OT on the Map: Quantifying Domain Shifts in Geographic Space
Haoran Zhang * 1 Livia Betti * 2 Konstantin Klemmer 3 4 Esther Rolf 2 David Alvarez-Melis 1 5 6
Abstract
1. Introduction Machine learning (ML) with geospatial data has been used for a range of impactful applications, such as crop yield prediction (Ansarifar et al., 2021), disaster forecasting (Linardos et al., 2022), and pollution monitoring (Hu et al., 2017). Due to the limited availability and quality of labeled datasets, domain scientists commonly train models on data-rich regions (often in Western countries) and then transfer the model’s predictive capabilities to target data-poor regions (often in the Global South) via domain adaptation. This approach is not straightforward. Distinct climates, cultures, and environmental conditions cause distribution shifts between regions (Martin Sudmanns & Lang, 2020; Federici et al., 2021), and, as a result, ML models may struggle to generalize effectively to unseen geographic domains (Rolf et al., 2024). Quantifying when and where a model can generalize has been a focus of recent work in geospatial domain adaptation (Meyer & Pebesma, 2021), which compares geospatial datasets through measures of similarity or distance.
arXiv:2604.16220v1 [cs.LG] 17 Apr 2026
In computer vision and machine learning for geographic data, out-of-domain generalization is a pervasive challenge, arising from uneven global data coverage and distribution shifts across geographic regions. Though models are frequently trained in one region and deployed in another, there is no principled method for determining when this cross-region adaptation will be successful. A well-defined notion of distance between distributions can effectively quantify how different a new target domain is compared to the domains used for model training, which in turn could support model training and deployment decisions. In this paper, we propose a strategy for computing distances between geospatial domains that leverages geographic information with Optimal Transport methods (G EO S P OT). In our experiments, G EO S P OT distances emerge as effective predictors of cross-domain transfer difficulty. We further demonstrate that embeddings from pretrained location encoders provide information comparable to image/text embeddings, despite relying solely on longitude-latitude pairs as input. This allows users to get an approximation of out-of-domain performance for geospatial models, even when the exact downstream task is unknown, or no task-specific data is available. Building on these findings, we show that G EO S P OT distances can preemptively guide data selection and enable predictive tools to analyze regions where a model is likely to underperform. Our code is available at https://github.com/ haoranzhang7/GeoSpOT.
When comparing geospatial datasets, two complementary notions of distance naturally arise. The first is based on geographic proximity; standard measures such as geodesic distance quantify how close two regions are in space. This approach is intuitive: geographically closer domains often share climatic, social, and environmental characteristics, which should enable more effective domain adaptation and knowledge transfer. Tobler (1970) formalized this intuition in the “first law of geography”, which states that “all things are related, but near things are more related.” However, purely spatial distances capture only the physical separation between locations and ignore the data collected at those locations—the features that predictive models actually operate on. A second notion of distance instead compares datasets in feature space, for example by using Optimal Transport (OT) on feature embeddings of the data (AlvarezMelis & Fusi, 2020). Such feature-based distances directly reflect similarity in the observable data (e.g., images, text, or other measurements), but they require that the data already exist for both domains—a costly and often impractical assumption in real-world geospatial settings. Moreover, these distances are not inherently aware of geographic structure, leaving important information unused.
1
Harvard University 2 University of Colorado Boulder 4 LGND AI, Inc. University College London 5 Kempner Institute 6 Microsoft Research. Correspondence to: Haoran Zhang <haoran [email protected]>, Livia Betti <[email protected]>. 3
Preprint. April 20, 2026.
1
OT on the Map: Quantifying Domain Shifts in Geographic Space
In this work, we combine these two perspectives by introducing G EO S P OT, a geographically-aware OT framework for comparing geospatial datasets. G EO S P OT integrates spatial and feature-based information by defining an OT ground cost that incorporates both feature similarity and geographic proximity. To incorporate location information in a semantically meaningful way, we leverage pretrained location encoders—models that take geographic coordinates (latitude, longitude) as input and produce embeddings that capture environmental and contextual characteristics of those locations. These encoders are pretrained in a self-supervised manner, often using CLIP-style image-location matching objectives (Klemmer et al., 2025; Vivanco et al., 2023). As a result, G EO S P OT can be applied independent of any specific dataset or task, enabling distance computation even when only geographic coordinates for the regions of interest are available.
studies have shown that incorporating relevant metadata— particularly geographic coordinates—into adaptation frameworks can enhance cross-region transfer (Yao et al., 2023; Crasto, 2025). In contrast, our work focuses on predicting domain transfer success a priori, even for the challenging case where no data beyond coordinates is available for the domain of interest. Previous work such as Meyer & Pebesma (2021) estimate model applicability by quantifying feature-space distances for individual samples. We instead propose to compare entire geospatial data distributions, introducing a principled way to anticipate geospatial adaptation challenges before model training. Dataset distances for domain adaptation. Rigorous, well-defined methods for quantitatively comparing datasets can guide domain adaptation decisions. Several distinct notions of dataset distances have been explored to predict cross-domain transfer success. Discrepancy distances measure the similarity over a set of functions from a hypothesis class (Kifer et al., 2004; Ben-David et al., 2006) yet are often computationally intractable or infeasible to compute. Other measures of distance employ information-theoretic measures of similarity (Achille et al., 2019) or learned domain relations (Yao et al., 2023), but depend on the model used to determine distances. More recent work leverages Optimal Transport (OT) as a flexible way to define dataset distances, encoding aspects of the data that are most relevant for learning, with extensions incorporating label information (Courty et al., 2017; Alvarez-Melis & Fusi, 2020; Tan et al., 2021), group structure (Redko et al., 2020), or hierarchical relationships (Yurochkin et al., 2019). Among these, Tan et al. (2021) combine the OT distance between domains with a label-dependent task distance, but in our work with label-agnostic setting, this reduces to the standard OT (Sinkhorn) distance between domains. Most closely related to our work, Alvarez-Melis & Fusi (2020) incorporate label information by modifying the ground cost to combine feature- and label-based distances; our approach follows this hybrid-metric principle, replacing label distance with geographic distance. OT approaches have been applied to geospatial ML: namely, for target shift (Redko et al., 2019) and training on noisy data (Damodaran et al., 2020). Our approach focuses on predicting cross-region transfer in the setting of geographically separate domains, explicitly encoding feature and spatial information in the OT ground cost. This geographically-aware OT formulation tailors dataset distances to geospatial applications, improving predictive power for transfer across regions.
