Road Network Representation Learning with the Third Law of  Geography
Authors: Haicang Zhou
Weiming Huang
Yile Chen
Tiantian He
Gao Cong
Yew-Soon Ong
Venue: NeurIPS 2024 poster (2024)
Keywords: Road network
the third law of geography
geographic laws
representation learning
Primary area: machine_learning_for_other_sciences_and_fields

Abstract: Road network representation learning aims to learn compressed and effective vectorized representations for road segments that are applicable to numerous tasks. In this paper, we identify the limitations of existing methods, particularly their overemphasis on the distance effect as outlined in the First Law of Geography. In response,  we propose to endow road network representation with the principles of the recent Third Law of Geography. To this end, we propose a novel graph contrastive learning framework that employs geographic configuration-aware graph augmentation and spectral negative sampling, ensuring that road segments with similar geographic configurations yield similar representations, and vice versa, aligning with the principles stated in the Third Law. The framework further fuses the Third Law with the First Law through a dual contrastive learning objective to effectively balance the implications of both laws. We evaluate our framework on two real-world datasets across three downstream tasks. The results show that the integration of the Third Law significantly improves the performance of road segment representations in downstream tasks.

Road Network Representation Learning with the Third Law of Geography
Haicang Zhou' Weiming Huang' Yile Chen' Tiantian He².3 Gao Cong' Yew-Soon 1..
College of Computing and Data Science, Nanyang Technological University, Singapore
2 Institute of High-PPrformance Computing, Agency for Science. Technology and Research, Singapore Centre for Frontier Al Research, Agency for Science, Technology and Research, Singapore
haicang001@e ntu. edu. sdu weiming. huang@nateko. .l. he twa.tiinnnnihpp....... at a-star www.aa..euuuseeee......ee sg, {yile. chen, gaocong, ASYSOng) Ontsu. .du. sg
Abstract
Road network representation learning aims to learn compressed and effective vectorized representations for road segments that are applicable to numerous tasks. In this paper, we identify the limitations of existing methods, particularly their overemphasis on the distance effect as outlined in the First Law of Geography. In response, we propose to endow road network representation with the principles of the recent Third Law of Geography. To this end, propose novel graph contrastive learning framework that employs geographic configuration-aweer aware graph augmentation and spectral negative sampling, ensuring that road segments with similar geographic configurations yield similar representations, and vice versa, aligning with the principles stated in the Third Law. The framework further fuses the Third Law with the First Law through dual contrastive learning objective to effectively balance the implications of both laws. We evaluate our framework on two real-world datasets across three downstream tasks. The results show that the integration the Third Law significantly improves the performance of road segment representations in downstream tasks. Our code is available at htttps://gitaei com/
www.eaiccaaaaeeeeeoeeeeeaeeeeeee Hangangiaaaggagnn /arner
Introduction
Road networks, which form fundamental infrastructure within urban spaces, describe the geometries and connectivity among road segments in transportation systems. Correspondingly, road networks serve indispensable components to support numerous smart city applications, such as traffic forecasting g [4], route inference [4, 20 42), and travel time estimation [19]. Motivated by the advancements of graph representation learning 29 37 the versatile utility of road networks has spurred research into developing effective and expressive representation learning methods for road networks. The objective is to derive functional and easily integrable representations of road segments that can align with the paradigm of neural network models.
Road networks are inherently regarded as graphs, which allow existing methods for road network representation learning to build upon graph representation learning techniques. In particular, apart from encoding the topological information of road networks, these methods further integrate additional spatial characteristics, such as geographical distance [2). which are unique to road networks. In these methods, the inductive bias induced by spatial characteristics is primarily based on the First Law of Geography (25), which states that "everything is related to everything else, but near things more related than distant things." This principle implies that spatially close road segments tend to have similar representations. For example, skip-gram based methods [ 39 40 define the context window based on hops among graph neighbors or spatial distance and derive road segment
38th Conference on Neural Information Processing Systems (NcurIPS 2024).

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representations similar to word2vec (24]. Besides, graph neural networks [ 17
36
43
52 based
methods 2 [5 employ message passing [3] and aggregation among road segments. Both
types of methods result in similar representations for connected or proximal road segments 29 43
While generally true and applicable, the First Law of Geography does not adequately capture the complexity of urban environments [55], particularly in terms of long-range relationships. Conse- quently, this limitation compromises the effectiveness of road segment representations in existing methods. This law predominantly emphasizes the distance decay effect, neglecting the influence of semantic factors of different areas on target variables [54] To mitigate the limitation, the Third Law of Geography [34 (55) was proposed to further consider geographic configurations, stating that "The more similar geographic configurations of two points (areas), the more similar the values (processes) of the target variable at these two points (areas)." The term geographic configuration refers to the description of spatial neighborhood (or context) around a point (area), and the term larget variable is the road representation in our context. As result, two road segments with similar geographic configurations should have similar representations, even they are disconnected and distant.
Recognizing the potential advantages of integrating the Third Law of Geography, we initiate pioneer- ing research that combines the principles of both the First Law and the Third Law in road network representation learning for the first time. To facilitate this integration, it is essential to leverage data sources that provide comprehensive insights into geographic configurations for road segments. Existing approaches commonly utilize data from OpenStreetMap [27]. which includes relatively basic features such as coarse-graing support the condition required in the First Law of Geography and are subsequently processed through specialized model designs, they are insufficient to address the application of the Third Law. To enhance the understanding of geographic configurations, we propose to utilize street view images (SVIs) 7 as an additional data source. Street view images capture the visual context of roads and their surroundings, offering more nuanced representation of geographic configurations. However, it is still non-trivial to tackle these two principles simultaneously.
road attributes (location, length. type, etc.). While these data
First, it is important to effectively enable the integration of the Third Law of Geography within the context of road networks. This law posits that similar representations are expected be derived for road segments with similar geographic configurations. To this end, the module should capture and reflect the similarity relationships among geographic configurations representations, ensuring that road representations faithfully preserve the similarity relationships. Second, it is critical to harmonize the implications of applying both the First and Third Law of Geography in road network representation learning. The First Law emphasizes the importance of spatial proximity, while the Third Law focuses on the significance of similarity in geographic configurations, irrespective of spatial proximity. In real-world scenarios, two distant road segments might exhibit very similar geographic configurations due to similar surrounding buildings and environments. Conversely, two directly connected and proximally close road segments might present vastly different geographic configurations - for example, one adjacent to a commercial area and the other near a park. Given these two conditions, a framework is required to synthesize road segment representations that align with both principles while mitigating potential discrepancies as highlighted.
the resulting road segment
To resolve these challenges, we propose new framework, namely Geographic Law aware road network representation learning (Garner). First, to effectively enable the integration of the Third Law, we devise graph contrastive learning framework [22 37 tailored for road networks. This graph
enhances conventional contrastive learning by incorporating geographic configuration-awan augmentation and spectral negative sampling. Specifically, we utilize SVIs to construct a geographic configuration view for road networks, which facilitates the augmentation of edge connections between road segments sharing similar geographic configurations, even if they are gcospatially distant. Then, we employ a Simple Graph Convolution (SGC) 43] encoder, which has the property of implicitly reducing the differences between the representations of connected road segments [43,, thereby map- ping the similarity relationships between geographic configurations to road segment representations in the contrastive learning process. To further align with the Third Law, the proposed contrastive learning framework is equipped with a novel spectral negative sampling technique. This sampling strategy can be mathematically demonstrated to support the principle of the Third Law in reverse way. ensuring that road segments with dissimilar geographic configurations are represented distinctly. Second, to harmonize the effects of both the First Law and Third Law, we propose a dual contrastive learning objective, which contrasts the topological structure view with the geographic configuration graph view and the spatial proximity graph view. We maintain shared parameters in the SGC encoder
2

