Figure 3 - available via license: Creative Commons Zero 1.0
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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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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 an...
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... µí±í µí±í µí±í µí± (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 í µí±¤í µí±í µí±í µí± (Mac Aodha et al., 2019) produces rather over-generalized species distributions due to the fact that it is a single-scale location encoder. í µí± í µí±ℎí µí±í µí±í µí±í µí° ¶+ (our model) produces a more compact and finegrained 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 í µí±í µí±í µí±í µí± (Mai et al., 2020b) are between these two. However, í µí±í µí±í µí±í µí± 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, í µí±¤í µí±í µí±í µí± 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. ...
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... example, in the white-browed wagtail example, í µí±¤í µí±í µí±í µí± 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. í µí±í µí±í µí±í µí± is better than í µí±¤í µí±í µí±í µí± but still produces a distribution covering the Southwest of China. ...
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... µí± í µí±ℎí µí±í µí±í µí±í µí° ¶+ 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 í µí±¤í µí±í µí±í µí± produces an over-generalized distribution (see Figure 13ab). í µí±í µí±í µí±í µí± 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 í µí±¤í µí±í µí±í µí± produces an over-generalized distribution (see Figure 13ab). í µí±í µí±í µí±í µí± produces a better distribution estimation (see Figure 13ac) but it still has a over-generalized issue. Our í µí± í µí±ℎí µí±í µí±í µí±í µí° ¶+ produces the best estimation among these three modelsa compact distribution estimation covering the exact West Africa region (See Figure 13ad). ...
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... µí±í µí±í µí±í µí± produces a better distribution estimation (see Figure 13ac) but it still has a over-generalized issue. Our í µí± í µí±ℎí µí±í µí±í µí±í µí° ¶+ produces the best estimation among these three modelsa compact distribution estimation covering the exact West Africa region (See Figure 13ad). ...
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... estimated spatial distributions of these four land use types from three location encoders, i.e., í µí±¤í µí±í µí±í µí±, í µí±í µí±í µí±í µí±, and í µí±í µí± í µí± are visualized. Just like what we see from Figure 13, similar observations can be made. í µí±¤í µí±í µí±í µí± usually produces over-generalized distributions. ...
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