Our experiments show that G EO S P OT distances reliably estimate cross-domain transfer performance across diverse downstream tasks. These findings advance our understanding of geospatial domain transfer by showing that purely spatial distances are insufficient to explain transfer success. Beyond estimation, we illustrate the practical utility of G EO S P OT through data selection experiments, where training sets chosen using distance-aware criteria yield models with significantly improved generalization to new domains.
2. Related Work Geographic distribution shifts. Machine Learning models trained on geospatial data often face substantial performance degradation when deployed in new regions due to geographic distribution shifts. Such shifts arise from regional variations in terrain, seasonality, and acquisition conditions (Ekim et al., 2025; Rolf et al., 2024), as well as differences in sensing instruments and collection protocols (Lynch & Wookey, 2021). For instance, while satellite images of houses in the United States and Egypt depict the same conceptual object, differences in architectural style, urban planning, and environmental factors produce distinct visual signatures. These shifts are exacerbated by the common practice of training on data-rich regions and deploying in under-sampled areas. Previous work provides empirical evidence for these distribution shifts, e.g., highlighting performance gaps when training data lack geographic diversity (Nachmany & Alemohammad, 2019; Shankar et al., 2017). Efforts to address such shifts in geospatial ML have focused primarily on post hoc adaptation and robustness. This includes work on out-of-distribution detection (Gawlikowski et al., 2021; Dimitrić et al., 2023; Le Bellier & Audebert, 2024; Ekim et al., 2025) and improved domain adaptation methods for remote sensing imagery (Lin et al., 2019; Fang et al., 2022; Makkar et al., 2022; Ismael et al., 2023). Recent
3. Geospatial Dataset Distances Problem Formulation. Our goal is to define a notion of similarity or distance between geospatial domains that jointly accounts for location and contextual information 2
OT on the Map: Quantifying Domain Shifts in Geographic Space Geodesic distance
United States
OR Brazil
Pretrained location encoder
Feature embedding distance
Location embedding distance
cross-domain distance Distribution-level domain distance to feature (image) Figure 1. OverviewPointwise of G EO S P OT domain distances: (Left) Pointwise cross-domain computation according embedding distance, raw geographic distance, or location embedding distance, highlighting the difference between the approaches. (Right) Distribution-level domain distance between the United States and Brazil. Red arrows represent transported mass under the coupling resulting from solving the optimal transport problem. Coupled images share similar visual features despite being far apart geographically.
(e.g., images or text associated with each location). Given a source domain Ds and a target domain Dt , we seek a principled distance between them that captures differences across both feature and location profiles.
continents, ecological regions, or grid cells on a longitude/latitude mesh. Their distinction may refer either to natural, physical attributes of the planet (e.g., ecological regions, climate zones) or refer to man-made definitions (e.g., voting districts, countries). Both carry different meanings, but can equally be characterized by distribution shifts among domains. To compute OT distances in a way that reflects both feature and location similarity, we first define a pointwise distance on the joint space Z = X × L as a convex combination of distances in each space:
Optimal Transport. Let Z ≜ X × L represent the joint feature-location space. We consider two finite datasets, (i) s (j) t Ds = {zs }ni=1 and Dt = {zt }nj=1 , corresponding to the source and target domains, whichP we treat as empirns ical probability measures: α = n1s i=1 δz(i) , β = s P n t 1 j=1 δzt(j) , where δz denotes the Dirac delta measure nt centered at z. Given a pointwise “ground” cost function cZ (·, ·) : Z × Z → R+ that quantifies the cost of matching elements across domains (and is often taken to be a distance metric dZ in the ambient space), optimal transport lifts this into a notion of distribution-level discrepancy between the entire domains through the following optimization problem: Z OT(α, β) = min cZ (z, z ′ )dπ(z, z ′ ), π∈Π(α,β)
dZ (z, z ′ )p = λdX (x, x′ )p + (1 − λ)dL (ℓ, ℓ′ )p
(1)
The hyperparameter λ controls the relative contribution of feature vs. geographic distances. For dX , we will often use a cosine-based dissimilarity between feature embeddings x and x′ extracted from pretrained image or text encoders. For dL , we consider two alternatives: (1) raw geographic (arc) distances between latitude–longitude coordinates, and (2) cosine distance between pretrained location embeddings.
Z×Z
where Π(α, β) is the set of joint probability distributions over Z × Z with marginals α and β. Intuitively, OT finds a coupling π that reallocates “mass” from points in the source domain to points in the target domain as efficiently as possible under the ground cost cZ . The value of the min-cost coupling between domains can be understood as a geometric-statistical quantification of their dissimilarity.
When both dX and dL are valid metrics and p ≥ 1, this ℓp combination defines a metric on the joint space Z. Here, however, we will often take dX to be a cosine-based dissimilarity, which does not strictly satisfy the triangle inequality. In such cases, dZ should be interpreted more generally as a ground cost rather than a true metric—a distinction that does not affect the validity of the OT formulation, which only requires nonnegative costs.
Geospatial Optimal Transport (G EO S P OT). Geospatial datasets contain both feature information (e.g., images or text) and the locations at which these features were collected, often stored as metadata. “Geospatial domains” can thus refer to distinct spatial units such as countries,
Throughout our experiments, we use the cosine distance dX (x, x′ ) = 1 − x⊤ x′ /∥x∥∥x′ ∥ between feature embeddings extracted from pretrained image or text models. For geographic distance dL , we consider two variants: (1) the raw geographic (arc) distance darc between the lat/lon 3
OT on the Map: Quantifying Domain Shifts in Geographic Space
per domain for training, we keep only countries with ≥1,000 data samples, resulting in a subset of 61,378 images from 19 domains.
coordinates, and (2) the cosine distance between pretrained location embeddings obtained from a location encoder. With this, we define the Geospatial Optimal Transport (G EO S P OT) distance between domains as Z G EO S P OT(Ds , Dt ) = min dZ (z, z ′ )p dπ(z, z ′ ). π∈Π(α,β)
4.2. Embeddings and Model Training We extract feature embeddings from image and text with commonly-used pretrained embedding models: a ResNet50 backbone pretrained on ImageNet (He et al., 2016), and BERT, a transformer-based language model (Devlin et al., 2019). We generate location embeddings from longitude and latitude coordinates using the pretrained SatCLIP and GeoCLIP location encoders. SatCLIP embeds geographic coordinates with spherical harmonics and is pretrained via a contrastive learning objective pairing satellite imagery with coordinates (Klemmer et al., 2025). GeoCLIP is another CLIP-based model that uses random Fourier features and hierarchical resolution to align locations with visual features from geo-tagged images (Vivanco et al., 2023).