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and jointly train the contrastive losses, thus simultaneously learning the consensus and discrepancies of these two laws in self supervised manner by minimizing the dual contrastive objective.
Our contributions can be summarized as follows.
We identify the limitations of existing methods in road network representation learning, and propose the integration of the Third Law of Geography to overcome the shortcomings. To the best of our knowledge, this is the pioneering attempt to integrate the Third Law of Geography in this area.
We develop novel graph contrastive learning framework model the Third Law through geographic configuration-wware graph augmentation and spectral negative sampling. Besides, we balance the influences of two geographic laws via a dual contrastive learning objective.
We conduct extensive experiments on two real-world road network datasets (i.e., Singapore and New York City), and evaluate our model on three downstream tasks. The experiments demonstrate that the integration of the Third Law significantly enhances the performance of road network representation learning.
2
Related work
Road network representation learning These works aim to learn representations for road segments or intersections, for various downstream tasks 4
4.8. 14 20). Recent studies model a road network
as a graph and build their method upon graph representation techniques by including geospatial information, and can be classified into two groups. Some [
23 39 40] adopt random walks to
generate paths and train a skip-gram model [29] incorporating geospatial information based on
distance [39] or spatial constraints. Others 22
48 use graph neural networks [17 36 to
ensure proximal or connected roads have similar representations. Some also include traffic data (e.g..
GPS trajectories of vehicles 3 32) to enhance the representation. The theoretical support behind these methods the First Law of Geography 25 However, this principle has overemphasized
spatial proximity and thus (54) proposes the Third Law of Geography, which argues that geographic configurations play critical roles geospatial data analyties. This paper pioneers research on modeling the geographic configurations and the Third Law for road network representation learning.
Unsupervised graph representation learning Graph representation learning aims to learn rep- resentations for graph components like nodes, edges, or entire graphs, where unsupervised node representation learning is most relevant to ours. Despite [2 33 on masked auto-encoding [TO], the majority relies on contrastive learning (5 or its variants, which usually comprises several compo- nents: graph augmentation, contrastive strategy, negative sampling, and loss function (e-g.. mutual information (MI) estimator). Graph augmentation [21 45) is to generate positive [ or negative [37
samples, though some recent studies try to remove it 226 49 Contrastive strategy chooses which two
components to contrast, such node-node contrast [30 56
or node-graph contrast 21). Negative
sampling is required by the loss. The loss is usually to maximize the MI g 37 50 between an entity with its positive samples and minimize the MI with its negative samples. Several recent studies have
also tried to develop new objectives for graphs 22 47). Unlike existing studics our method further encodes geographic laws and more data sources to feed the contrastive loss.
Preliminaries and problem definition
Definition (Graph). A graph is denoted as G EV, X), where V and & denote the set of nodes and edges respectively. Let n [V] denote the number of nodes and m = [E] denote the number of edges. X E R f is the feature matrix, with each row X, representing the features on node i. Let A E R denote the adjacency matrix of G. describing the connections in E. If node i and node are disconnected, then A., = 0; otherwise A., * O. By adding self-loops, we define = + I.
Definition (Graph Laplacian matrix). The Laplacian matrix of a graph G is defined as = where D is the diagonal degree matrix with D the degree of node i and Di.j = 0 Vi + j. Definition& 3 (Road Network). Road networks are composed of road segments and intersections (junctions) of road segments. We use the term "road" to denote road segment in later sections for brevity. Road networks can be regarded graph, which is denoted as G (V, E, X, P). Each road
A,
3

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3rd Law
Sample
Encoder
Contractivn loss (with spectral regaliso sampling)
G!!
Street view image
Augmentation
Lad
Sample
S1
Total Loss
GTM
Road Network
1st
Controstive loss
Sample
GNN
X
1st Lave
gP
Figure 1: Architecture of Geographic law aware road network representation learning (Garner).
segment is modeled node, and connected roads are linked by edges. X; represents the feature vector of road i. Besides, road networks contain P. which stores the geospatial locations of nodes.
Problem Definition (Road network representation learning). Given road networks 9 EV,,, X, C), where C' denotes the geographic configurations, our objective is to learn function :p (X, C.A.P) + Z E Raxf, where the i-th row Z, of Z denotes the representation of road i.
We defer the definitions and discussions of geographic laws in Appendix A.
Method
In this section, we present the details of Garner, which enables the integration of the Third Law of geography for learning road representations: roads with similar geographic configurations should exhibit similar representations, and vice versa. The proposed Garner is built on the recent advances in contrastive learning and spectral graph theory. Fig. [ consists of the following components: (1) Data preprocessing: it produces initial road features that encode the geographic configuration. (2) Graph augmentation: it generates graph adhering to the Third Law of Geography, where roads with similar geographic configurations are connected. (3) GNN encoder: it serves as the backbone for deriving road representations from both the original graph (the topology of the road network) and the augmented graphs. (4) Graph contrastive loss: enhanced with spectral negative sampling strategy, it effectively integrates the Third Law (the upper part in Fig. D. (5) Dual contrastive lcarning objective: it aims to harmonize the effect of the First Law with the Third Law (lower part in Fig.
Iillustrates the framework of Garner, which
Garner inspired by recent studies on contrastive learning 22 showing that by maximizing the mutual information (MI) between different views. the information from these views can be fused properly, and by contrasting different views of the graph the quality of the representation can be improved [9]. By applying contrastive loss on the augmented and original graph, Garner can effectively learn the road representation according to both the third law and the original road network, and fuse their information properly. The cross-contrast strategy also allows Garner fuse the Third Law and the First Law with proxy, instead of directly contrasting the laws. This allows Z to learn their consensus, while [ and Z can learn the discrepancies of the two laws.
4.1 Representation of geographic configuration and data preprocessing
As mentioned in Section D we utilize street view images (SVIs) proxies represent geographic configurations for road segments. Specifically, each street view image is encoded into vectorized representation with pre-trained image encoder (e.g., CLIP BI). Then, we match these SVIs to roads according to their geospatial locations. As multiple SVIs can correspond to a single road in our datasets, we aggregate the representation of these matched SVIs with average pooling in such cases. After that, the geographic configuration (GC) for road segments can be described as matrix C' e RRxxe We note that a small portion of roads not align with any SVIs. For these roads, we set their GC to be the average representation of other roads. Moreover, road segments may possess other

