GeoVeX: Geospatial Vectors with Hexagonal Convolutional Autoencoders
Authors: Daniele Donghi
Anne Morvan
Venue: Submitted to ICLR 2023 (2023)
Keywords: Representation learning
Geospatial Embedding
Convolutional Autoencoders on hexagonal grids
OpenStreetMap
H3 hexagons

Abstract: We introduce a new geospatial representation model called GeoVeX to learn global vectors for all geographical locations on Earth land cover (200+ million embeddings). GeoVeX is built on a novel model architecture named Hexagonal Convolutional Autoencoders (HCAE) combined with a Zero-Inflated Poisson (ZIP) reconstruction layer, applied to a grid of Uber's H3 hexagons, each one described by the histogram of OpenStreetMap (OSM) geographical tags occurrences. GeoVeX is novel on three aspects: 1) it produces the first geospatial vectors trained on worldwide open data, enabling wide adoption on every downstream tasks which may benefit from enriched geographical information, requiring only location coordinates; 2) it represents the first use of hexagonal convolutions within autoencoder architectures, to learn latent representations of an hexagonal grid; and 3) it introduces a spatial-contextual Poisson reconstruction loss function for autoencoder architectures suitable for training on sparse geographical count data. Experiments demonstrate that GeoVeX embeddings can improve upon state-of-the-art geospatial location representations on two different downstream tasks: price prediction in the travel industry and hyperlocal interpolation of climate data from weather stations. 

Under review as a conference paper at ICLR 2023
GEOVEX: GEOSPATIAL VECTORS WITH HEXAGONAL CONVOLUTIONAL AUTOENCODERS
Anonymous authors Paper under double-blind review
ABSTRACT
We introduce a new geospatial representation model called GeoVeX learn global vectors for all geographical locations on Earth land cover. GeoVeX is built on novel model architecture named Hexagonal Convolutional Autoencoders (HCAE) combined with Zero-Inflated Poisson (ZIP) reconstruction layer, ap- plied to a grid of Uber's H3 hexagons, each one described by the histogram of OpenStreetMap (OSM) geographical tags occurrences. GeoVeX is novel two aspects: first, it produces pre-trained task-agnostic geospatial vectors with H3 and OSM that are, for the first time, contextualized on the neighboring hexagons features, by leveraging an hexagonal convolutional autoencoder applied on an H3/OSM grid centered the location to embed; secondly, it introduces zero- inflated Poisson autoencoder reconstruction layer, to adapt a standard autoencoder network to train on sparse geographical count data distributed on an hexagonal grid. Experiments demonstrate that GeoVeX embeddings improve upon two state- of-the-art geospatial location representations models, Hex2Vecc and Space2 on two different downstream tasks: worldwide listings price prediction in the travel industry, and hyperlocal interpolation of climate data from weather stations. The qualitative analysis of the latent representation structures learnt by GeoVeX show- cases the higher quality of the geographical structures learnt by the geographically contextualized embeddings learnt by GeoVeX.
INTRODUCTION
Entity embedding is ubiquitous in a variety of Machine Learning tasks thanks to its many advan- tages: it captures the semantics of each entity in the context of a given domain; it enables transfer learning to different related tasks; it reduces the sparsity of the entity representation and compresses the feature space. In NLP domain, global word embedding models, such as Word2Vec (Mikolov al. 2013), GloVe (Pennington et al. 2014) and BERT (Devlin et al. (019)) have been successful at capturing the word semantics of big open-source vocabularies (e.g. Wikipedia, Gigaword) and are used to transfer learning multiple downstream tasks, such as sentiment analysis (Tang al. 2014
Deho et al. 2018 Alammudi & Alghamdi]] 202I), question retrieval (Zhou et al.) (015). and medical semantics Wang al.] 2018). Similar approaches inspired by NLP have been since then proved to be useful many industrial domains, where multiple models have been proposed for learning the latent representations of entities specific to an industry, such as Product2 Vec (Biswas et al.) 2017)
and User2Ves Vec (Hallac et al. 2019) in e-commerce, or Wave2Vec (Baevski et al. 2020) in speech representation, just to name few.
In comparison, in the field of Geographic Information Science (GIS), a global set of task-agnostic embeddings for geographical space representation can benefit multiple domains and use cases, such as: price prediction for houses (Wang et al.] (20TT) hotel rooms (Kisilevich et al, 2013). and vaca- tion homes (Islam et al., 20222 Pradip Suthar 2022); interpolation of climate variables such as temperature and pressure (Wu & Li 2013); computer vision tasks with geo-located images (Berg ct al. 2014). These tasks, just to name a few, have in common the application some transforma- tions to the spatial coordinates, but they do not leverage the spatial distribution of geo entities (such as parks, water, beach, buildings, streets, bars, etc.), which convey a more rich information of the geographical context. Besides, in terms of modelling, previous approaches to learn geospatial em- beddings have a set of limitations, such as being non non-contextual, task-specific and/or eepciic (Sec. 2 that we address with novel model architecture and loss function formulation (Sec. (.6).

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[Without
Task
Task
Features
Model
[With Geo
Task Features
lat/Ing
Look-up Pre-Trained
Task Features + GeoVeX Embedding
Task Model
GeoVeX Embeddings
Figure I: Workflow to use GeoVeX embeddings in downstream tasks: the task features are expanded by simply concatenating the GeoVeX embedding associated to the H3 hexagon corresponding the latitude (lat) and longitude (Ing) coordinates of each task item, without retraining the embeddings.
Our new approach to learn the geospatial embedding of each location on Earth, based on nearby geographical entities, aims to pre-train a finite set of embeddings that can cover the whole Earth, so that they can be stored and used with ease extra features in any Machine Learning task where entities have latitude and longitude coordinates. The general workflow is summarized in Fig. [ To achieve the goal of wide adoption multiple downstream tasks, we leverage Uber Hexagonal Hierarchical Spatial Index grid system named H33 to spatially index the data coordinates into small regions of approximately the same size, since H3 minimizes map distortion. A pair of coordinates (i,j) is thus represented by unique H3 hexagonal id for which we learn GeoVeX embedding.