Z×Z
(2) In practice, computing dZ for G EO S P OT requires two design choices: (1) the relative weighting of feature vs. location information (via λ in Equation (1)), and (2) the choice of geographic distance representation in computing dL . We explore both of these design choices in Section 5.
4. Experimental Setup 4.1. Datasets We conduct our experiments on three datasets that differ in data modality, scale, and the nature of their class distributions and domain shifts. Data preprocessing details are provided in the Appendix and code release.
We compute G EO S P OT dataset distances using the Python Optimal Transport (POT) library (Flamary et al., 2021; 2024). To improve efficiency, we use the entropically regularized Sinkhorn divergence instead of solving the exact OT problem, with regularization parameter ϵ = 0.01. For model training, we fine-tune pretrained ResNet50 encoders for image tasks and BERT models for text tasks, replacing the original classifier head with a linear layer sized to the target classes. Separate learning rates are used for the backbone and the new head, preserving pretrained representations while enabling faster adaptation in the task-specific layer.
Geo-YFCC. The Geo-YFCC dataset (Dubey et al., 2021) is a large-scale domain generalization benchmark consisting of more than 1.1 million geotagged samples of 1,261 classes from 62 different country domains, subsampled from the YFCC100M collection of Flickr images (Thomee et al., 2016). Each sample in the dataset has one or more associated labels. We convert this to single label classification by duplicating entries, consistent with the original work. The majority of samples also contain text information in the form of Flickr image description in the metadata. To explore robustness of G EO S P OT distances across visual and textual modalities, we use this dataset for two separate experimental conditions: one using the georeferenced image samples (Geo-YFCC-Image) and another using the georeferenced text captions (Geo-YFCC-Text).
5. Predicting Domain Transfer Performance We assess the quality of G EO S P OT distances by examining its correlation with out-of-distribution model performance of a trained classifier across different domain pairs. For each source-target domain pair (Ds , Dt ), we train two models (Ms , Mt ) on the respective training sets of Ds and Dt , and we evaluate both models on the test set of the target domain. We measure the relative change (∆) in test performance with respect to in-distribution training as
FMoW-Wilds. FMoW-Wilds is a classification benchmark emphasizing distribution shifts across spatial and temporal dimensions (Koh et al., 2021), adapted from the original FMoW (Functional Map of the World) dataset (Christie et al., 2018). FMoW-Wilds contains RGB satellite images at size 224 × 224 pixels, each labeled with one of 62 land use or building classes. We focus on geospatial distribution shifts and disregard the temporal component. We further restrict to countries with abundant training data spanning most categories for reliable training and evaluation. This selection yields a subset of 152,196 samples from 25 countries around the globe.
∆Ds ,Dt =
AccDt (Ms ) − AccDt (Mt ) × 100%, AccDt (Mt )
(3)
where AccDt (Ms ) represents performance of a model transferred from the source domain to the target domain, and AccDt (Mt ) represents in-sample performance of a model trained and tested on the target domain. This quantity, which is typically negative, can be interpreted as the penalty incurred when training on a source domain different from the target. Values closer to zero indicate better transferability, while larger negative values reflect poorer cross-domain generalization. Our goal is to estimate ∆Ds ,Dt with G EO S P OT distances, which depend only on the features and/or loca-
GeoDE. GeoDE is a geographically diverse classification dataset with 61,940 crowd-sourced images, evenly distributed across 40 common object classes and 6 global regions (Ramaswamy et al., 2023). To ensure sufficient data 4
OT on the Map: Quantifying Domain Shifts in Geographic Space
Algorithm 1 Source domain selection s Input: Source {D1s , . . . , DN } and target Dt datasets; number of source domains to select K ≤ N . Output: Set of source domains SK . I0 ← ⌈N ⌉; S0 ← ∅ for t = 1 to K do it ← arg min G EO S P OT St−1 ∪ {Dis }, Dt It ←
tions of the source and target domains (but not labels). To evaluate how well G EO S P OT distances correlate with domain transfer performance, we measure this association with Spearman’s rank correlation (ρ), and the coefficient of determination, (R2 ) of G EO S P OT distances with ∆Ds ,Dt across pairs of source and target domains.
i∈It−1
Figure 2 compares how well G EO S P OT distances computed from single modalities explain transfer degradation across source-target domain pairs. All plots exhibit negative correlation, i.e., larger G EO S P OT distances are associated with larger drops in test accuracy of target domains, consistently across datasets. For the Geo-YFCC-Image and GeoDE datasets, G EO S P OT with ResNet50 embeddings yields the highest magnitude ρ across the embedding types (|ρ| ≈ 0.71 and |ρ| ≈ 0.34, respectively). For these two datasets, this is closely matched by G EO S P OT with GeoCLIP embeddings, with |ρ| ≈ 0.70 for Geo-YFCC-Image and |ρ| ≈ 0.33 for GeoDE. Notably, G EO S P OT with GeoCLIP embeddings achieves the highest rank correlation in Geo-YFCC-Text and FMoW-Wilds (|ρ| ≈ 0.54 and |ρ| ≈ 0.65, respectively), indicating that GeoCLIP-based representations generalize well across modalities.
It−1 \ {it }; St ← St−1 ∪ {Dist }
of ResNet50 (image) features consistently yields a stronger |ρ| value than the location modality alone, indicating that image features provide useful information for domain transfer. In particular, we see that for the Geo-YFCC-Image and GeoDE datasets, using ResNet50 + GeoCLIP yields the strongest rank correlation for this dataset (|ρ| ≈ 0.74 for Geo-YFCC-Image, |ρ| ≈ 0.38 for GeoDE), which is notably stronger than either modality alone. In contrast, when location embeddings are informative for the task at hand, such as embeddings generated by GeoCLIP, the resulting location information complements the image information, as we conclude from a higher |ρ| value from ResNet50 + GeoCLIP. However, when location embeddings are less representative of spatial similarity, or less relevant for the task, incorporating them does not boost predictive performance.
G EO S P OT with GeoCLIP embeddings consistently serves as a reliable predictor of ∆Ds ,Dt across datasets, despite depending solely on location information. Notably, as a model pretrained on geotagged Flickr images, GeoCLIP still tracks transfer difficulty well in FMoW-Wilds, even though the task is predicting land use category from satellite images. This may suggest that GeoCLIP models encode human and environmental patterns that correlate with domain shifts in remote-sensing imagery through training on globally distributed and semantically meaningful data.