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basic attributes available from OpenStreetMap, such as the road type and length. We follow previous literature 3 to encode the features into matrix X. Finally, the GC and additional road features are projected and concatenated form ( concat([CWe.. X.CCC,WWWW.... W&)) which serves as input to our proposed framework.
4.2 Geographic configuration aware graph augmentation
We propose a graph augmentation technique according to the similarity of the geographic configu- ration. We first define similarity measure for geographic configuration as sim(C,, Cj). Here, we use norm-based measure sim C, C2) = 1/(1 + +ICC - C2ll), while cosine similarity and Gaussian kernel could also be possible choices. Then, we build an augmented similarity graph based on the similarity sim C, Cý). In a similarity graph, similar node pairs (i.e., node pairs with large similarity scores) will be connected by edges. Popular choices for building the similarity graph include kNN graphs and threshold graphs [3]. We empirically find that the two choices produce very close results, and we therefore choose KNN graph because of their high efficiency. In kNN graph, each node is connected with k nodes, which have the highest similarity with it, and k is a small number, so the kNN graph is very sparse. We name this process geographic configuration aware graph augmentation and use matrix S E {0, j to denote the adjacency matrix of the augmented similarity graph Gll),
4.3 Graph encoder
To facilitate the integration of the Third Law, we employ Simple Graph Convolution (SGC) 44 as the backbone of our graph encoder tackle the augmented similarity graph, described as follows:
Z = ge, (S, H (0)) = SK H (0) θ
(I)
where S D= Ds is the degree matrix of Š = S is the learnable parameter, and Z E R is the output representation. As discussed in |3]56)], the simple graph convolutional operation acts low pass filter, making the representation Z of connected nodes similar. Specifi- cally, according to [56], the SGC encoder in equation is designed to minimize tr [Z" Ls Z), which equivalent to the following equation:
1 tr Ir(Z"Le LsZ)
- Sty -
Σ
-
The details of the calculation can be found in Appendix B.1
this equation, Sty is non-zero and only if node and are connected in the augmented graph GlJ), Therefore, by minimizing tr( tr(Z" Lg Lg)), Z), the difference between Z, and Zj is reduced for every connected node pair, thus aligning with the objective of the Third Law, where the representations of nodes (i.e., road segments) with similar geographic configuration are minimized. In addition, another SGC encoder with different learnable parameters is used to encode the nodes in the original graph glo), which represents the topological structure of road networks. As a result, we obtain two outputs, Z from the original graph glol, and z from the augmented graph çlu,, Given the large number of road segments in city, we adopt sam-lamningg technique to enhance the efficiency and scalability. In particular, in each iteration in training, we maintain the same set of nodes for each graph view, and only edges connecting sampled nodes are retained. The subgraphs are then processed through the graph encoders.
4.4 Contrastive loss
Previous studies show that information from different views can fused properly by maximizing their mutual information (MI) [. which can also improve the quality of representations [9] Inspired by these, we maximize the MI between the original graph glo) and the augmented graph glil.
V
C = IV
10) 2 + MT(Z.". Z
(3)
Here [V/] denotes the number of nodes in the graph. z / is the representation of the whole graph by applying graph pooling operation on Z In our implementation, we choose the mean
5

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pooling. The MI estimator MI(-,) -) is a widely used one based on
divergence [7
MI
M 0 2 (glol gh))
log ((Z 0 ) + E (goolcch))
log(1 D(Z 2 11
(4)
MT MT! ( (ight),.to) log D (z ) + Buu gI01)
[log(1 D( 2 ))
(5)
where the discriminator D is achieved by bilinear layer (i.e., D(a, b) - a² Wb) (22]. glo) and Glu) are negative samples required by the mutual information estimator. Specifically, glo) is the negative
sample generated by shuffling the rows of inputs H (0), following [22 37.. and then [ is produced through the graph encoder gög- We then explain how to generate Gl"l.
4.5 Spectral negative sampling
In graph contrastive learning, negative sampling is usually implemented by graph corruption such as feature shuffling (37) and edge modification 466. In the road network context, extend beyond these conventional methods by introducing a novel spectral negative sampling technique to integrate the Third Law of Geography. To be specifie, the Third Law not only posits that "roads with similar geographic configurations should have similar representations," but also implies that "roads with dissimilar geographic configurations should have dissimilar representations: Our proposed strategy elegantly refines the objective in Equation 2 in the contrastive learning process, thereby implicitly addressing the reverse implication of the Third Law.
To achieve this, we recall that equation reelaees closely to the objective of the sparsest cut problem (Chapter 10 of [44] and [49) ) which seeks to find cuts that minimize the number of edges between subsets of nodes. Correspondingly, nodes are densely connected within each subset, while between different subsets, nodes sparsely connected.
{SS V 8)
useg == min S
| - S]
where the numerator denotes the number of edges across node sets S and V - S, and the denominator is the multiplication of number of nodes in the two sets. useg can be computed as
Enseee x,)²
min xx. Lga 1E(o.1)"-(0.1) x Lxx
usCg =
min #c (0,1)" (0.1} Et, =2
(7)
where x; is the i-th element of vector æ, and K is complete graph, which has the same nodes as G. Following [49]. we apply continuous relaxation in this formula and extend it to the matrix form:
ta LzZ
min ZEROX tr Lx
(8)
where Ls is the graph Laplacian matrix by regarding S as the adjacency matrix, and Lx is the graph Laplacian matrix of the complete graph K.. Minimizing equation & is equivalent to minimizing the nu- merator and meanwhile maximizing the denominator, with the same Z. Recall that the SGC encoder (equation p has the effect of minimizing the numerator tr( z Lş Z). Subsequently, we design the negative sample based on Z and K. The negative sample can achieve that by discriminating positive samples from negatives, the model has the effect of maximizing the denominator tr(Z" Lx Z). This can be achieved by another SGC with the same parameter as in equation] !
Z go; (Ák, H H)) A Z AK SK
H (0) θ
(9)
where Ax is the adjacency matrix of KC, Ax D D 0.5 achieves minimizing the denominator. (See the details of the computation Appendix (B.2) Finally, regarding K. (with Z as its output) as the negative sample and discriminating positive samples from in the MI estimator (equation & achieve maximizing the denominator tr Z Lx Z) in equation
Ax 0.5 Ax
Ax/n. Z 90, (Ax, H))
However, performing SGC on the complete graph IC entails a time and space complexity of Onn?).
which is computationally infeasible for large graphs. To tackle this, we further conduct an efficient approximation for the complete graph IC according to spectral graph sparsification (33]
(1 - 2 d
tz Z) tr Zx < (1+ 2vd tr(
tr(
(10)
d
For notation simplicity, we omit superscripts and use Z to denote ( in this section.

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where IC is a d-regular graph (i.e., each node has d edges connected to it) with "all of whose non zero Laplacian cigenvalues lie between d 2vd - and d + 2vd d - -I" and each edge weight as n/d. Consequently, can optimize tr(Z" Kx Z) by optimizing tr(22 I" Z) Then we simply replace Ax the right hand side of equation with Ag and get the outputs of the negative sample as
A H O O
(11)
which works well in our experiments.
To summarize, generate the negative sample G d-regular graph K. with the node V, with the same node feature G Then perform SGC the negative sample, and finally use the output representation Z to compute mutual information in The negative sampling strategy is inspired by the sparest cut and can maximize tr(Z" Lx 0.5 E. شド= Z; Zyll² where the majority node pairs
(i.j) have dissimilar geographic configuration, because of the sparsity the positive sample G 34 Therefore, we can achieve the reverse implication of the Third Law roads with dissimilar geographic configuration have dissimilar representations.
4.6 Fusing the Third Law and the First Law
While the integration of the Third Law has been effectively achieved through module designs, the First Law remains beneficial, especially in regions that manifest identical functionality, thus encouraging representations of nearby roads within the regions to be similar. Therefore, it is important to further incorporate the inductive bias introduced by this law into the contrastive learning process. To achieve this, adopt another graph augmentation technique based graph diffusion (), which generates another graph view g( with the following adjacency matrix:
D a a) 1/2 AD AD-1//2-1
(12)
which can be fast approximated by 18] Then the SGC encoder go, is employed to produce the output Z from gl The graph diffusion process connects near roads, and the SGC encoder can pull the near roads to have similar representation due to the property of SGC (as section 4.3). Then
we use the same loss for g(o) and the augmented graph Gi2).
L2
MI ( 00 2!!1) + MI!! 2
(13)
M
By introducing this component, our Garner is endowed with a dual contrastive objective that maximizes the mutual information between the topological structure with the geographic configuration view, as well as the spatial proximity view, in alignment with the principles of these two laws. Then we train the model (Fig. by combining Li and L2:
L C1 + Lz.
(14)
We find that the model adeptly learns to balance these considerations through parameter sharing the SGC encoder (. performing well without the need for manual tuning the weights of the two loss functions. Therefore, we do not introduce additional hyper- paremeerressrss to adjust their weights. During inference, we aggregate the outputs from the three graph encoders as the road segment representations
for downstream tasks: Z = (2 + z + //3)
Experiments
In this section, evaluate the proposed method and the output road representation following previous literature 3 The road representation is evaluated on three downstream tasks. We also perform case study show the impact of the Third Law, and ablation studies and hyper-parameter sensitivity tests to analyze the proposed method.
5.1 Experimental setups
For implementation, the adjacency matrix of K will be normalized to its degree matrix, and thus the weight n/d will not change the scale of Z.
7