To learn Geo embeddings that have a geographical semantic, we associate each H3 hexagon to the geographical tags of the entities obtained from OpenStreetMap (OSM) OSM is project that creates and distributes free worldwide geographic data, and, as of January 2022, has =7 billion nodes and #4 million map changes per day. This makes it the equivalent of Wikipedia for word embeddings: a massive, scalable, and information-rich global open dataset for creating and updating global embeddings. In particular, OSM contains nodes, ways and relations, which together can be transformed to points, lines and polygons, each one characterized by a set of semantic tags, such as amanity:bar motorayym forert By intersecting these OSM entities with the H3 hexagons, and by using a Or--Ods-oodss (BOW) model on their tags, each hexagon can be sparsely described by a K -idimensionna histogram vector, where K the size of a subset of the vocabulary of OSM geographical tags, where each element represents the number of times an entity with the respective tag is contained or intersects the hexagon itself. This information needs then to be properly aggregated to produce an embedding while, at the same time, taking into account the information from neighboring hexagons, which provide the geographical context. This concept follows the first law of geography: everything is related to everything else, but near things are more related than distant things (Tobler] 1970). The convolution operation, borrowed from Computer Vision, presents in this domain challenges address: 1) not square, but hexagonal grids, and 2) different distribution of each "channel": not dense pixel values, but highly sparse counts. Geo VeX model aims bridge the gap of convolutional neural networks usage on these hexagonal grids described by sparse counts.
In summary, the contributions of our work are:
1. the GeoVeX architecture design to learn task-agnostic pre-trained location embeddings with H3 and OSM that are for the first time contextualized the neighboring hexagons. We demonstrate their expressive power qualitatively, by using an analysis of the cosine similarities (Sec. 4.1.. and quantitatively, by adding the embeddings to the feature set of and
two downstream tasks: price prediction in the worldwide travel industry (Sec. temperature interpolation of climate data from weather stations (Sec. A.6);
2. the novel Zero-Inflated Poisson (ZIP) autencoder's probabilistic decoder block, which is trained with a spatial contextual loss function, to adapt the standard reconstruction layer of autoencoders network to the case of zero-inflated spatial contextual count data produced by the H3 grid and the OSM entity tags counts (Sec. (36).
'nttps//engg.bbercoo//h3 hhtps:/wwww.oppentteemmapooog
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RELATED WORK
Global geospatial embeddings Hex2Vec (Wožniak & Szymañski, 2021) and Space2Vec Mai
jt al., 2020) are the closest approaches to our work, since they create pre-trained rreation-specifi embeddings, which can add geospatial information to any downstream task without any task-specific retraining nor any manual location imputation logic.
Vex2Vec (Wožniak & Szymański 2021) is state-of offte--f-th-arr work that uses H3 hexagons described by OSM entities, and develops an approach to learn geospatial embeddings. GeoVeX follows a similar approach to create the training setup (H3 as grid methodology, and OSM as provider of geographical entities), but is different in terms of both model design and loss function formulation. In fact, Hex2 Vec embeddings are not contextualized, since the embedding of an H3 hexagon does not consider any information of the surrounding hexagons (e.g. an hexagon described with just the tag "street" is always embedded equally worldwide, without any distinction if this hexagon is surrounded by others with tags of "offices" or "ski-lifts" or "beaches"). Regarding the loss, the authors proposed a skip-gram model with negative sampling, paired with a triplet loss function: for each hexagon to embed (the triplet anchor), the positive hexagon is taken from the first adjacent ring of hexagons, and the negative hexagon is sampled from at least rings away from it. It is easy to see that imposition of complete similarity between the hexagon to embed (the anchor) and its adjacent ones (the positives) in the loss formulation is not always appropriate since it imposes perfect similarity of beach-like hexagon's embedding with a town-like one in case they are adjacent. Finally, the authors applied the approach only to 54 cities, and without quantitative analysis of the improvements on down-stream tasks.
Space2Vec (Mai et al. 2020) is one of the state-of-the-an methods proposed to encode a pairs of coordinates a high dimensional embedding which can be used in downstream tasks. In particular uses trigonometric functions with different frequencies to encode a given position in space instead of using the simple pairs of coordinates in modeling task. The approach can actually be considered as a worldwide embedding model in the sense that any coordinate on Earth can be transposed to a latent representation. However, the embeddings are not learnt based on the geographical entities (e.g. buildings, streets, bars, etc.), so Space2 Vec vectors cannot be really considered as pre- traitra embeddings aiming at learning geographic characteristies of location, in order to draw similarities of different regions on Earth.
Local task-specific geospatial embeddings Other approaches to learn geospatial embeddings in GIS domain are trained for specific tasks and/or specific regions, so they cannot be used as pre- trained geospatial embeddings without task-specific retraining and/or without manual imputation logic. Region2Vec (Xiang 2020) combines Point Of Interest (POI) and mobile sensors data obtained in a specific region in China; Zone2Vec (Du et al. 2018) uses trajectories generated by taxis in Beijing. Urban2Ved Vec (Wang et 20200)) uses Street View images and focuses only on the urban use cases, where such images are available. RegionEncoder (Jenkins et al., 2019) combines mobility from taxis, categories of POI and satellite images to create a model specific to two urban regions. Tile2Vec (Jean et al., 2019) applies an unsupervised representation learning on satellite images, while using the triplet loss formulation, which leads to the same issues described for Hex2 Vec. In (Islam) ct a (022). the authors apply Moran Eigenvector Spatial Filtcring (MESF) for the specific task of predicting AirBnB listing price in San Jose County in US. In (Mac Aodha al. 2019). the location encoder is specifically learnt from photos to improve specific image-classificatte
tasks, and learnt embeddings cover only the locations in the task-specifi training dataset. In (Sheehan et al., 2019), the authors learn task -peccifc location embeddings from geolocated Wikipedia articles, which cover limited set of coordinates, thus requiring manual imputation logic for unknown locations.