6. Constrained Dataset Selection We investigate whether G EO S P OT distances can guide data subset selection to improve model performance under a constrained training budget, a setting that mirrors common challenges in real-world geospatial ML deployment. Our central question is whether G EO S P OT distances can inform the choice of source domains for a given target. Intuitively, source domains with smaller G EO S P OT distances to the target domain are semantically more related, and thus training on these domains should yield models that generalize more effectively to the target distribution.
In comparison, G EO S P OT distances based on SatCLIP embeddings are informative but weaker (e.g., |ρ| ≈ 0.55 for Geo-YFCC-Image), because SatCLIP is pretrained with satellite imagery, a much more distinct image modality to Geo-YFCC samples than Flickr images, which GeoCLIP is pretrained on. By contrast, G EO S P OT results on geodesic distances demonstrate the weakest predictability (e.g., |ρ| ≈ 0.42 for both Geo-YFCC-Image and for GeoYFCC-Text), and with the geodesic metric, many pairs cluster at high G EO S P OT distances yet span a wide spread over performance change. This suggests purely geographic distances are much less suitable to predict performance drops for domain transfer, whereas G EO S P OT distances derived from semantically meaningful embedding spaces provide a stronger proxy for domain shifts.
To test this hypothesis, we design a greedy subset selection algorithm (Algorithm 1) that selects K source domains by iteratively minimizing the combined G EO S P OT distances to the target domain. At iteration t, the algorithm adds the domain that, when pooled with the t − 1 previously selected domains, yields the smallest overall G EO S P OT distance to the target. After selecting K domains, we uniformly sample equal amounts of training data from each source domain until the budget (e.g., 2, 000 samples) is reached. The model is then trained on the combined set, as described in Section 4.2 and evaluated on the target domain’s test set. We compare against two baselines under the same training budget: (1) global training, where the model uses data from all non-target domains (equivalent to setting K to the total
Table 1 additionally reports performance when we combine image/text and location modalities to compute G EO S P OT distances, using λ = 0.5 in Equation (1) (results for additional values of λ included in the appendix). Across all combinations of modalities for image datasets, the inclusion 5
OT on the Map: Quantifying Domain Shifts in Geographic Space
(a) Geo-YFCC-Image
(b) Geo-YFCC-Text
(c) FMoW-Wilds
(d) GeoDE Figure 2. G EO S P OT distances correlate with transfer performance (i.e., performance difference) between train and test domains, measured in a zero-shot transfer setting. G EO S P OT distances are computed with a single modality (λ = 1 for ResNet50/BERT, and λ = 0 for the location embeddings). Results are consistent across different embedding spaces (columns) and different datasets (rows). In the scatterplots, each point represents a source-target domain pair. For each plot, we also show the best-fit line and report Spearman’s rank correlation coefficient (ρ) and the coefficient of determination (R2 ).
6
OT on the Map: Quantifying Domain Shifts in Geographic Space Embedding modalities ResNet50/BERT GeoCLIP ResNet50/BERT + GeoCLIP SatCLIP ResNet50/BERT + SatCLIP Geodesic ResNet50/BERT + Geodesic
Geo-YFCC-Image |ρ|
R
2
0.71 0.70 0.74 0.55 0.67 0.42 0.59
0.51 0.49 0.56 0.30 0.45 0.18 0.31
Geo-YFCC-Text |ρ|
R
2
0.40 0.54 0.58 0.48 0.50 0.42 0.45
0.15 0.31 0.34 0.22 0.24 0.16 0.17
FMoW-Wilds
GeoDE
|ρ|
R
2
|ρ|
R2
0.46 0.65 0.62 0.49 0.56 0.24 0.36
0.14 0.41 0.29 0.25 0.28 0.09 0.15
0.34 0.33 0.38 0.24 0.28 0.17 0.25
0.19 0.08 0.15 0.07 0.10 0.02 0.05
Table 1. Correlation of single-modality and multi-modality G EO S P OT distances. Spearman correlation magnitude (|ρ|) and coefficient of determination (R2 ) measure how well variation in G EO S P OT distances explains variation in zero-shot source-target domain transfer difficulty (∆Ds ,Dt defined in Equation (3)). Rows correspond to different combinations of data modalities used to compute the G EO S P OT distances. Indented rows are those for which two distinct data modalities are used, i.e., 0 < λ < 1 in Equation (1).
Figure 3. G EO S P OT distances can guide design of training datasets that transfer well to a given target domain. We show zero-shot performance in the target domain, with models pretrained on subsets of size N = 2, 000, sampling train locations most similar to the target domain based on different G EO S P OT distances. Results are shown for the Geo-YFCC-Image dataset.
number of source domains), and (2) random subset training, where K source domains are selected uniformly at random and sampled in equal proportions.
the United States. For Brazil, G EO S P OT-GeoCLIP performs best overall, matching the geodesic-based selection at K = 1. For the United States, the closest domain under all distances is Canada, hence the matching results; for K = 2, G EO S P OT-GeoCLIP selection achieves the highest accuracy, while for K = 5, G EO S P OT-ResNet50 performs best, with both outperforming the global subset.
We evaluate Algorithm 1 on Geo-YFCC-Image and Geo-YFCC-Text datasets under varying conditions of data scarcity. Figure 3 shows the results for three target countries (China, Brazil, and the United States) using K ∈ {1, 2, 5} source domains under a total budget of N = 2, 000 data points for Geo-YFCC-Image. Results for Geo-YFCC-Text and for other budgets are provided in the Appendix. All experiments are run for five different random seeds for data sampling; we report the mean test accuracy across runs. For the random-subset baseline, the seeds are additionally used to uniformly sample K source domains.
Figure 4 visualizes the greedily selected domains obtained by minimizing the combined G EO S P OT distance to Brazil. GeoCLIP-based G EO S P OT distance identifies not only geographically close domains (e.g., Argentina, Colombia), but also some that are geographically distant but likely related in other ways (e.g., France, Portugal). Notably, the domains that minimize the combined distance are not necessarily the individually closest to the target; rather, they are collectively complementary in distribution, such that their union minimizes the overall G EO S P OT distance.