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Datasets We use data from two cities, i.e. Sin- gapore and New York City (NYC). The datasets in- clude road networks from OpenStreetMap (OSM, (27] and street view images (SVIs) from Google Map (77). The statistics can be found in Table
Table 1: Dataset Statisties
City
# Roads
# Edges
# SVIs
Singapore
45,243
138,843
136,399
NYC
139,320
524,565
254,239
Downstream tasks The road representation is evaluated on three downstream tasks: road function prediction, road traffic inference, and visual road retrieval. Road function prediction is classification task determine the functionality of road. Road traffic inference is a regression task predicting the average speed of vehicles on each road. Visual road retrieval involves finding the roads where the road image should be located. While road traffic inference widely used in previous literature 22 23 we introduce road function prediction and visual road retrieval as two new but meaningful evaluation tasks for road representations. More details for downstream tasks can be found in Appendix C.1
Evaluation metries For road function prediction, we use Micro-F1, Macro-F1, and AUROC (the area under the ROC curve) as the evaluation metrics. For road traffic inference, we use MAE (mean absolute error), RMSE (root mean square error), and MAPE (mean absolute percentage error) as the evaluation metrics. For visual road retrieval, we use recall 10 and MRR (mean reciprocal rank).
The proposed Garner is compared with seven strong baselines, including Deepwalk 229, MVGRL [9] CCA-SSG 447, GGD (51), RFN [5], See [39] and SARN [2]. Some other include other data types (e.g.. GPS trajectory data of vehicles) as inputs. However, GPS trajectory data are only available in very few cities, and we did not find them for one of our datasets (NYC). Thus, we cannot run these methods for comparison in our experiments. More details of the baselines can be found in Appendix C.2
Baselines
recent methods 3 23 32
Hyper-parameter settings We use the same hyper-paramette parameters on all the datasets. The road features, and image embeddings are projected into 256 dimensions. The configuration aware graph augmentation, and d = 22 for spectral negative sampling. The hyper- parameters for graph diffusion is a 0.2, suggested by [8]. The hidden dimension and the dimension of the representation are set as 512. Other detailed settings can be found in Appendix C.3
in kNN graph for geographic
5.2 Experimental results
Table 2: Results in Road Function Prediction, with the best in bold and the second best underlined
Singapore
NYC Macro-F1 (%)
Methods
Micro-F1 (%) 1
Macro-FI F1 (%)
AUROC (%)
Micro-FI (%)
AUROC (%) t
Deepwalk
62.76 + 11.49
13.30 + 0.10
63.23 + 0.47
78.09 + 0.18
14.62 + 0.02
58.49 + 0.33
MVGRL.
66.61
+: 0.50
30.67 0.66
74.34 + 0.46
78.23 = 0.23
17.39 0.23
69.96 0.35
CCA-SSG
64.28 0.37
22.55 0.49
70.26
0.37
78.20 0.24
15.97 0.15
68.15 0.24
GGD
64.21 + 0.39
20.58 0.40
68.97 0.40
78.14 = 0.25
15.75 + 0.16
66.11 = 0.33
REN
62.75 - 0.44
12.85 0.06
54.64 0.44
com
oom
oom
SRN2Vec
64.02 + 0.45
22.47 0.37
71.18 0.40
SARN
66.49 + 0.47
22.59
+: 0.51
72.74 +: 0.50
78.14 # 0.21
14.62 -: 0.02
68.54 + 0.30
Garner
81.40 + 0.30
62.45
0.64
93.27 + 0.22
82.97 + 0.16
47.22 +: 0.42
89.30 + 0.21
"oom" means out-of-memory.
Table 3: Results in Road Traffic Inference, with the best in bold and the second best underlined
Singapore RMSE
NYC RMSE
Methods
MAE
MAPE 1
MAE 1
MAPE J.
Deepwalk
3.43 + 0.03
4.31 + 0.05
0.721 + 0.038
4.31 = 0.03
5.92 + 0.05
0.267 + 0.002
MVGRL
3.04 + 0.04
3.82 + 0.04
0.629 + 0.041
3.91 = 0.02
5.16 +16
0.243 + 0.001
CCA-SSG
3.31 + 0.03
4.15 0.04
0.674 + 0.037
4.03 = 0.03
5.34 + 0.04
0.253
+ 0.003
GGD
3.37
4.27
0.684 1.043
4.80 0.03
6.63 1: 0.06
0.267 0.002
RFN
3.54
4.48 0.04
0.71710.00
oom
SRN2Vec
3.44
4.47
0.569 1669-000 0.025
SARN
3.40 0.03
4.32 + 0.05
0.697 0.038
4.66 0.04
6.39 0.07
0.262 0.002
Garner
2,80 + 0.03
3.52 + 0.04
0.579 + 0.030
3.30 - 0.02
4.40 + 0.03
0.207 + 0.002
"oom" meany out-of-memory.
8

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We compare the proposed Garner with base- lines in three downstream tasks, and the exper- imental results can be found in Table 2 3 and In road function prediction and road traffic infer- ence, we report the mean results and standard de- viation of 30 runs for each model. Among all the tasks, Garner performs significantly better than all the baselines. Specifically, road function prediction, Garner outperforms the best base- line by up to 22% in Micro-F1, 171% % in Macro- FI. and 25% in AUROC. In road traffic infer- ence tasks, Garner outperforms the best base- lines by up 18.5% in MAE, 17% in RMSE,
Table 4: Results on Visual Road Retrieval, with the best in bold and the second best underlined
Singapore
NYC
Methods
Recall@ 1
MRR
Recall 10
MRR f
Deepwalk
0.0083
0.0913
0.0013
0.0709
MVGRL
0.0088
0,0818
0.0324
0.1071
CCA-SSG
0.0755
0.0036
0.0807
GGD
0.0095
0.0920
0.0019
0.0695
0,0766
SRN2Vec
0,0123
0.0725
0om
dom
SARN
0.0143
0.1019
0.0036
0.0766
Garner
0.4600
0.3387
0,5531
0.2985
"oom" means out-of of-oooory....
and 17.4% in MAPE. This is because the geographic configuration can provide more details about the roads. For example, the geographic configurations of roads in living apartments and business regions are very different. Thus, the functions of these two roads can be more easily discriminated according geographic configuration aware road representation. As for road traffic inference, the geographic configuration provides more details about the conditions of roads. Thus, it is beneficial for traffic systems. On visual road retrieval, all the baselines give results similar random guesses, while Garner gives decent results. The results show that the street view images and geographic configurations provide very different information, which is not presented road network data. But that information can be well captured by our proposed Garner. We also find that some baselines use up GPU memory and cannot run on Tesla GPUs We discuss the scalability issue Appendix C.4
5.3 Model analysis
Case study We conduct a case study comparing the First and Third Laws of Geography. The case study will show the distinctive effect of the Third Law. We randomly select anchor road, compute its representation similarity with other roads (according to cosine similarity), ) and display the top 10 most similar roads. The anchor road in red, the top 10 similar roads by the First Law are shown in blue, and those by both laws are in orange. The results can be found in Fig. 2 With only the First Law, similar roads are much closer the anchor. With both laws, similar roads are further but have similar geographic configurations, as shown by comparing street view images. This demonstrates that the Third Law ensures similar representations for roads with similar configurations, regardless of distance.
Ohap
Figure 2: Case study: the top 10 most similar roads found by the First Law only and both laws.