Convolutional Autoencoders In terms of network architecture, our design is inspired by recent works on Convolutional Autoencoders (CAE), among which the deep CAE architecture of Guo et al. (017)) represents an example of the state of the art. In addition, (Hahner & Garcke| 2022) recently introduced the use of hexagonal convolutional autoencoders. However, these architectures are designed to work with images, and not with tensors that represent zero-ini vero-inflated count variables, so we propose some modifications to account for this.
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3 PROPOSED APPROACH: GEOVEX
In this section, first, we formalize the problem of training geospatial embeddings of pair of coor- dinates on Earth, then we present the proposed GeoVeX model architecture, its input format and its novel specific components: hexagonal convolutions, the zero-inflated Poisson reconstruction layer for the autoencoder, and the loss function used to train the network.
3.1 PROBLEM FORMALIZATION
Given a pair of latitude and longitude coordinates on Earth p (x, y)
R define a function Fo(p) : I - Rº parameterized by 0 which maps the point p to D-dimensional embedding = Fo()). which represents the geographical characteristics of the space nearby the given point proportionally to the distance to it, in accordance to Tobler (1900).
where fo : RK x x + IR" is the GeoVeX encoder, and t: IR2 + RK is the function which assigns the vector of counts the point p resides, and GeoVeX pre-trained embedding can later be concatenated existing features of any downstream task involving entities described by latitude and longitude coordinates. This effectively serves to expand the features set used by the model addressing the machine learning task solve.
In this work, we propose to formulate the F' function as Fe(p) = fe(t(p),
l(p) of K geographical tags of the entities that intersect the hexagon where
is the set of count vectors of n' neighbor hexagons of p. The
3.2 GEOVEX MODEL 3D TENSOR INPUT FROM 2D HEXAGONAL CELLS
In this section we briefly describe the GeoVeX 3D input tensor required by the network architec- ture. GeoVeX uses an hexagonal tiling system, which is the state-of-the-art representation of geographical grid, because it guarantees the isotropy of local neighbourhoods (Wang et al. 2020aa.. By analogy with image domain, in GeoVeX the first 2 dimensions represent the 2D coordinates of the hexagon spatial coordinate system and the 3rd dimension describes the count of K OSM tags of the entities intersecting a given H3 cell, following the Bag-Of- OfrWsrds (BOW) model. After cleaning and preprocessing, we cut the number of tags to the top K = 1024 most frequent ones with worldwide minimum coverage, since the vocabulary presents long tail distribution. More details can be found in Section A.3 of Appendix.
Each hexagon's neighborhood is defined by the r-rings neighboring cells deseribed in Fig. 2 for r = 7 rings around the point (0, 0) (r- = 7 has been experimentally defined to fit our GPU memory constraints). The importance of each ring decays with distance center, in alignment with the first law of geography [Tobler] 1970). This is implemented using a distance weighting kernel in the model loss function formulation Sec. neighboring hexagons proportionally to the hexagonal distance to it, making them contextualized. This is not the case for Hex2Vec model design, instead.
that the representation of hexagon is influenced by
Transposition of the 2D hexagonal grid to 2D matricial form, for the first 2 dimensions of the 3D- tensor, is done via axial coordinate system representation (see) Luo al. (2019) for more details on different transposition methods), and is depicted in Fig. 3 The final 3D representation is (2r+1) x 12r+1) x K. To enable correct convolutions within this network design, the dimensions of the input matrix are required to be power of 2, which can be achieved through padding. Since we trained the network with r = 7 the input of the GeoVeX model a 16 x 16 x 1024 3D tensor.
3.3 MODEL ARCHITECTURE
The architecture of GeoVeX network is summarized Fig. 4 The base design is the one of a Convolutional AutoEncoders (CAE) network (Guo et al. 2017 which is composed of two main g(h). where
components: the encoder h = fz) and the decoder z' is its latent representation learnt by applying the encoder block, and z' is the reconstructed tensor created by the decoder block. The parameters of the CAE network are updated by minimizing the reconstruction error described in Sec.B.6.
the input tensor,
The encoder is a set of convolutional blocks stacked on the 3D input tensor to extract hierarchical features. The output units of the convolutions flattened to form vector, and are passed
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3.14
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Figure 2: The hexagonal grid of the r-rings cen- tered on the hexagon to embed, with the ax- ial coordinates ji, assigned each hexagon based on its position in the grid.
Figure 3: The transposed hexagonal grid rep- resented a 3D matrix, using the axial co- ordinates transposition and assigning the OSM counts as 1024 tensor channels. In grey, the padding cells that are not valid.
fully connected layer with D units, the final dimension of GeoVeX embedding. In practice, we have found that D 32 is good trade-off between expressiveness and cost to store 200+ millions vec- tors worldwide. The imput tensor is thus transformed by the encoder into a 32-unit latent embedding representation h, forcing the autoencoder to capture the most salient features that minimize the loss function. The decoder is defined as set of convolutional transposed layers to transform embedded feature back to original input, followed by novel Zero-Inflated Poisson layer of contribution to reconstruct the count tensor in input (Sec. 3.5). Batch Normalization (Toffe & Szegedy (015)) used re-center and re-scale the counts tensor input and output of every convolution opera- tion. The usage of Batch Normalization and ReLU is aligned to (Ioffe & Szegedy) (001)); we apply the normalization before the non-linearity and we remove the redundant bias term in the convolu- tion operation. In terms of up/sub sampling, GeoVeX uses convolutional layers with stride of 2, instead of convolutional layers followed by pooling layers (as (Hahner & Garcke (002)), both the encoder (standard convolution) and the decoder (transposed convolution, sometimes referred as "deconvolution"). since (Springenberg al. (2014) demonstrated that replacing all the pooling operations in network with sondeed-convluttoon improves overall performance.
