Figure 3 - uploaded by Gengchen Mai
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An illustration for map projection distortion: (a)-(d): Tissot indicatrices for four projections. The equal area circles are putted in different locations to show how the map distortion affect its shape.
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We propose a general-purpose spherical location encoder, Sphere2Vec, which, as far as we know, is the first location encoder which aims at preserving spherical distance. • We provide a theoretical proof about the spherical-distance-kept nature of Sphere2Vec. • We provide theoretical proof to show why the previous 2D location encoders and NeRF-style...
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... Mai et al., 2020b) is between the two. For more examples, please see Figure 13 and 14. ...
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... are no map projection can preserve distances at all direction. The so-called equidistant projection can only preserve distance on one direction, e.g., the longitude direction for the equirectangular projection (See Figure 3d), while the conformal map projections (See Figure 3a) can preserve directions while resulting in a large distance distortion. For a comprehensive overview of map projections and their distortions, see Mulcahy and Clarke (2001). ...
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... are no map projection can preserve distances at all direction. The so-called equidistant projection can only preserve distance on one direction, e.g., the longitude direction for the equirectangular projection (See Figure 3d), while the conformal map projections (See Figure 3a) can preserve directions while resulting in a large distance distortion. For a comprehensive overview of map projections and their distortions, see Mulcahy and Clarke (2001). ...
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... have a better understanding of how well different location encoders model the geographic prior distributions of different image labels, we use iNat2018 and fMoW data as examples and plot the predicted spatial distributions of different example species/land use types from different location encoders, and compare them with the training sample locations of the corresponding species or land use types (see Figure 13 and 14). ...
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... Figure 13, we can see that (Mac Aodha et al., 2019) produces rather over-generalized species distributions due to the fact that it is a single-scale location encoder. + (our model) produces a more compact and fine-grained distribution in each geographic region, especially in the polar region and in data-sparse areas such as Africa and Asia. ...
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... distributions produced by (Mai et al., 2020b) are between these two. However, has limited spatial distribution modeling ability in the polar area (e.g., Figure 13d and 13s) as well as data-sparse regions. ...
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... example, in the white-browed wagtail example, produces an over-generalized spatial distribution which covers India, East Saudi Arabia, and the Southwest of China (See Figure 13m). However, according to the training sample locations (Figure 13l), white-browed wagtails only occur in India. is better than but still produces a distribution covering the Southwest of China. ...
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... example, in the white-browed wagtail example, produces an over-generalized spatial distribution which covers India, East Saudi Arabia, and the Southwest of China (See Figure 13m). However, according to the training sample locations (Figure 13l), white-browed wagtails only occur in India. is better than but still produces a distribution covering the Southwest of China. + produces the best compact distribution estimation. ...
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... produces the best compact distribution estimation. Similarly, for the red-striped leafwing, the sample locations are clustered in a small region in West Africa while produces an over-generalized distribution (see Figure 13ab). produces a better distribution estimation (see Figure 13ac) but it still has a over-generalized issue. ...
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... for the red-striped leafwing, the sample locations are clustered in a small region in West Africa while produces an over-generalized distribution (see Figure 13ab). produces a better distribution estimation (see Figure 13ac) but it still has a over-generalized issue. Our + produces the best estimation among these three models -a compact distribution estimation covering the exact West Africa region (See Figure 13ad). ...
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... a better distribution estimation (see Figure 13ac) but it still has a over-generalized issue. Our + produces the best estimation among these three models -a compact distribution estimation covering the exact West Africa region (See Figure 13ad). ...
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... Notable examples include the works of [4] and [5], which utilize the spatial context as geographic priors and loss function components respectively to refine the learning tasks. On the other hand, the works such as [6] and [7], encode the spatial information into semantic embeddings, providing more flexibility of incorporating such information into the deep learning models. Despite their effectiveness, these methods often fall short in addressing the complex interactions between locations and their intrinsic spatial properties. ...
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... This geo-encoded CNN model was later applied to global-scale vegetation canopy height mapping with satellite imagery [38], where the geolocations served as a prior. Other state-of-theart geolocation encoders include Space2Vec [39], Sphere2Vec [40], PE-GNN [41], and a more recent algorithm that is based on the spherical harmonic basis functions [42]. Multi-scale sinusoidal functions are favoured in building these encoders (e.g., [39], [42]), thanks to their merits of being bounded in value, infinitely extended in space, and possessing a multiresolution scalability. ...
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... Secondly, location encoding of geolocation data [45,18], one of the key components of SRL, has been proved useful for various geospatial tasks such as fine-grained species recognition [42,51], satellite image classification [5,53,19,35], weather forecasting [8,37], and so on. However, no benchmark has been developed to systematically evaluate the location encoders' impact on model performance in tasks with diverse task setups, dataset sizes, and geographic coverage. ...
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... Fostering cross-disciplinarity: Our community has shown that spatially explicit machine learning models do not only increase the accuracy of (Geo)AI models when applied to geographic data but also inform and improve more general models in various domains [12,14,13,15,5,23,20], e.g., leading to a broad interest in location encoding methods outside of GeoAI. Conversely, researchers from the broader AI community [16] try to utilize notions such as the MAUP to study problematic coverage and representation biases in training data for image-based foundation models. ...
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... Representing a location using its neighbor fuzzy locations (Li et al. 2020) or a Markov transition matrix (Wang et al. 2019) can be regarded as a type of fixed-location encoding method. In contrast, methods such as Space2Vec (Mai et al. 2020) and Sphere2Vec (Mai et al. 2023) focus on preserving the distance relationship between locations while making the vectors trainable based on different downstream tasks. In this study, we introduce a location encoding method that suits discrete location representation methods. ...