---

Ablation studies We conduct ablation studies by: (1) gradually removing the components in Garner; (2) using different similarity measure build the augmented graph. The ablation results on road function predictions are listed in Table 5 and 6 while results on other tasks can be found in Appendix C.5 We show that the street view images, utilized to describe the geographic configurations, provide significant improvements in the quality of the road representation by comparing "Garner sns - -aug" and "Garner sms aug SVT". We also find that explicitly modeling the Third Law of geography provides significant improvements by comparing "Garner" and "Garner sns aug". Spectral negative sampling also provides obvious improvements in the Macro-Fl score and visual road retrieval. As for the choice of similarity measure, kNN similarity graphs are better than threshold similarity graphs on Road Function prediction, while slightly worse on Road Traffic Inference. Meanwhile using euclidean distance generate similar results using cosine similarity. As building KNN graphs is much faster than threshold graphs, we choose kNN graphs as the default setting.
Table 5: Ablation studies on Road Function Prediction
Singapore
NYC
Methods
Micro-FI (%) 1
Macro-F] (%)
AUROC (%)
Micro-FI (%) 1
Macro-FI (5)
AUROC (9)
Garner sug SVI
66.61
0,50
30.67 0.66
74.34 0.46
78.23 0.23
17.39 a: 0.23
69.96 0.35
Carnar sns aug
50.21
0.60
37.14
0.44
Garner sB8
80.65 + 0.31
60.57
+ 0.68
92.46 0.26
82.62 2 0.19
45.78 +: 0.52
88.61 = 0.18
Garner
$1,40 0.30
62.45
= 0.64
93.27
0.22
82,97
0.16
47.22
= 0.42
89.30 0.21
sns" means to generate negative samples only with feature shuffling. "- aug" means without geographic
configuration aware graph augmentation. SVI" means without street view images as inputs.
Table 6: Ablation studies of similarity measures on Road Function Prediction
Methods
Singapore
NYC
Micro-F1 (%)
Macro-F1 (%)
AUROC 1
Micro-F1 (%)
Macro-F1 (%)
AUROC (%)
knn-dist
81.40 + 0.300
62.45 = 0.64
93.27 =
82.97 = 0.16
47.22 + 0.42
89.30 0.21
kna-cos
81.30 +: 0.34
62.26 : 0.56
92.94 =
82.95 = 0.18
46.98 0.56
89.13 : 0.18
threshold dist
79.01 1: 0.56
56.71 1: 0.93
91.15 1 0.26
81.39
1 0.23
40.16 0.50
86.32 1 0.23
threshold-cos
79.45 + 0.32
57.76 + 0.53
91.71 0.23
82,51 0.20
45.07 0.59
88.73 + 0.19
Parameter sensitivity analysis We conduct sensitivity analysis on two hyper-parameters introduced by our method. They are the degree (k) of the augmented kNN similarity graph and the degree (d) of the negative graph. The results are visualized in Fig- 3 and more results are listed in Appendix C.6 In these figures, the shadows show the standard deviation. In our experiments, we find that the results are not sensitive to the syper-parameters.
Sensitivity analysis in road function prediction NYC Singapore
Sensitivity analysis in road function prediction
NYC Singapore
83
83
Micro-F1 F1 (9)
Micro-FF F1 (9))
02
82
87
79
78
78
10
30
40
10
15
20
30
Degree of similarity graph
Degree of negative graph
Figure 3: Sensitivity analysis of hyper--paameete and d.
6 Conclusion
In this paper, we embark on pioneering research investigating the Third Law of geography for road network representation learning. To model the Third Law, we introduce street view images to capture the geographic configuration and design a new contrastive learning framework with geographic configuration aware graph augmentation and spectral negative sampling. The experiments show that the proposed method brings significant improvements in road network representation and downstream tasks. There are certainly many future directions, such as modeling more geographic laws, designing new evaluations, and using other kinds of real-world data.
10

---

Acknowledgments and Disclosure of Funding
This research was supported in part by Distributed Smart Value Chain programme which funded under the Singapore RIE2025 Manufacturing, Trade and Connectivity (MTC) Industry Alignment (Award No: M23LAa0001), as well as cash and in-kind contribution from Sin- gapore Telecommunications Limited (Singtel), through Singtel Cognitive and Artificial Intelligence Lab for Enterprises (SCALE@NTU)""
This research was also partially funded by the Knut and Alice Wallenberg Foundation (KAW 2019.0550).
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A Backgrounds
A.1 Discussion the Laws of Geography
Definition (The First Law of Geography, or Tobler's First Law of Geography, 225 ). Everything is related to everything else, but near things are more related than distant things.
Definition 5 (The Third Law of Geography, (54)). The more similar geographic configurations of two points (areas), the more similar the values (processes) of the target variable at these two points (areas).
To illustrate the Third Law of Geography, consider two roads surrounded by residential buildings. Even though two roads are located very far apart, according to the third law, as they have very similar geographic configurations, they should still have similar representations.
As extensively discussed in the paper, this study has been substantially informed by the theories in geography and geographic information science, particularly the First Law of Geography and the Third Law of Geography. In fact, our study has also been partially informed by the Second Law of Geography, which is arguably about spatial heterogeneity. The Second Law of Geography implies that geographic variables and processes exhibit uncontrolled variance [6]. We are informed by this law from the perspective that the spatial proximity graph and the original graph only connect those close enough road segments, rather than forming complete graphs. This methodological choice acknowledges the considerable heterogeneity in the influence exerted by more distant roads.
B Additional calculation and proofs
B.1 Details of calculation in section 4.2
tr(Z" LzZ) = Σ Σ Ze (Ls)as
k fJ
Σ Σ Z (Ls) + Σ Z. (bs)sa)
Z (LS). +
2, + Σ 22,((Ls)s))
2
$51
1
B. R (S., + ,2Z S.,)) Siy)
2
i
1
2z,0)
2
1
Σ
-
2
B.2
Details of calculation in section 4.5
Here we show that AK SK ( H
Recall that S = D3 1/2 SD 1/2 is a symmetric matrix where each row or column is summed to 1.
Ax is matrix with A, = 1 Vi Ax Ak/n. Thus
(Ax Σ Sis5 = - Si,
Then we have
A A For the power of Ag, we have the following result for every and j
(15)
(AxAx)is = (AAc),(Ak)))
Σ
1
1
n
n
n'
15

---

where n is the dimension of Ax (i.e., Ax E E)) The matrix form of the result is
AcÂc Ax
(16)
Combining them together, we have
A S* H θ (.
AK)S* H
AKŠK H H
(...((AA()))
AOO
Additional contents for experiments
C.1 Downstream tasks
Road function prediction a classification task that determines the functionality of a road. The label of the functionality is one of ("commercial", "construction", "education", "fairground", "indus- wwwg/oiwi///ee
trial ", "residential". "retail", "institutional") (https://vil http:///wii..oenssttettttn... openstreetmap.
landuse), which is derived from the neighborhood region (land use). The labels of road function not from the road network data and were not considered in previous literature. In our experiments, get the functionality from the land use data in OSM, while other data sources are also feasible. However, the functionality of regions is only available in several cities. Therefore, this task is very meaningful in generating labels and analyzing the urban status in lot of cities.
Road traffic inference is a regression task predicting the average speed of vehicles on each road. is widely used to evaluate the effectiveness of road representations in previous literature [2] 3 23
Visual road retrieval retrieval task, where the input an image and underlying database stores road segments (e.g., a vector database of road embeddings). This task is to query roads where the input image should locate. real-world scenario is that, a traveller want visit some positions in city. He / She gets some pictures, but may not know where they are located. This task can help them find those places in seconds.
C.2 Baselines
29 is a network embedding algorithm to learn compressed vectorized node representations according to the structure of the graph. It first samples some random walks (i.c., sequences of nodes) from the graph. The nodes in random walks are regarded as words, while each random walk is regarded model on the random walks and learns the representations of nodes. Deepwalk does not consider the features on each node.
Deepwalk
sentence. Then Deepwalk trains skip-gram [24]
MVGRL [9] is very powerful graph contrastive learning method. It generates another graph view via graph diffusion process. Then, it maximizes the mutual information between the original graph and the augmented graph, following node-graph contrastive strategy. In our method, we incorporate the First Law based on this model.
CCA-SSG 47 is an unsupervised graph representation method. Instead of using conven- tional mutual information estimators, CCA-SSG builds its contrastive loss upon Canonical Correlation Analysis. does not need instance-level discrimination and negative sampling, and thus more efficient and scalable than contrastive based methods.
GGD [51 is built upon the graph contrastive learning framework but replaces the traditional mutual information estimator with a "group discrimination" loss. The new loss does not require complicated mutual information estimation but only needs to discriminate whether a sample is from a positive or negative sample. Therefore, much faster than graph contrastive learning methods based mutual information estimation.
RFN 15 is a road network representation method based graph attention networks [36 It regards junctions (intersections of roads) as nodes build a primal graph and its line graph, where road segments nodes and connected road segments are linked. It then
16