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Mas Cony
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Inpat
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Flaisn 1S584
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HCAF ENCODER
ICAF DECODER
Figure 4: Illustration of the GeoVeX network architecture, showing the different layers of the Hexag- onal Convolutional Autoencoders (HCAE) neural network with Zero-Inflated Poisson (ZIP) prob- abilistic head layer to reconstruct the hexagonal matrix with geographical entity tags count. Each hexagonal convolution block and hexagonal transposed convolution block composed by the re- spective convolution operator followed by Batch Normalization and ReLU operations.
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3.4 HEXAGONAL CONVOLUTIONS
The main building block of both the encoder and the decoder is the hexagonal convolution oper- ator, which aims at extracting relevant geographical features different granularity. The network assumes in input an hexagonal grid transposed to a two dimensional matrix using the the axial co- ordinate system representation as described in Sec. 3.2 In this representation, unused matrix cells are put in the corners, avoiding empty cells in the middle of the matrix and supporting the hexago- nal convolutional autoencoder network described below. In this context, is shown that hexagonal convolutions give better results than standard convolutions in case of hexagonal shaped data (Steppal & Holch 2019 Hoogeboom et al. 2018). In particular, the hexagonal convolution is achieved by multiplying the 3x3 convolution kernel with 3x3 mask to set to zero the kernel at top-left and bottom-right cells (the mathematical formula of the 3x3 masked hexagonal convolution is given in Section A.1 of Appendix).
3.5 BERO-INFLATED POISSON RECONSTRUCTION LAYER
Since the network is intended to be used with geographical count data assigned each hexagon, the Poisson head layer is needed since the variable to reconstruct is coming from a counting process. Moreover, expects a large number of zeros, since it is evident that for any given hexagon on Earth, only few geographical tags from the full vocabulary of tags are present: this hypothesis shall be verified in the data using the respective tests (Yang et al., 2010 Van den Broek 1995). Under this scenario, multiple studies have demonstrated that the best fit to such data with excess of zeros is provided by zero-inflated distributions (Ridout et al. 1998 Beckett et al. 2014 Lambert 1992 Unhapipat et al. 2018).
The
Poisson (ZIP), which is denoted by Z1P(T, A). has two parameters л and X, and has the following probability mass function, where S and X 420 0:
T (1 e if -c)
vi fl)
(1- (11
111
x el
(1,2,,,
(1)
In the GeoVeX model, the parameters and À are estimated in the last layer of the decoder, and are used by the above ZIP mixture model to reconstruct, from the H3 embedding, the OSM count of each geographical tag k of each hexagon axial coordinates j. In fact, the final decoder layer produces two output variables for each coordinate i, j. k: and gx. The first one is activated with sigmoid function to produce æ (Lambert 1992), and the second one activated with the exponential function to ensure that À > 0, as is obviously required:
(1)
Tij.k
(2)
+ (9mls...(())
A = (A)
(3)
where 9x (h), 9xIR.,,e are the two output layers of the decoder network which are conditioned on embedding and produce the estimated से and X for each coordinate i, (Fig.
3.6 GEOVEX LOsS FUNCTION
GeoVeX adapts the Negative Log-Likeliben (NLL) loss function in the context of a hexagonal grid to align with the design of the input data. In fact, the loss formulation encourages first the learning (and, thus, the reconstruction) of the geographical tags count describing the hexagon to embed, and then decay the importance of learning (and, thus, reconstructing) the tags count in each external ring of hexagons, by weighting the loss of each hexagon based on its position in the grid, thus justified simply by grid construction.
In details, the formulation of the GeoVeX loss function is an adaptation of the NLL loss with Zero- Inflated Poisson distribution, in the context of a spatial relationship among the neighbouring regions. Based on the ZIP mass function (Eq. [ and given that we have samples in each learning batch, the log-likelihood function of each element of the 3D reconstructed tensor can be derived as:

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N = In -0) mlksk In
log CTT, V)
Σ n=1
+ (1- -e Aniss.n
[Vnnjajk > 0)[In(1 - Fnjaaah) Aaligah + Mulfij. In Ampaaa - (n( n=1
(4) where n the n-th sample, i and j are the two axial coordinates, is the k-th geographical tag count, and a. denotes an indicator variable that takes value 1 if the condition is verified, and zero otherwise. See derivation in (Hossain & Howlader 2015) and (Lamberl 1992). To make the loss of each grid hexagon weighting proportional to the ring where it is located, apply two positional weights to the ZIP NLL loss of each hexagon of the grid, based on its i, axial coordinates:
the distance weighting kernel Wasst decays the importance of each subsequent neighbour- ing r-ith ring of hexagons, based on the inverse of the distance from the central hexagon to the ring number (i.e. ring 1 applies weight of 1/2, while ring 7 applies weight of 1/8);
the numerosity weighting kernel W num equalizes the importance of each hexagonal r-ith ring, by subdividing the loss among the hexagons that compose it, so that each ring has same total importance in the final loss. By construction, each ring composed of 6 times the number of the ring number (i.e. ring r 1 has 6 hexagons, while ring = 7 has 42 hexagons, so each hexagon has to weight r to make each ring equal in importance)
The mathematical formulations in Eq. and 6 are justified by construction (based on the semantic imposed by using an hexagonal grid centered on the hexagon embed), where is the hexagonal ring number, and j - jl < R is simple condition to explicitly put to zero the loss at the invalid top-left and bottom-right values the axial coordinates matrix representation.