Across all target domains, selecting source domains according to any G EO S P OT distance consistently outperforms random selection. For China, domains chosen based on the ResNet50-based distances yield the best performance for K = 1, 2, and the strongest G EO S P OT-based method surpasses the global subset at K = 2, 5. Increasing K improves performance for China but offers only marginal gains for Brazil, and, interestingly, hurts performance for
7. Applicability Maps G EO S P OT distances exhibit strong explanatory power for cross-domain performance. To better understand their structure, we visualize them as global applicability maps: ge7
OT on the Map: Quantifying Domain Shifts in Geographic Space
Figure 4. Complementary—not nearest—domains form optimal pools that jointly minimize the combined G EO S P OT distance. Source domains selected by Algorithm 1 using GeoCLIPbased G EO S P OT distances for target domain Brazil in Geo-YFCCImage dataset. Points represent the combined G EO S P OT distances if that country were to be added to the source domains chosen at previous K values. Values below each selected domain show their individual G EO S P OT distances to Brazil when K = 1.
ographic heatmaps colored by the relative G EO S P OT distance from a reference domain (Figure 5). Regions with lower values (yellow/orange) correspond to domains that are closer in the joint feature-location space and thus more similar or transferable. Figure 5. Visualizing G EO S P OT distances can identify relevant domains for data-sourcing or deployment. Applicability maps for the United States (black, dotted) for different types of G EO S P OT distances on the Geo-YFCC Dataset. Color scales are normalized within each panel.
These maps support two complementary interpretations: 1. Transfer applicability: Given a model trained on a given domain, identify other spatial domains in which the model is expected to maintain its predictive performance
8. Discussion In this work, we introduced GeoSpatial Optimal Transport (G EO S P OT), a geographically aware distance measure that combines feature and location information to quantify dissimilarity between geospatial domains. Across four diverse geospatial datasets, G EO S P OT distances consistently predict cross-domain transfer difficulty. Distances based on image/text and pretrained location embeddings show substantially stronger explanatory power than raw geodesic distance alone. The performance of G EO S P OT distances based on location embeddings alone is particularly noteworthy, demonstrating that meaningful, task-agnostic estimates of geospatial domain transferability can be obtained even before any observations, features, or labels are collected. Beyond prediction, we show that G EO S P OT can guide training data selection for zero-shot domain adaptation and visualize where models are likely to transfer successfully—or benefit most from additional data—before any data acquisition occurs.
2. Data sourcing: Given a target domain of interest, identify other source domains whose data are likely to provide the most effective training signal for the target. With G EO S P OT distances, a practitioner who, for example, has a model trained in the United States could use Figure 5 to predict that their model could reliably transfer to countries such as Canada and Australia. A practitioner who wants to tackle a task within the United States, but has no training data available there, might also look at Figure 5 to determine which other countries to obtain training data from, to train a model that transfers best to the US. These applicability maps provide an interpretable, data-driven visualization of model generalization potential across geography. Derived from G EO S P OT distances and supported by the experimental evidence in Sections 5 and 6, they offer a principled way to assess where a model trained in one region can be reliably deployed, and which regions are most promising sources of transferable data for new tasks.
Our findings open several directions for future work. We focus on image and text classification, but extending 8
OT on the Map: Quantifying Domain Shifts in Geographic Space
G EO S P OT to a broader range of prediction tasks could further test its generality. In addition, our dataset selection experiments primarily demonstrate feasibility; future work could refine the selection algorithm to improve performance and scalability.
Damodaran, B. B., Flamary, R., Seguy, V., and Courty, N. An entropic optimal transport loss for learning deep neural networks under label noise in remote sensing images. Computer Vision and Image Understanding, 191:102863, 2020. Devlin, J., Chang, M.-W., Lee, K., and Toutanova, K. BERT: Pre-training of deep bidirectional transformers for language understanding. In Burstein, J., Doran, C., and Solorio, T. (eds.), Proceedings of the 2019 Conference of the North American Chapter of the Association for Computational Linguistics: Human Language Technologies, Volume 1 (Long and Short Papers), pp. 4171–4186, Minneapolis, Minnesota, June 2019. Association for Computational Linguistics. doi: 10.18653/v1/N19-1423. URL https://aclanthology.org/N19-1423/.
Acknowledgements This material is based upon work supported by the NSF Graduate Research Fellowship under Grant No. DGE 2040434. We would like to acknowledge use of Jetstream2 at Indiana University through allocation CIS240692 from the Advanced Cyberinfrastructure Coordination Ecosystem: Services & Support (ACCESS) program, which is supported by National Science Foundation grants #2138259, #2138286, #2138307, #2137603, and #2138296. DAM acknowledges the Chan Zuckerberg Initiative Foundation for establishing the Kempner Institute for the Study of Natural and Artificial Intelligence, and NSF Award No. 2229881, NSF AI Institute for Societal Decision Making (NSF AISDM).
Dimitrić, D., Risojević, V., and Simić, M. Nearest neighbor based out-of-distribution detection in remote sensing scene classification. In 2023 22nd International Symposium INFOTEH-JAHORINA (INFOTEH), pp. 1–4. IEEE, 2023.
References
Dosovitskiy, A., Beyer, L., Kolesnikov, A., Weissenborn, D., Zhai, X., Unterthiner, T., Dehghani, M., Minderer, M., Heigold, G., Gelly, S., Uszkoreit, J., and Houlsby, N. An image is worth 16x16 words: Transformers for image recognition at scale. ICLR, 2021.
Achille, A., Lam, M., Tewari, R., Ravichandran, A., Maji, S., Fowlkes, C. C., Soatto, S., and Perona, P. Task2Vec: Task embedding for meta-learning. In Proceedings of the IEEE/CVF international conference on computer vision, pp. 6430–6439, 2019.
Dubey, A., Ramanathan, V., Pentland, A., and Mahajan, D. Adaptive methods for real-world domain generalization. In IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), June 2021.
Alvarez-Melis, D. and Fusi, N. Geometric dataset distances via optimal transport. Advances in Neural Information Processing Systems, 33:21428–21439, 2020.
Ekim, B., Tadesse, G. A., Robinson, C., Hacheme, G., Schmitt, M., Dodhia, R., and Ferres, J. M. L. Distribution shifts at scale: Out-of-distribution detection in earth observation. In Proceedings of the Computer Vision and Pattern Recognition Conference, pp. 2265–2274, 2025.
Ansarifar, J., Wang, L., and Archontoulis, S. V. An interaction regression model for crop yield prediction. Scientific Reports, 11(1):17754, 2021. ISSN 2045-2322. doi: 10.1038/s41598-021-97221-7. URL https:// doi.org/10.1038/s41598-021-97221-7.
Fang, Z., Yang, Y., Li, Z., Li, W., Chen, Y., Ma, L., and Du, Q. Confident learning-based domain adaptation for hyperspectral image classification. IEEE Transactions on Geoscience and Remote Sensing, 60:1–16, 2022.