---

designs relational fusion layers that can perform message passing between both graphs. However, this also significantly increases memory usage, especially on large graphs.
SRN2Vec 39 is a the road network representation method based on random walk and skip-gram model [4]] To include geospatial information for road networks, it generates random walks according to both the graph topology and geospatial distance. To incorporate the basic features from OSM (e.g., road type), it introduces additional learning objectives such as classification for road type.
SARN [2] is road network representation framework based graph contrastive learning. It builds a weighted adjacency matrix according to the road network topology, distance similarity, and angular similarity. It then follows GCA (57] to produce augmented graphs by dropping edges according to the weights. It also designs a negative sampling technique according to the distance. Finally, the model is trained InfoNCE loss [35
C.3 Settings and implementation details
We use the Adam optimizer [16] with the learning rate as 0.001 and set the training iterations as 2500
with early stopping. The sampling size is set as 4000. For the settings of baselines, we follow their default setting but set the dimension of representation 512, the same as our method.
All the code is implemented with Python=3.1 11.8, 2yTorch=2.1 (CUDA=11.) 1.8) (28), DGL.2.1 41 All the experiments are executed on a Ubuntu Server (Ubuntu 20.04), with 8 x Nvidia Tesla V100 (32GB) GPUs, Intel(R) Xcon(R) Gold 6148 CPU @ 2.40GHz (40 cores and 80 threads) and 512
GB memory. The code of baselines is generally obtained from the authors' GitHub repo The only exception is that we use the DGL's implementation (https: /tt::///ittttt wttpuucoooocccecceooooocooeeceeo dmlc/ htt///mmccgll//eeee tgt/tree// master/ Master/exanpe ewwmples/eeeeeee..e.ee /pytorcc/ of Deepwalk and MVGRL for better efficiency.
C.4 Scalability
In our experiments, we find that some of the previous works are not scalable in our datasets. The reason could be that previously, they used much smaller datasets. Specifically, the road networks in [5] 39 have less than 10,000 nodes, less than one-tenth of our datasets, and thus, they do not need consider the scalability issue. In our method, as we perform sub-sampling process before applying graph convolution and loss, the memory usage on GPU does not grow with the data size, and thus, the proposed Garner is scalable large road networks.
C.5 Additional results on ablation studies
The ablation studies on Road Traffic Inference and Visual Road Retrieval are listed in Table and Table respectivvl..
Table 7: Ablation studies on Road Traffic Inference
Singapore RMSE
NYC
Methods
MAE
MAPE J
MAE
RMSE L
MAPE
Garner -nss- aug- SVI
3.04 + 0.04
3.82 0.04
0.629
0.041
3,91 + 0.02
5.16 + 0.03
0.243 0.001
Garner sns-- aug
2,99 1 0.02
3.74 0.03
0.610 0.036
3.53 0.02
4.70 0.04
0.221 0.002
Garner sns
2.82 - 0.02
3.54 = 0.03
0.606 = 0.040
3.35 + 0.02
4.45
+ 0.03
0.210 = 0.002
Garner
2,80 + 0.03
3.52 + 0.04
0.579 + 0.030
3.30 + 0.02
4.40
0.03
0.207 + 0.002
sns" " means without spectral negative sampling, but with feature shuffling to generate negative samples. aug"
means without geographic configuration aware graph augmentation. "- SVI" means without street view images inputs.
17

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Sensitivity analysis road function prediction
Sensitivity analysis in road function prediction
Singapare
Singaporc
Macro-F1 (%)
Macro-F1 (%)
60
55
50
45
45
10
20
10
15
Degree of similarity graph
Degree of negative graph
Sensitivity analysis road function prediction
Sensitivity analysis in road function prediction
NYC Singapore
NYC Singapore
93
92
92
AUROC
AUROC
91
90
89
10
20
10
1.5
Degree of similarity graph
Degree of negative graph
Sensitivity analysis in road traffic inference
Sensitivity analysis in road traffic inference
NYC
Singapore
Singapore
3.4
3.3
3.2
3.1
15
20
Degree of similarity graph
Degree of negative graph
Sensitivity analysis road traffic inference
Sensitivity analysis in
NYC Singapare
NYC Singapore
4.6
RMSE
4.2
3.8
3.6
3.6
15
20
Degree of similarity graph
Degree of negative graph
Sensitivity analysis in road traffic inference
Sensitivity analysis in road traffic inference
NYC Singapore
NYC Singapore
0.6
MAPE
0.5
MAPE
0.5
0.4
0.4
0.3
30
40
15
20
25
30
Degree of similarity graph
Degree of negative graph
Figure 4: Sensitivity analysis of hyper-paramete k and d.
18