i if i- R otherwise
Wdisti.j
1/(1+ +ra)))
(5)
if ifi=j=0 if - 5 R
1/(6 rig)
(6)
0
otherwise
The two loss weighting kernels are depicted in Fig. Bad 7 in Sec. Aec. Appendix, to help visual- ization of the kernel effect. By combining the two weighting kernels, the loss to minimize is the sum of the ZIP negative log- log-likelhoood loss of each k-th geographical tag count each i, element of the hexagonal grid (Eq. D weighted based on its grid position using the kernels Waist and W nami
L log L(T, 7)s- Waist Wnum
M
log L(T,, 2)s5k
Wdists.s
Wnnm;
M
Eij=1 Waistis 2ij=1 Wnumis
EXPERIMENTS
We evaluate the task-agnostic Geo vectors with qualitative analysis of the latent structures using cosine similarities, and with a quantitative analysis of the improvement of performances on down-stream task.
4.1 QUALITATIVE EXPERIMENTS
In this analysis, we perform a qualitative comparison between Geo VeX and Hex2Vec embedding vectors, where both models are trained on the same exact worldwide input data from H3 and OSM

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(200+ millions vectors worldwide), and with the same size of embeddings space (32), to not provide any advantage based on a different representation space. Space2Vec embeddings do not represent any geographical characteristic they cannot be used for unsupervised geographical explorations.
First, we selected a sample of different cities all around the world, from different continents, each characterized by mix of urban, suburban, green and water regions: Los Angeles, London, Cape Town, Tokyo and Mexico City. Then, we calculated the cosine similarity between an anchor point located in downtown (the exact center of the image) and each other point located in the region, to evaluate the potential discovery of clusters of locations with similar characteristics. The cosine similarities are shown in Fig. the blue color indicates higher similarity to the center point location, and the red color indicates lower similarity.
The cosine similarity calculated using the GeoVex embeddings is shown in upper images: we can see that the geographic semantic captured by the model is aligned to human expectations, to some degree: adjacent hexagons tend to have similar embeddings until they are very different terms of nearby geographical entities, and clusters of locations can be defined to delineate similar regions.
The cosine similarity calculated using Hex2Vec shown bottom images from Fig. 5 this case, there is no evident human-readable semantic that can be extracted by this plot. We can conclude that the Hex2Vec model formulation does not perform well in terms of assigning similar embeddings to adjacent hexagons, there are very few smooth clusters of hexagons that can be seen inside these more noisy patterns.
Figure 5: The cosine similarity calculated using embedding vectors from GeoVeX (top) and Hex2Vec (bottom), using the yellow hexagon of the center point location as anchor item, for Los Angeles, London, Cape Town, Tokyo and Mexico City.
4.2 QUANTITATIVE EXPERIMENTS
We conducted quantitative experiments on the impact of using GeoVeX vectors additional features in two downstream tasks: 1) prediction of worldwide vacation rental listings price in the travel industry (Sec. 4 and 2) hyperlocal interpolation of temperatures from weather stations (Sec. A.6 in Appendix). In both cases, the embeddings are pre-trained, agnostic of downstream tasks, frozen and then used as-is as additional features, to demonstrate that the task-agnostic learnt representations are meaningful.
Expressiveness of GeoVeX, Hex2Vec and Space2Vee vectors evaluated with a feature abla- tion study, by comparing models using: 1) Common task features (Baseline); Additional features: 2) GeoVeX vectors; 3) Hex2Vec vectors; 4) Space2Vec encoding vectors; 5) both GeoVeX and Space2 both Hex2Vec and Space2Vec.
All competing models are trained with the same Gradient Boosting Machines (GBM) regression model architecture, which enables the discovery of interactions among features. For each task, the model hyperparameters are optimized through random search (see Sec.A..4p Appendix for details how to reproduce the experiments setup). For fair comparison, Space2Vec hyper-parameters
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have been optimized for best task performance, since this model requires manual parameters to be configured, and Hex2Vec pre-trate pre-trained embeddings are learnt with same data and same embedding size of GeoVeX.
Vacation Rentals Price Prediction Task Open-source Inside Airbnb J 1M+ list-
ings located worldwide and describes each vacation rental listing with lodging characteristics, ge- ographical coordinates, neighborhood name and daily price. which the value to predict, after conversion to a common currency. The hypothesis is that the geographical characteristics of the location influence its price, and thus GeoVeX vectors improve model performance when added as contextual geographical features. See Section A.5 of Appendix for the list of cities and regions obtained, so to replicate the experiment setup.
In terms of features, the baseline model is designed with the set of state-of-the-art features form [Islam et al.) 2022), where base geographical information is composed latitude, longitude and neighborhood name. Its intent is not be used performance benchmark, but to underline how much information the additional geospatial embeddings bring on top of a state-of-the-ar set of task-specific features. The loss function is the Mean Squared Error (MSE) of the logarithm of the price, and the metrics monitored are both the loss and the Mean Absolute Error (MAE) of the price. The listings split into training, validation and test with ratios 10%;00%;00% with two splitting methods: a common random split, and a split by city names, to evaluate how well the model is able to generalize new unseen geographical areas (i.e. out of training space). Table shows the average performance of all models trained 7 times, together with the respective standard deviation.
We can see that the GeoVeX vectors are useful in both test strategies. For unseen cities, the GBM model with GeoVeX vectors confidently outperforms every other tested model, suggesting that Geo VeX improves both upon Hex2Vec, Vec, to compress geographical information useful to predict out-of-space, and upon Space2 Vec, which encodes the location coordinates without considering the geographical entities. For unseen coordinates (random split), the GBM model with Geo VeX vectors paired with Vec is the only model able to confidently improve the baseline performance.
Table Experiment results for the price prediction task. The lower the better.
