonly map a position embedding PE(x) through a learnable neural network NN(·) to produce a location embedding.PE(x) normalizes or decomposes location features, while NN(·) captures interactions between locations and target labels.
  • Discretization-based location encoder: Discretization-based encoders assign locations to grid, hexagon, or triangle units, but ignore spatial dependencies and use a single fixed scale.Incorrect discretization choices can substantially affect performance and efficiency.
  • Discretization-based location encoder: Finer or multi-level discretization can address varied point densities, but increases the number of tiles and learnable parameters, potentially causing overfitting.Adaptive strategies use smaller tiles in dense areas and larger tiles in sparse areas.
  • Direct and sinusoidal encoders: Direct encoders apply neural networks to normalized coordinates, whereas sinusoidal encoders first transform normalized coordinates with sinusoidal functions.Direct encoders can distinguish nearby locations, but their performance depends on appropriate location-feature normalization.
  • Direct and sinusoidal encoders: Sinusoidal wrapping makes longitudes at -180° and 180° equivalent, but applying the same strategy to latitudes makes the South and North poles identical.The wrapping strategy is therefore not spherical distance-preserving.
  • Sinusoidal multi-scale location encoder: Multi-scale sinusoidal encoders use multiple frequencies, with λ_min controlling the highest spatial resolution and enabling distance-preserving behavior for theory-based encoders.The highest and lowest frequencies govern the spatial scales represented by the encoding.

4.2. Aggregation location encoder EncpPqpxq

Aggregation location encoders augment a point’s representation with features from a neighborhood, using iterative aggregation and feature-combination operations. They range from fixed kernel or global neighborhoods to local and hierarchical aggregation, with kernel methods exposing a memory–accuracy trade-off.

  • General framework: An aggregation location encoder jointly represents a location and aggregated features from its neighborhood through repeated aggregation and feature-combination layers.A final readout function produces the aggregated location embedding.
  • Encoder categories: Neighborhood definitions classify aggregation encoders into kernel, global, local-neighborhood, and hierarchical-neighborhood categories.The neighborhood N(x) determines which locations contribute to the representation.
  • Kernel-based location encoder: Kernel-based encoders compare each location with a fixed set of kernel centers using a predefined kernel function, then concatenate the resulting kernel features.Examples include GPS2Vec and the RBF baseline in Space2Vec.
  • Kernel-based location encoder: Kernel-center-set size creates a performance–efficiency trade-off: sparse small sets reduce memory and parameters but can reduce encoding quality, whereas large sets improve accuracy but increase memory and training demands.Predictions also depend on the distribution of kernel centers and can perform poorly in data-sparse regions.
  • Global aggregation location encoder: Global aggregation uses all locations as a point’s neighborhood, as illustrated by PointNet’s shared multilayer perceptrons, max pooling, feature concatenation, and readout operations.PointNet first produces point embeddings, aggregates them globally, and combines the result with point-wise features.
  • Local and hierarchical aggregation: Local aggregation restricts neighborhoods by spatial proximity or shared voxels, while hierarchical aggregation repeatedly downsamples point sets and propagates features across levels.In hierarchical encoding, the final point subset is a small skeleton of the original point set.

4.3. Comparison among different models

The paper compares location encoders by input scope, computational properties, scale, distance preservation, and direction awareness. Single-location encoders are faster, whereas aggregation encoders capture spatial context and can provide richer features.

  • Single-location encoders process each location independently, while aggregation encoders jointly consider a location and its neighborhood.
  • Aggregation encoders update embeddings when neighborhood structure changes, whereas single-location encoders remain unaffected by added points.
  • Single-location encoders offer higher inference speed, while aggregation encoders are time-consuming but provide richer predictive features.
  • Task input and application priorities guide model choice: single locations favor fast encoders, while point sets and accuracy-oriented applications favor aggregation encoders.
  • Most reviewed models are parametric, whereas RBF and adaptive-kernel models can be parametric or non-parametric depending on kernel-center-set size.
  • Multi-scale encoders better capture non-uniform densities, and empirical comparisons identify differences in distance preservation and direction awareness among models.Sinusoidal-frequency and hierarchical-neighborhood strategies are two distinct multi-scale designs.

5. Applying location encoding to different types of spatial data

Location encoding extends beyond point-set tasks to polylines, polygons, graphs, and rasters. The paper describes workable approaches for sequences and spatial graphs while emphasizing unresolved challenges in topology-aware polygon encoding and geographic raster positions.

  • Polyline: Polylines can be encoded as ordered sequences by embedding each location and feeding the embeddings into a sequential neural network.
  • Polygon: Polygon encoding supports geographic entity alignment, topological reasoning, and geographic question answering, but satisfactory general solutions remain unavailable.
  • Polygon: Existing polygon methods have limited coverage: bounding-box sampling misses fine-grained geometry, while GCAE cannot handle holes or multipolygons.
  • Graph: Spatial graphs can incorporate location encoders into node representations, while point sets can first be converted into distance-weighted spatial graphs for GNN processing.
  • Graph: Distance-weighted graph methods can lose spatial layout and direction information, so aggregation encoders are advocated for capturing relations among locations.
  • Raster: Raster Transformers can encode pixel features and positions before self-attention, and geographic pixel locations may transfer knowledge from unlabeled geospatial data.Patch-based self-attention lowers computational cost, while geographic rather than image positions are proposed for earth-surface pixels.

6. Conclusion and Vision for Future Work

The paper formalizes location encoding, unifies existing encoders, compares their properties, and surveys applications across spatial data types. It identifies polygon, spatiotemporal, spherical, and unsupervised encoding as important directions for future work.

  • The review defines location encoding as an inductive, task-agnostic technique and organizes models into single-point and aggregation encoders.
  • Existing location encoders are unified under shared formulation frameworks and compared across their characteristics and spatial-data applications.
  • Future directions: Polygon representation remains an unsolved problem requiring topology-aware encoders for simple polygons, polygons with holes, and multipolygons.
  • Future directions: Future work should address temporal information, its preserved properties, and integration with location encoding; one reported combination improved performance by 0.25%-1.37%.
  • Future directions: No existing location encoder preserves spherical surface distance, motivating spherical-aware methods for large-scale geospatial datasets.
  • Future directions: Most reviewed encoders use supervised training, leaving unsupervised location encoding as an open research direction.
  • The review provides no code implementation.

Notes on contributors

The contributors are researchers whose affiliations and expertise span GeoAI, geoinformatics, spatial studies, GIScience, spatial data science, knowledge graphs, and machine learning.

  • Gengchen Mai studies spatially explicit machine learning, geospatial knowledge graphs, and geographic question answering at Stanford.
  • Krzysztof Janowicz focuses on geoinformatics, spatial knowledge representation, reasoning, and human conceptualizations of space.
  • Yingjie Hu researches GeoAI and spatial data science at the University at Buffalo.
  • Song Gao works on place-based GIS, geospatial data science, human mobility, and social sensing.
  • Bo Yan researches geospatial knowledge graphs and machine learning in the geospatial domain.
  • Rui Zhu studies geospatial semantics, spatial statistics, and their interaction with GeoAI.
  • Ling Cai researches qualitative spatial-temporal reasoning, temporal knowledge graphs, neuro-symbolic AI, and urban computing.
  • Ni Lao specializes in machine learning, knowledge graphs, natural-language understanding, and large-scale inference.
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