Ben-David, S., Blitzer, J., Crammer, K., and Pereira, F. Analysis of representations for domain adaptation. Advances in neural information processing systems, 19, 2006. Christie, G., Fendley, N., Wilson, J., and Mukherjee, R. Functional map of the world. In CVPR, 2018.
Federici, M., Tomioka, R., and Forré, P. An informationtheoretic approach to distribution shifts. In Ranzato, M., Beygelzimer, A., Dauphin, Y., Liang, P., and Vaughan, J. W. (eds.), Advances in Neural Information Processing Systems, volume 34, pp. 17628–17641. Curran Associates, Inc., 2021. URL https://proceedings.neurips. cc/paper_files/paper/2021/file/ 93661c10ed346f9692f4d512319799b3-Paper. pdf.
Courty, N., Flamary, R., Habrard, A., and Rakotomamonjy, A. Joint distribution optimal transportation for domain adaptation. Advances in neural information processing systems, 30, 2017. Crasto, R. Robustness to geographic distribution shift using location encoders. arXiv preprint arXiv:2503.02036, 2025. 9
OT on the Map: Quantifying Domain Shifts in Geographic Space
Flamary, R., Courty, N., Gramfort, A., Alaya, M. Z., Boisbunon, A., Chambon, S., Chapel, L., Corenflos, A., Fatras, K., Fournier, N., Gautheron, L., Gayraud, N. T., Janati, H., Rakotomamonjy, A., Redko, I., Rolet, A., Schutz, A., Seguy, V., Sutherland, D. J., Tavenard, R., Tong, A., and Vayer, T. POT: Python optimal transport. Journal of Machine Learning Research, 22(78):1–8, 2021. URL http: //jmlr.org/papers/v22/20-451.html.
Le Bellier, G. and Audebert, N. Detecting out-ofdistribution Earth observation images with diffusion models. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pp. 481–491, 2024. Lin, Y.-X., Tan, D. S., Cheng, W.-H., Chen, Y.-Y., and Hua, K.-L. Spatially-aware domain adaptation for semantic segmentation of urban scenes. In 2019 IEEE International Conference on Image Processing (ICIP), pp. 1870–1874. IEEE, 2019.
Flamary, R., Vincent-Cuaz, C., Courty, N., Gramfort, A., Kachaiev, O., Quang Tran, H., David, L., Bonet, C., Cassereau, N., Gnassounou, T., Tanguy, E., Delon, J., Collas, A., Mazelet, S., Chapel, L., Kerdoncuff, T., Yu, X., Feickert, M., Krzakala, P., Liu, T., and Fernandes Montesuma, E. POT python optimal transport (version 0.9.5), 2024. URL https://github.com/PythonOT/ POT.
Linardos, V., Drakaki, M., Tzionas, P., and Karnavas, Y. L. Machine learning in disaster management: Recent developments in methods and applications. Machine Learning and Knowledge Extraction, 4(2):446–473, 2022. ISSN 2504-4990. doi: 10.3390/make4020020. URL https: //www.mdpi.com/2504-4990/4/2/20.
Gawlikowski, J., Saha, S., Kruspe, A., and Zhu, X. X. Outof-distribution detection in satellite image classification. In RobustML Workshop at ICLR 2021, pp. 1–5. ICLR, 2021.
Lynch, J. and Wookey, S. Leveraging domain adaptation for low-resource geospatial machine learning. arXiv preprint arXiv:2107.04983, 2021.
He, K., Zhang, X., Ren, S., and Sun, J. Deep residual learning for image recognition. In 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 770–778, 2016. doi: 10.1109/CVPR.2016.90.
Makkar, N., Yang, L., and Prasad, S. Adversarial learning based discriminative domain adaptation for geospatial image analysis. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 15:150–162, 2022. doi: 10.1109/JSTARS.2021.3132259.
Hu, K., Rahman, A., Bhrugubanda, H., and Sivaraman, V. HazeEst: Machine learning based metropolitan air pollution estimation from fixed and mobile sensors. IEEE Sensors Journal, 17(11):3517–3525, 2017. doi: 10.1109/ JSEN.2017.2690975.
Martin Sudmanns, Dirk Tiede, H. A. and Lang, S. Assessing global Sentinel-2 coverage dynamics and data availability for operational Earth observation (EO) applications using the EO-Compass. International Journal of Digital Earth, 13(7):768–784, 2020. doi: 10.1080/ 17538947.2019.1572799. URL https://doi.org/ 10.1080/17538947.2019.1572799.
Ismael, S. F., Kayabol, K., and Aptoula, E. Unsupervised domain adaptation for the semantic segmentation of remote sensing images via one-shot image-to-image translation. IEEE Geoscience and Remote Sensing Letters, 20:1–5, 2023.
Meyer, H. and Pebesma, E. Predicting into unknown space? Estimating the area of applicability of spatial prediction models. Methods in Ecology and Evolution, 12(9):1620– 1633, 2021.
Kifer, D., Ben-David, S., and Gehrke, J. Detecting change in data streams. In VLDB, volume 4, pp. 180–191. Toronto, Canada, 2004.
Nachmany, Y. and Alemohammad, H. Detecting roads from satellite imagery in the developing world. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops, pp. 83–89, 2019.
Klemmer, K., Rolf, E., Robinson, C., Mackey, L., and Rußwurm, M. SatCLIP: Global, general-purpose location embeddings with satellite imagery. AAAI, 2025.
Ramaswamy, V. V., Lin, S. Y., Zhao, D., Adcock, A. B., van der Maaten, L., Ghadiyaram, D., and Russakovsky, O. GeoDE: a geographically diverse evaluation dataset for object recognition. In NeurIPS Datasets and Benchmarks, 2023.
Koh, P. W., Sagawa, S., Marklund, H., Xie, S. M., Zhang, M., Balsubramani, A., Hu, W., Yasunaga, M., Phillips, R. L., Gao, I., Lee, T., David, E., Stavness, I., Guo, W., Earnshaw, B. A., Haque, I. S., Beery, S., Leskovec, J., Kundaje, A., Pierson, E., Levine, S., Finn, C., and Liang, P. WILDS: A benchmark of in-the-wild distribution shifts. In International Conference on Machine Learning (ICML), 2021.