Model
Split Randomly
Split By City MAE Price
MSE In(Price)
MAE Price
MSE In(Price)
Baseline
0.281 + 0.005
51.61 + 0.46
0.492 + 0.017
72.69 + 1.15
w/ GeoVeX
0.285 + 0.008
52.29 + 0.61
0.465 + 0.007
70.30 + 0.26
w/ Vex2Vec
0.286 0.010
52.20 + 0.91
0.489 + 0.008
71.33 + 0.42
w/ Space2Vec
0.290 - 0.013
52.51 1.17
0.508 0.010
72.56 + 0.61
w/ GeoVeX & Space2
0.271 0.009
50.65 + 0.89
0.492
71.99
+ 0.66
w/ Hex2Vec & Secce2Vec
0.280 = 0.004
51.59 = 0.35
0.487 0.010
72.53
+ 0.44
5 CONCLUSION
We presented VeoVeX, representation model which learns geospatial vectors as latent represen- tations of the location's geographical characteristics, contextualized on the neighboring locations. GeoVeX is based on novel architecture named Hexagonal Convolutional Autoencoder (HCAE) with Zefo-tnflated Poisson (ZIP) reconstruction layer to learn from hexagonal grids described with zero-inflated counts of the geographical tags of OSM entities. Qualitative analysis showcases the improvement of representation structures compared to state-of-the-an titative experiments on real open data support the fact that the pre-trained GeoVeX embeddings can improve models in multiple domains without task-specific re-training. In future, we aim to analyze the impact of changing the H3 grid resolution, test different zero-inflated probabilistic distributions, compare the task-agnostic vectors against some task-specialized versions, and tackle broader set of downstream tasks that involve geolocated entities, such as: climate-relatee tasks (e.g. effect of urbanization on temperatures), classifications of geolocated images, ranking of geolocated items.
Vec model. Then, quan-
hhtp://nssideaiirth.cco

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A
APPENDIX
A.I MATHEMATICAL FORMULA OF 3x3 MASKED HEXAGONAL CONVOLUTION
The mathematical formulation of the 3x3 masked hexagonal convolution is the following:
W-1,1
W0,1
W1,1
0
1
Yx = H4 X (W& O Mx) X
1-1.0
Wo.0
W1,0
+
* *x (8)
W-1,-1
Wp,
W1,-1
where H is the 3x3 masked hexagonal convolution kernel; W is the standard 3x3 convolution kemnl;; M is the 3x3 hexagonal mask; X is the input tensor; * is the convolution operation; @ is the element- wise multiplication operation; i and j are the two axial coordinates; is the 3rd channel of the tensor, representing the normalized count of the k-th OSM tag in the first convolution, and the k-th normalized filter in the subsequent convolutions.
A.2 VISUAL. REPRESENTATION OF THE LOSS KERNELS
In this section, show the plots of the weighting kernels used in the loss formulation: the distance weighting kernel and numerosity weighting kernel. The kernels are plotted in the axial coordinates system, projected to 2D matrix form. For each i, pair of coordinates, the weight is displayed.
ml
700
Figure 6: The distance weighting kernel.
Figure 7: The numerosity weighting kernel.
A.3 H3 AND OPENSTREETMAP DATA PREPARATION
The construction of the database of hexagons described by respective geographical entities is done as follows. First, we calculate the set of hexagons that lie within the boundary of each country shape, using resolution 8 (best trade-off between data granularity, computational power and mem- ory needed to compute the expensive geospatial operations). The result is a set of 200+ millions hexagons to cover the Earth's 's lands. Then, from the worldwide OSM database of geographical entities, we extract: 150 millions points, identified by their coordinates; 220 millions of lines, identified by set of coordinates; 500 millions of multi-polyyons, consisting of one more set of coordinates describing the polygons, and one or more set of coordinates describing the holes in the polygons. These three types of entities geographically intersected with the hexagons, and Bag-Of- Words (BOW) model is used to count the OSM geographical tags attributed to the entities intersecting each hexagon.
The extraction the set of points, lines and polygons covering all the meaningful entities that can be used describe the world is done with GDAL ogr2ogr [ The initial selection of OSM keys is done based on both the outcome of the analysis done in Wožniak & Szymański (202)), with some
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other tags kept and cleaned since relevant to extended use (e.g. highways). In addition, filtered out the tags with the value containing the following post-fixes: :yes and :no, since we found them to be not consistent and misleading. We also filtered out tags that are only available in few countries, so not relevant worldwide.
The geographical operations clean, manipulate and intersect OSM entities with H3 hexagons achieved using Apache Sedona on an Apache Spark 6 cluster with a total of 10 Tb of memory and 1280 cores. Once the geospatial joins of hexagons and OSM entities are computed, second level of sort and filtering is performed, in order to select the most meaningful features used to describe the hexagons of the world. In fact, based on the analysis of aggregated statisties, it is clear that some key=value pairs are only valid in few parts of the world (c.g. administrative tags), so we keep only pairs that are assigned hexagons at least 20 countries. Finally, we sort the pairs by descending distinct count of hexagons with that pair assigned, and we select the top 1024 tags. This cut-off is chosen using trade-off between the quality of additional descriptors and the GPU memory constraint during model training.
A.4 HYPERPARAMETER SELECTION FOR TASKS MODELS
For each task and for each model to train, we optimize the following LightGBM hyper-parametten by performing a random search with 60 trials, since can be proven that if the close-to-optimal region of hyperparameters occupies at least 5% of the grid surface, then random search with 60 trials will find that region with high probability (Bergstra & Bengio 2012):
depthh random int from 0 to 32;
JeaJeeves: random int from to 2048:
min data in leaf: random int from 20 to 10000;
min gain JoainJo_splii random int from 0 15;
max threshold: random int from 32 to 1024;
longgig-fractiinn random float from 0.2 to 0.95, with step of 0.1; fraction: random float from 0.3 to 0.95, with step of 0.1; learning rate: range of float from 0.001 to 0.2;
lambdall: random int from 0 to 100, with step of 5; lambda 12: random int from 0 to 100, with step of 5;
extra_tres: random true or false.