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Table 8: Ablation studies on Visual Road Retrieval
Singapore
NYC
Methods
Recall 10 f
MRR f
Recall 10 f
MRR f
Garner sns aug SVI
0.0088
0,0818
0.0324
0.1072
Garner sns aug
0.2002
0.3013
0,2803
0,2555
Garner sns
0.3426
0.3112
0.4776
0.2805
Garner
0.4600
0.3387
0.5531
0.2985
ans" " means without spectral negative sampling, but with feature shuffling to generale negative samples. aug means without geographic configuration aware graph augmentation. "- SVT" means without street view images inputs.
C.6
Additional results on sensitivity analysis
D
Further discussions
D.1 Linitations
This paper is based on the Third Law of Geography and the Third Law of Geography. Though the two laws generally true, the method in this paper may fail where the two laws not applicable. For example, the First Law may fail on extremely large areas or limited data 555
The potential negative societal impact includes: (1) Our method requires street view images (SVIs) along roads. However, SVIs may not be up-to-date and thus our methods may provide outdated information. Also, SVIs cannot provide everyday changes in city. (2) method currently does not consider adversarial attacks from data, and thus may provide incorrect information for downstream tasks if it is attacked.
D.2 Broader Impact
As discussed in the introduction, road network representation learning provides fundamental in- struments for various downstream tasks in urban computing. It can improve the traffic system in cities and enhance safety. It also provides essential references for urban planners who want to know various facets of the cities. We also admit that there could be some negative societal impacts. We committed to ensuring our models are fair, unbiased, and respectful of individuals' privacy, also acknowledge potential risks, such as misuse of the technology.
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Reviews:
[{"review_id": "MfN5wRo3dM", "reviewer": "Reviewer_MjEv", "summary": "This paper proposes a novel framework, termed Garner, for road network representation learning that leverages both the Third Law of Geography and the First Law of Geography. It emphasizes both spatial proximity and geographic configuration similarity.  Street view images  are used to capture similarities in road surroundings by geographic configuration-aware graph augmentation, spectral negative sampling, and a dual contrastive learning objective. ​Experiments demonstrate that integrating the Third Law significantly improves performance in downstream tasks like road function prediction, traffic inference, and visual road retrieval.", "questions": "Q1: Why maximize the MI between the original graph $G^{[0]}$ and the augmented graph $G^{[1]}$? The two graphs have different semantics.", "limitations": "Adequately addressed", "rating": 4, "confidence": 3, "soundness": 2, "presentation": 3, "contribution": 2, "strengths": "S1: Street view images from OpenStreetMap are used as proxies for geographic configurations. \n\nS2: Considering the reverse implication of the Third Law: roads with dissimilar configurations should have dissimilar representations.\n\nS3: The proposed method is validated on Singapore and New York City road networks with street view images.", "weaknesses": "W1: The novelty of this paper is limited, as geographic configuration has been modeled in many studies on urban computing.\n\nW2: The choice of the lose, ie, to maximize the MI between the original graph $G^{[0]}$ and the augmented graph $G^{[1]}$, is not well justified and is difficult for me to understand.\n\nW3: Several key factors, such as points of interest (POIs), are not taken into consideration.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "The authors would like to thank the reviewer for providing constructive comments. We have made the following clarifications to address your concerns.\n\nResponse to the Weaknesses:\n\n1. The novelty of our paper is listed as follows:\n   - We introduce the **Third Law of Geography**, a fundamental principle in geographical sciences, which has not been explored in previous studies in road network representation learning.\n   - We design **novel graph contrastive learning** techniques, i.e., **geographic configuration-aware graph augmentation** and **spectral negative sampling**, where spectral negative sampling is inspired by the sparsest cut problem and spectral graph sparsification in spectral graph theory. \n   - According to [1], the definition of \"geographic configuration\" is \"the makeup and the structure of geographic variables over some spatial **neighborhood** around a point.\" Thus, the term \"geographic configuration\" requires information from both a spatial entity and its **neighborhood**. \n\n   To the best of our knowledge, all of the above have not been explored in the literature of geospatial entity representation learning. We hope this clarification makes our novelty much easier to follow.\n\n2. The original graph $\\mathcal{G}^{[0]}$ and the augmented graph $\\mathcal{G}^{[1]}$ contain different information from different views. Our goal is to fuse information from both views and generate better output representations of road segments. In particular, the augmented graph $\\mathcal{G}^{[1]}$ is constructed according to the Third Law of Geography. As written in our paper, \"Previous studies show that information from different views can be fused properly by maximizing their mutual information (MI) [2,3], which can also improve the quality of representations [3].\" Inspired by these, we maximize the MI between the original graph $\\mathcal{G}^{[0]}$ and the augmented graph $\\mathcal{G}^{[1]}$ so as to allow the output representation to learn from the view constructed according to the Third Law of Geography.\n\n3. Thanks for your suggestions. We do not include POIs in the paper due to the following reasons: \n   - **Focus on the Third Law of Geography**: Our paper focuses on the Third Law of Geography. In our paper, street view images (SVIs) can already model geographic configurations and the third law very well. Thus, SVIs are sufficient to illustrate our concepts and achieve our research objectives.\n   - **Distribution and Coverage of POIs**: We would like to argue that POIs are currently not appropriate for our problem. A major issue is observed that POIs are unevenly distributed in cities [10], and a large portion of road segments do not have nearby POIs. In contrast, SVIs cover almost every road in a city, and we can sample SVIs for each road segment. \n   - **Commercial Bias of POIs**: Another issue is that POIs are provided by Internet Web Maps for map search, and thus their contents are mainly for commercial functions (e.g., restaurants), leading to poor performance in non-commercial regions such as industrial or residential areas [10, 11]. However, there are many roads outside commercial regions where POIs may not provide sufficient information for subsequent analytical tasks. In contrast, SVIs can provide meaningful information across diverse regions.\n   - **Future Work**: We acknowledge that it is very interesting to identify an appropriate way to consider POIs in Garner in future work. And we will try our best to achieve this in the future.\n\n\n\n---\n\n[1] Spatial prediction based on Third Law of Geography. Annals of GIS, 2018.\n\n[2] Learning representations by maximizing mutual information across views. In NeurIPS.\n\n[3] Contrastive multi-view representation learning on graphs. In ICML.\n\n[4] Graph convolutional networks for road networks. In SIGSpatial 2019.\n\n[5] On representation learning for road networks. ACM Trans. Intell. Syst. Technol 2021.\n\n[6] Spatial structure-aware road network embedding via graph contrastive learning. In EDBT 2023.\n\n[7] Robust road network representation learning: When traffic patterns meet traveling semantics. In CIKM 2021\n\n[8] Jointly contrastive representation learning on road network and trajectory. In CIKM 2022\n\n[9] Learning effective road network representation with hierarchical graph neural networks. In KDD 2020\n\n[10] Urban2vec: Incorporating street view imagery and pois for multi-modal urban neighborhood embedding. In AAAI 2020\n\n[11] Knowledge-infused Contrastive Learning for Urban Imagery-based Socioeconomic Prediction. In WWW 2023", "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": "", "extra_scores": {}}, {"review_id": "NZJbw8Vwde", "reviewer": "Reviewer_UWD1", "summary": "This paper introduces Garner, dual geographic-configuration-aware graph contrastive learning framework for road representation learning. Both the third law of geography and the first law of geography are considered by using street view images, geographic configuration aware graph augmentation,  and spectral negative sampling. The effectiveness of Garner is tested on three downstream tasks:  road function classification, road traffic prediction, and visual road retrieval.", "questions": "1. Why can the averaging pool of CLIP-image embeddings of SVI along a road represent its geographic configuration?\n2. Could you do an ablation study on different similarity measures in Section 4.2?