Redko, I., Courty, N., Flamary, R., and Tuia, D. Optimal transport for multi-source domain adaptation under target shift. In The 22nd International Conference on artificial intelligence and statistics, pp. 849–858. PMLR, 2019. 10
OT on the Map: Quantifying Domain Shifts in Geographic Space
Redko, I., Vayer, T., Flamary, R., and Courty, N. Co-optimal transport. Advances in neural information processing systems, 33(17559-17570):2, 2020. Rolf, E., Klemmer, K., Robinson, C., and Kerner, H. Position: mission critical - satellite data is a distinct modality in machine learning. In Proceedings of the 41st International Conference on Machine Learning, ICML’24. JMLR.org, 2024. Shankar, S., Halpern, Y., Breck, E., Atwood, J., Wilson, J., and Sculley, D. No classification without representation: Assessing geodiversity issues in open data sets for the developing world. arXiv preprint arXiv:1711.08536, 2017. Tan, Y., Li, Y., and Huang, S.-L. Otce: A transferability metric for cross-domain cross-task representations. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp. 15779–15788, 2021. Thomee, B., Shamma, D. A., Friedland, G., Elizalde, B., Ni, K., Poland, D., Borth, D., and Li, L.-J. YFCC100M: the new data in multimedia research. Commun. ACM, 59(2):64–73, January 2016. ISSN 0001-0782. doi: 10.1145/2812802. URL https://doi.org/10. 1145/2812802. Tobler, W. R. A computer movie simulating urban growth in the detroit region. Economic Geography, 46(sup1): 234–240, 1970. doi: 10.2307/143141. URL https: //doi.org/10.2307/143141. Vivanco, V., Nayak, G. K., and Shah, M. GeoCLIP: Clipinspired alignment between locations and images for effective worldwide geo-localization. In Advances in Neural Information Processing Systems, 2023. Yao, H., Yang, X., Pan, X., Liu, S., Koh, P. W., and Finn, C. Improving domain generalization with domain relations. arXiv preprint arXiv:2302.02609, 2023. Yurochkin, M., Claici, S., Chien, E., Mirzazadeh, F., and Solomon, J. M. Hierarchical optimal transport for document representation. Advances in neural information processing systems, 32, 2019. Zhu, Y., Kiros, R., Zemel, R., Salakhutdinov, R., Urtasun, R., Torralba, A., and Fidler, S. Aligning books and movies: Towards story-like visual explanations by watching movies and reading books. In The IEEE International Conference on Computer Vision (ICCV), December 2015.
11
OT on the Map: Quantifying Domain Shifts in Geographic Space
A. Optimal Transport framework
For Geo-YFCC-Image dataset, after removing samples with unreadable images, we obtain 1,809,363 data samples in total (including duplicates from the single-label conversion).
To compute G EO S P OT distances, we use the Sinkhorn divergence method, an entropically regularized approximation that is computationally more efficient than solving the exact Optimal Transport problem. The entropic optimal transport problem, given regularization parameter ϵ, is formulated as Z min cZ (z, z ′ )dπ(z, z ′ ) π∈Π(α,β) Z×Z Z +ϵ π(z, z ′ ) log π(z, z ′ )dπ(z, z ′ ).
For the Geo-YFCC-Text dataset, we compile text samples by combining the title and description fields. We remove any samples with no text in either of these fields. We also remove any URLs and normalize whitespace to a single whitespace. B.1.2. FM OW-W ILDS
Z×Z
Function Map of the World is a large dataset of highresolution satellite images collected around the globe for classification of buildings and land use (Christie et al., 2018). The Wilds benchmark further adapts this dataset into domain adaptation tasks with focus on spatial and temporal distribution shifts (Koh et al., 2021).
Sinkhorn divergence corrects for the regularization-induced bias of entropic OT by subtracting self-similarity terms, and is defined as 1 1 Sϵ (α, β) = OTϵ (α, β) − OTϵ (α, α) − OTϵ (β, β), 2 2
The FMoW-Wilds dataset contains 523,846 RGB images with associated spatiotemporal metadata, including latitude, longitude, country_code, and year. Temporally, FMoW-Wilds spans the years 2002-2018. Because we focus on geographic domains, we restrict the data to 2016-2017 to minimize the temporal distribution shifts. Spatially, FMoW-Wilds primarily defines domains at the continental level (Asia, Europe, Africa, the Americas, and Oceania). Due to substantial intra-continental variability and the limited number of continental domains, we instead define geographic domains at the country or region level, where more specialized traits and distributions may be observed beucase of geographic, cultural, and socioeconomic factors. To ensure there is sufficient training data and class coverage, we select the 25 countries or regions with the most training samples by country_code, and this subset contains 152,196 image samples in total.
which satisfies Sϵ (α, α) = 0 for all α and preserves several geometric properties of true OT distances. In our experiments, we compute all OT-based distances using the POT (Python Optimal Transport) library (Flamary et al., 2021; 2024). We set the entropic regularization parameter to ϵ = 0.01, and we use uniform sample weights for both the source and target domains. For numerical stability, we apply max normalization to the cost matrix for each source-target domain pair, dividing all costs by the largest value observed among any pair of elements across the two domains.
B. Experiment Details B.1. Datasets In this section, we discuss the preprocessing steps we apply to obtain the data used for our experiments.
The FMoW-Wilds dataset is originally divided into train, validation, test, and sequestered splits. We use the official FMoW-wilds train, validation, and test splits for our experiments.
B.1.1. G EO -YFCC The Geo-YFCC dataset consists of more than 1.1 million geotagged samples (Dubey et al., 2021). Each sample includes an image, title, description, and user_tags. Labels are derived from the user_tags field, which may contain more than one label per sample. Following the methodology of (Dubey et al., 2021), we expand this into a single-label dataset, duplicating samples that have more than one user_tag to generate instances for each label. We use the original train and test splits and partition a portion of the training data into a validation set. Within each geographic domain, the size of train, validation, and test set is approximately 6:2:2. When splitting our data into the train-validation-test partitions, we ensure that no instance appears in more than one split to prevent data leakage.
B.1.3. G EO DE The GeoDE dataset contains 61,940 images with location metadata, including gps_position, region, and ip_country (Ramaswamy et al., 2023). We use the country metadata to partition the dataset into 42 country-level domains. After removing countries with fewer than 1,000 samples, we retain 19 domains spanning different regions and continents around the globe, yielding a cleaned subset of 61,379 images. We then randomly split the cleaned dataset into train, validation, and test sets using a 6:2:2 ratio.