For each model using Space2Vec coordinates encoding, the following additional typee-parameters optimized, using a range of values suggested by the authors:
lambda_min: random value in: 0.1, 1, 10, 100, 500;
lambda min: random value in: 1000, 10000, 40000;
num num.frequencies: random value in: 8, 16, 32, 64.
A.5 VACATION RENTALS PRICE PREDICTION TASK DETAILS
The cities and regions for which we obtained listing prices from by inside-airbnb open data are the following: Antwerp, Asheville, Athens, Austin, Bangkok, Barcelona, Beijing, Belize, Bergamo, Berlin, Bologna, Bordeaux, Boston, Bristol, Broward County, Brussels, Buenos Aires, Cambridge, Cape Town, Chicago, Clark County (NV), Columbus, Copenhagen, Crete. Denver, Dublin, Edin- burgh, Euskadi, Florence, Gauteng, Geneva, Girona, Greater Manchester, Hawaii, Hong Kong, Is- tanbul, Jersey City. Lisbon, London, Los Angeles, Lyon, Madrid, Malaga, Mallorca, Menorca, Mex- ico City, Milan, Montreal, Munich, Naples, Nashville, New Brunswick, New Orleans, New York City, Oakland, Oslo, Ottawa, Pacific Grove, Paris, Portland, Porto, Prague, Puglia, Quebec City,
"httss//scdoma.apcch...rg "htpps//spark.ppcche.org
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Rhode Island, Rio De Janeiro, Rome, Salem (OR), San Diego, San Francisco, San Mateo County, Santa Clara County, Santa Cruz County, Santiago. Seattle, Sevilla, Shanghai. Sicily, Singapore, South Aegean, Stockholm, Taipei. Thessaloniki, Tokyo, Toronto, Trentino, Twin Cities (MSA), Va- lencia, Vancouver, Vaud, Venice, Victoria, Vienna, Washington DC, Zurich.
A.6 HYPERLOCAL TEMPERATURES INTERPOLATION TASK
ARPA Lombardia is regional agency for environment protection which provides open weather sensors data] in the area of Milan (Italy). The data contains 1,4 millions of hourly temperature samples, recorded by weather stations from January 2010 to August 2022 Milan and nearby. Each sample is described by: the temperature, the date, the hour, and the coordinates of the weather station. The task is the interpolation of the temperature between weather stations, which is modeled prediction of the temperature in an unknown location. This is achieved by removing subset of stations from the training data and by comparing the model predictions with the actual temperatures observed by the test stations. The hypothesis is that the geographical characteristics of the location help to explain the differences in recorded temperatures from nearby sensors.
The experimental setup is the same in Sec. 4.2 Baseline model denotes the model relying on all the available features when geospatial data are only latitude and longitude which are the date components (year, month and week of year) and the hour of the day. The loss function is the MSE of the temperature, and the metrics monitored are both the loss and the MAE. The temperature records are split into training. validation and test with ratios 109;;000:1199 by randomly sampling the sensors, to analyze the performance of estimating the temperatures at an unknown location.
Table 2 shows the performance of the different models on the test set. We can see that the GBM models with GeoVeX emebddings (both alone and combined to Space2 confidently outperform every other model. This shows that GeoVeX vectors help improving the estimation of tempera- tures in this region with mix of urban and green areas, by providing the geographical context of each location.
Table 2: Experiment results for the hyperlocal temperature interpolation task. The lower the better.
Model
MSE Temperature
MAE Temperature
Baseline
11.144 + 0.094
2.651 + 0.012
w/ GeoVeX
10.656 + 0.135
2.615 0.016
w/ Hex2Vec
10.862 0.110
2.628 : 0.010
w/ Space2
10.880 + 0.105
2.639 - 0.012
w/ GeoVeX & Space2
10.651 + 0.090
2.613 0.012
w/ Hex2Vec Veece2Vec
10.870 = 0.172
2.629 + 0.019
15


Reviews:
[{"review_id": "R9s5FI53gD8", "reviewer": "Reviewer_pWwW", "summary": "", "questions": "", "limitations": "", "rating": 6, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "Authors proposed GeoVEX as a framework for global representation learning in gespatial settings. The apprach leverages the H3 geospatial indexing system and data from Open Street Maps to create an embedding for each location on earth. An autoencoder like network architecture was introduced for the embedding generation which includes a novel hexagonal convolutional operation and adds a Zero-Inflated Poisson probabilistic output layer. The learnt representations were tested for the tasks of vacation rentals price prediction and temperature interpolation. ", "summary_of_the_review": "There is enough contribution for the paper to be accepted but it would be stronger with a better set of downstream task evaluations and comparisons to other approaches for those.", "strength_and_weaknesses": "-- Strengths:\n- Approach is novel, technically sound, and relevant to many applications\n- Great potential impact\n- Article is well written and set in context\n\n-- Weaknesses:\n- Not enough evaluation was done to fully test the power of the learnt representations. Only two downstream tasks were tested without comparing performance to other strong approaches\n- Further ablation studies are needed to understand better the proposed approach. How important is the use of the ZIP output layer? What is the performance without it? How GeoVex would perform using other geographic systems?", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "PYCLOV5TQj", "reviewer": "Reviewer_Fj26", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "This paper aims to learn general-purpose location embeddings which are useful for downstream geospatial prediction tasks. The idea is to learn this representation by binning geographic entity occurrence data from OpenStreetMap (OSM) and applying a convolutional autoencoder with a special custom decoder head. The binning and convolution are done on a hexagonal grid. The proposed method (GeoVeX) is compared against two competing approaches to geospatial representation learning (Hex2Vec and Space2Vec) on two datasets. ", "summary_of_the_review": "This paper tackles an interesting problem and I enjoyed reading it. However, some of the (rather strong) claims made by the paper seem to be inadequately supported or incorrect. In addition, there are some important details missing (hyperparameters, tuning procedures, split construction) which makes it difficult to take the experimental results at face value. ", "strength_and_weaknesses": "# Strengths\n* Learning geospatial representations that generalize to many downstream tasks is an interesting and worthwhile goal. \n* The idea of autoencoding OSM data is a reasonable approach to geospatial representation learning.