12
OT on the Map: Quantifying Domain Shifts in Geographic Space
Setting
Image Classification
Text Classification
Optimizer Weight decay Scheduler Epochs Early stopping
1 × 10−5 for backbone, 1 × 10−4 for classification head Adam 1 × 10−4 Cosine annealing (ηmin = 1 × 10−6 ) 20 Patience 5, start at epoch 10
AdamW 0.01 Cosine (γ = 0.1) 50 Patience 10, start at epoch 20
Train batch size Eval batch size
64 512
64 512
Learning rate
2 × 10−5
Table 2. Training hyperparameters used for image and text classification tasks.
B.2. Distance Computation
in Table 2.
We compute G EO S P OT distances using embeddings from several pretrained models to encode information from different modalities. For image embeddings, we use ResNet50 models initialized with ImageNet-1K pretrained weights (He et al., 2016); for text embeddings, we use the bert-based-uncased model, which is pretrained on BookCorpus (Zhu et al., 2015) and English Wikipedia. For location embeddings, we use the location encoders from SatCLIP and GeoCLIP models. SatCLIP has multiple pretrained checkpoints that combine different vision backbones with varying spatial resolution L, where L denotes the number of Legendre polynomials used in the sphericalharmonics location encoding (Klemmer et al., 2025). In our experiments, we use the SatCLIP checkpoint with a ResNet50 backbone and spatial resolution L = 40, which yields higher-resolution, fine-grained location embeddings. For GeoCLIP, we use the pretrained model with ViT-L/14 vision backbone (Vivanco et al., 2023).
C. Results C.1. Ablation Studies We further conduct ablation studies to assess how the choice of backbone models used for domain transfer can affect our results. Figure 6 reports the correlation between G EO S P OT distances and zero-shot transfer performance using ViTSmall models for image classification on the Geo-YFCCImage and FMoW-Wilds datasets. The observed trends closely match with the results with ResNet50 transfer performance in Figure 2. C.2. Combined G EO S P OT Distances In this section, we study the effect of varying λ in Equation (1). Table 1 reports results for λ = 0.5, and we also evaluate λ at evenly spaced values between 0 and 1 in increments of 0.1, i.e., λ ∈ {0.0, 0.1, 0.2, . . . , 0.9, 1.0}.
B.3. Model Training
Across all datasets, we observe that selecting an appropriate value of λ yields an improvement in the rank correlation coefficient (ρ). The optimal value of λ varies by dataset and appears to depend on the relative scale of the two distance components (the image/text embedding distances, dX , and the location-based distances, dL ). For instance, in the GeoYFCC-Text dataset, the BERT-derived embedding distances span a smaller range of values compared to the corresponding location distances (see Figure 2). As a result, larger values of λ tend to perform better. Developing principled methods for selecting an optimal λ to improve the explanatory power of G EO S P OT distances is an interesting direction for future work.
Image Classification We evaluate both ResNet50 (with around 25.6 million parameters) (He et al., 2016) and ViT-Small (with around 22.1 million parameters) (Dosovitskiy et al., 2021) for image classification experiments, covering convolutional neural network and vision transformer architectures. For ResNet50, we initialize the model with ImageNet-1K pretrained weights from the torchvision library. For ViT-Small models, we use the vit small patch16 224 backbone and load model weights pretrained on ImageNet-21K and fine-tuned on ImageNet-1K. Text Classification We train BERT models for text classification tasks. We use BertForSequenceClassification models from HuggingFace and load bert-base-uncased pretrained checkpoint.
C.3. Constrained Dataset Selection We provide additional results for the constrained dataset selection experiments under larger budgets. For the GeoYFCC-Image dataset, we report results for budgets N =
We report hyperparameters used for all training experiments 13
OT on the Map: Quantifying Domain Shifts in Geographic Space
(a) Geo-YFCC-Image
(b) FMoW-Wilds Figure 6. Correlation between G EO S P OT distances and zero-shot transfer performance with ViT-Small models on Geo-YFCCImage and FMoW-Wilds.
(a) Geo-YFCC-Image
(b) Geo-YFCC-Text
(c) FMoW
(d) GeoDE
Figure 7. Rank Correlation (|ρ|) across datasets as a function of the weighting parameter λ. Each panel shows how |ρ| changes as the image/text and location-based information are combined, weighted by λ.
5, 000 and 10, 000 in Figure 8, in addition to N = 2, 000 reported in Section 6. For the Geo-YFCC-Text dataset, we report results for budgets N = 2, 000, 5, 000 and 10, 000 in Figure 9.
with G EO S P OT distances with an appropriate choice of K either matches or outperforms the global baseline. For constrained dataset selection on the Geo-YFCC-Text dataset (Figure 9), increasing the number of selected domains (K) leads to improved performance for China, but yields little or no improvement for Brazil or the United States. Selecting with respect to G EO S P OT-BERT dis-
Figure 8 shows that selecting the dataset with respect to G EO S P OT distances consistently outperform the random sampling baseline. For these additional budgets, selecting 14
OT on the Map: Quantifying Domain Shifts in Geographic Space
(a) Budget N = 5,000
(b) Budget N = 10,000 Figure 8. Constrained dataset selection for Geo-YFCC-Image: Zero-shot performance on the target domain with models pretrained on subsets selected via different G EO S P OT distances.
tances frequently outperforms other dataset selection methods, although for the United States at K = 2, G EO S P OTGeoCLIP and G EO S P OT-SatCLIP achieve higher accuracy. C.4. Applicability Maps As mentioned in Section B.1, the Geo-YFCC-Image and Geo-YFCC-Text datasets differ in samples due to additional data cleaning for the text dataset. As a result, the corresponding G EO S P OT distances differ slightly between the two datasets. In the plotting of the applicability maps, we use the Geo-YFCC-Text G EO S P OT distances to plot all maps except for the ResNet50 map, for which we use the Geo-YFCC-Image dataset. We show additional applicability maps in Figure 10 and Figure 11. Because the maps vary substantially across countries, we render each set of maps as a larger figure to ensure maps can be viewed at sufficient resolution. Specifically, we show applicability maps for the United States, Brazil, China, and France across all G EO S P OT distances. As previously mentioned, we normalize the color scale for each embedding type.
15
OT on the Map: Quantifying Domain Shifts in Geographic Space
(a) Budget N = 2,000
(b) Budget N = 5,000
(c) Budget N = 10,000 Figure 9. Constrained dataset selection for Geo-YFCC-Text: Zero-shot performance on the target domain with models pretrained on subsets selected via different G EO S P OT distances.
16
OT on the Map: Quantifying Domain Shifts in Geographic Space
Figure 10. Applicability maps for the United States (left) and Brazil (right).
17
OT on the Map: Quantifying Domain Shifts in Geographic Space
Figure 11. Applicability maps for China (left) and France (right).
18