\n* The proposed ZIP head is novel to the best of my knowledge. \n\n# Weaknesses\n* A key claim of the paper is that it produces \"the first geospatial vectors trained on worldwide open data\" - this does not seem to be true as written. For instance, [mac2019presence] learns embeddings for each location on earth from freely available data from iNaturalist. See also [sheehan2019predicting], which represents locations using embeddings of nearby geo-located Wikipedia articles. \n* A key claim of the paper is that the proposed method learns \"task-agnostic global geospatial vectors.\" Are they task agnostic? It is not obvious to me that using OSM data makes it \"task agnostic\" automatically, since OSM contains a limited set of categories with a particular focus on certain land use / land cover categories. More broadly, if the claim is that the proposed method learns significantly more general features than prior methods, it would probably make sense to demonstrate this on more than two datasets. \n* A key claim of that paper is that it is \"the first use of hexagonal convolutions within autoencoder architectures.\" First, I would like to be convinced that this is significant by itself. Can't hexagonal convolutions can be used with any convolutional architecture? Is there a reason we wouldn't expect it to work for autoencoders? Second, it seems like [hahner2022mesh] may have done this first - please comment and clarify. \n* It's a bit tricky to interpret the results in Table 1 and Table 2 without more context. The magnitude of the performance differences between the methods seems small, and the ranking of methods seems to depend on the metric. Given this, it may be important to report average results across a few training runs (both the representation learning and the GBM) to determine whether we are observing robust performance differences or random fluctuations.\n* GeoVeX several components, including the use of hexagonal spatial units, the ZIP head, and special terms in the loss function, none of which are characterized with an ablation study. The relative importance of these components is therefore unclear. \n\nMinor comments:\n* The paper claims that a linear probe does not work well in this context because GBM does better than the linear probe when combined with the baseline features. But isn't this what we'd expect if the baseline features are not very good? We would expect linear regression to work better with more powerful features. \n* Why are GeoVeX features always combined with task-specific features (Figure 1)? Why not evaluate the utility of the features on their own for downstream tasks? \n* In the related work section, the paper notes that Space2Vec \"uses trigonometric functions with different frequencies to model a given position in space... However, the embeddings are not learnt based on the nearby geographical entities...\" - note that [mac2019presence] does both of those things, where the geographic entities are species observations. \n\n@inproceedings{sheehan2019predicting,\n  title={Predicting economic development using geolocated wikipedia articles},\n  author={Sheehan, Evan and Meng, Chenlin and Tan, Matthew and Uzkent, Burak and Jean, Neal and Burke, Marshall and Lobell, David and Ermon, Stefano},\n  booktitle={Proceedings of the 25th ACM SIGKDD international conference on knowledge discovery \\& data mining},\n  pages={2698--2706},\n  year={2019}\n}\n\n@inproceedings{mac2019presence,\n  title={Presence-only geographical priors for fine-grained image classification},\n  author={Mac Aodha, Oisin and Cole, Elijah and Perona, Pietro},\n  booktitle={Proceedings of the IEEE/CVF International Conference on Computer Vision},\n  pages={9596--9606},\n  year={2019}\n}\n\n@inproceedings{hahner2022mesh,\n  title={Mesh Convolutional Autoencoder for Semi-Regular Meshes of Different Sizes},\n  author={Hahner, Sara and Garcke, Jochen},\n  booktitle={Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision},\n  pages={885--894},\n  year={2022}\n}", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "2: Several of the paper’s claims are incorrect or not well-supported.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "9hbAw6WO21s", "reviewer": "Reviewer_3Ztx", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "The paper proposes to learn spatial embedding for coordinates based on H3 hexagons and convolutional autoencoders using the OSM’s tag data. ", "summary_of_the_review": "In brief, learning global spatial embedding is a valuable task. However, the currently proposed method and the used data lack significant contribution beyond existing work.", "strength_and_weaknesses": "S1. The problem is important and using convolutional autoencoders in building global spatial embeddings seems to be novel.\n\nW1. The method is very similar to Hex2Vec (both based on hexagons and OSM data). The performance improvement in the experiments is also very marginal.\n\nW2. The scale effect is very important for spatial big data analysis. However, the current method only learns representation for a fixed scale of the spatial region (H3 hexagon), which may not be useful for practical spatial data analysis.\n\nW3. The evaluation is only conducted for US and Italy, which cannot well support the motivation that the learned embedding is for the whole earth.\n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "2: Several of the paper’s claims are incorrect or not well-supported.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "70orfa6IGR", "reviewer": "Reviewer_zeEd", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "The author proposed to a new geo-encoding method called GeoVeX. The idea is to train an autoencoder on the OSM data projected to H3. Experiments show that GeoVeX outperforms baselines like Hex2Vec and Space2Vec.\n", "summary_of_the_review": "Vote for weak reject due to lack of novelty.\n", "strength_and_weaknesses": "Strength\n- The paper is clearly written and experiments demonstrated GeoVeX's improvement.\n\nWeakness\n- The novelty of the paper is limited. The general idea (using OSM + H3) is very similar to the Hex2Vec paper.\n- The paper lacks ablation study on understanding why the proposed method work.\n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}]

Author rebuttal:

Decision: Reject