\n3. Under Equation 8, you wrote \"we design the negative sample based on Z and K, ..., by discriminating positive samples from negatives\". Could you explain the intuition why the discriminative between positive and negative samples can minimize Equation 8?", "limitations": "The author need to add a paragraph about their limitations and some potential negative societal impact of their work", "rating": 6, "confidence": 4, "soundness": 4, "presentation": 3, "contribution": 3, "strengths": "1. The contributions of the proposal Garner framework are clearly highlighted.\n2. The idea of jointly considering the third law of geography and the first law of geography is intriguing.\n3. The statistical significance of the first two tasks are listed which is very good.", "weaknesses": "1. IMHO, the emphasis of learning the third law of geography is a bit oversold. Why can the averaging pool of CLIP-image embeddings of SVI along a road represent its geographic configuration? To me, the SVI pooled embedding can be simply treated as the visual feature of each road. \n2. In terms of Section 4.2, other than the norm-based measure as the similarity measure, can you do an ablation study on different similarity measures?\n3. Some math symbols are not well-explained which makes the paper a bit hard to read. For example, what are L_S, L_K, D_S, D_K? L and D are defined, but the subscriptions need to be explained. What are \\mathbf{x}_i and \\mathbf{x}_j in Equation 7?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "The authors thank the reviewer for providing constructive and detailed comments, which may significantly improve this paper. We are pleased to inform you that all your concerns have been successfully addressed. Please see the detailed response to each of your comments listed below. \n\n\nResponse to the weaknesses:\n\n1. In A-Xing Zhu's paper [1] on the Third Law of Geography, the term \"geographic configuration\" is defined as \"the makeup and the structure of geographic variables over some spatial **neighborhood** around a point.\" In our scenario, the target variable is the output representation of roads, and thus we should include variables and features that can effectively describe the roads. The street view images (SVIs), which provide the visual features of a road, also include important descriptions of a road. For example, the surface condition of a road and the number of lanes in a road (, which is not available for the majority of OSM data,).  Also, the geographic configuration includes descriptions of a point itself and its neighborhood. Street view images describe both the visual features of a road and its **neighborhood**, e.g., its surrounding buildings, regions etc. Therefore, we consider SVIs a suitable proxy to describe the geographic configuration of a road. To use SVIs in our model, we need to: (1) encode the images into vectorized representations; (2) aggregate multiple street view images along each road segment. To this goal, our implementation is \"the averaging pool of CLIP-image embeddings of SVI along a road.\"\n2. Following your suggestion, we have conducted an ablation study with different similarity measures. As mentioned in the paper, popular choices for similarity measure includes: norm/distance-based similarity, cosine similarity, Gaussian kernel. However, Gaussian kernel $\\exp ( -\\frac{(a - b)^2}{2 \\sigma^2} )$ is a monotonic function of distance, and also a bijective function of distance. Thus we only conduct experiments on norm/distance-based similarity and cosine similarity. The results are listed in the following table. We observe that, with different similarity metrics, the model achieves very **similar** results.\n  \n   **Road Function Prediction on Singapore**\n   \n   | Metric | Micro-F1 (%) $\\uparrow$ | Macro-F1 (%) $\\uparrow$ | AUROC (%) $\\uparrow$ |\n   | ------ | ----------------------- | ----------------------- | -------------------- |\n   | norm   | 81.40 $\\pm$ 0.30        | 62.45 $\\pm$ 0.64        | 93.27 $\\pm$ 0.22     |\n   | cosine | 81.30 $\\pm$ 0.34        | 62.26 $\\pm$ 0.56        | 92.94 $\\pm$ 0.21     |\n   \n   **Road Function Prediction on NYC**\n   \n   | Metric | Micro-F1 (%) $\\uparrow$ | Macro-F1 (%) $\\uparrow$ | AUROC (%) $\\uparrow$ |\n   | ------ | ----------------------- | ----------------------- | -------------------- |\n   | norm   | 82.97 $\\pm$ 0.16        | 47.22 $\\pm$ 0.42        | 89.30 $\\pm$ 0.21     |\n   | cosine | 82.95 $\\pm$ 0.18        | 46.98 $\\pm$ 0.56        | 89.13 $\\pm$ 0.18     |\n   \n   **Road Traffic Inference on Singapore**\n   \n   | Metric | MAE $\\uparrow$  | RMSE $\\uparrow$ | MAPE $\\uparrow$   |\n   | ------ | --------------- | --------------- | ----------------- |\n   | norm   | 2.80 $\\pm$ 0.03 | 3.52 $\\pm$ 0.04 | 0.579 $\\pm$ 0.030 |\n   | cosine | 2.82 $\\pm$ 0.02 | 3.54 $\\pm$ 0.03 | 0.585 $\\pm$ 0.024 |\n   \n   **Road Traffic Inference on NYC**\n   \n   | Metric | MAE $\\uparrow$  | RMSE $\\uparrow$ | MAPE $\\uparrow$   |\n   | ------ | --------------- | --------------- | ----------------- |\n   | norm   | 3.30 $\\pm$ 0.02 | 4.40 $\\pm$ 0.03 | 0.207 $\\pm$ 0.002 |\n   | cosine | 3.32 $\\pm$ 0.02 | 4.44 $\\pm$ 0.03 | 0.208 $\\pm$ 0.002 |\n\n3. Sorry for the confusion. Following the conventions in graph learning, the subscript of $\\boldsymbol{L}\\_{\\boldsymbol{S}}$ indicates that this is a graph Laplacian matrix induced by some adjacency matrix $\\boldsymbol{S}$, which is similar to $\\boldsymbol{D}$, the degree matrix. In particular, $\\boldsymbol{D}\\_{\\boldsymbol{S}}$ is the degree matrix of a graph with adjacency matrix $\\boldsymbol{S}$, i.e., $(\\boldsymbol{D}\\_{\\boldsymbol{S}})\\_{i, i} := \\sum_{i=1}^{n} \\boldsymbol{S}\\_{i}$, and $\\boldsymbol{L}\\_{\\boldsymbol{S}} := \\boldsymbol{D}\\_{\\boldsymbol{S}} - \\boldsymbol{S}$. $\\boldsymbol{D}\\_{\\mathcal{K}}$ and $\\boldsymbol{L}\\_{\\mathcal{K}}$ are the degree matrix and graph Laplacian matrix of the complete graph $\\mathcal{K}$ respectively. Equation 7 is listed as follows:\n   $$\n   usc\\_{\\mathcal{G}} = \\min\\_{\\boldsymbol{x} \\in \\\\{0, 1\\\\}^n - \\\\{\\boldsymbol{0}, \\boldsymbol{1}\\\\}} \\frac{\\sum_{(i, j) \\in \\mathcal{E}} (\\boldsymbol{x}\\_i - \\boldsymbol{x}\\_j)^2}{\\sum_{(i, j)}(\\boldsymbol{x}\\_i - \\boldsymbol{x}\\_j)^2} \n       = \\min\\_{\\boldsymbol{x} \\in \\\\{0, 1\\\\}^n - \\\\{\\boldsymbol{0}, \\boldsymbol{1}\\\\}} \\frac{\\boldsymbol{x}^T \\boldsymbol{L}\\_{\\mathcal{G}} \\boldsymbol{x}}{ \\boldsymbol{x}^{T} \\boldsymbol{L}\\_{\\mathcal{K}} \\boldsymbol{x}},\n   $$\n   where $\\boldsymbol{x}$ is a n-dimensional vector, $\\boldsymbol{x}\\_i$ is the $i$-th element of vector $\\boldsymbol{x}$. $\\forall i$, $\\boldsymbol{x}\\_i$ is either $0$ or 1, but $\\boldsymbol{x}$ cannot be a vector of all $0$s or $1$s. These explanations are represented as $\\boldsymbol{x} \\in \\\\{0, 1\\\\}^n - \\\\{\\boldsymbol{0}, \\boldsymbol{1}\\\\}$. The semantic meaning of this equation is that, the sparsest cut problem partitions nodes into two subsets and $\\\\{0, 1\\\\}$ denotes the which subset a node should belong to.", "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": "", "extra_scores": {}}, {"review_id": "GEibjsUGXj", "reviewer": "Reviewer_ggbs", "summary": "This paper proposes a novel method for learning representations of road networks. It highlights the limitations of existing methods that primarily use the First Law of Geography, which emphasizes spatial proximity. The authors introduce a new framework, Garner, that incorporates the Third Law of Geography, focusing on geographic configuration similarities. They employ a graph contrastive learning approach with geographic configuration-aware graph augmentation and spectral negative sampling. The framework is evaluated on real-world datasets from Singapore and New York City, showing significant performance improvements in downstream tasks.", "questions": "1.\tHow does the proposed method perform on road networks with significantly different characteristics (e.g., rural vs. urban)? As the authors said in section 4.5: \"roads with dissimilar geographic configurations should have dissimilar representations.\"\n2.\tAre there any examples or case studies demonstrating the practical implementation of Garner in different urban contexts?\n3.\tWhat are the computational requirements and scalability aspects of the proposed method for larger datasets? For example, if we want to measure the similarity between different cities, we need to use national or global maps.\n4.\tHow does the model deal with dynamically changing road networks, such as those undergoing construction or frequent changes? Does the whole model need to be re-trained after the changes?", "limitations": "1.\tThe authors should consider testing their method on a more diverse set of datasets to ensure broader applicability.\n2.\tConsideration of temporal changes in road networks and how the model adapts to these changes would strengthen the practical application of the method.", "rating": 5, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "1.\tThe paper introduces a novel application of the Third Law of Geography, providing a fresh perspective in the field of geographic information systems. The methodology is robust, with thorough theoretical grounding and comprehensive empirical evaluation.\n2.\tThe paper provides a solid theoretical basis for its methods. The mathematical proofs are thorough and well-constructed\n3.\tThe proposed approach demonstrates substantial improvements in real-world datasets, highlighting its practical value.", "weaknesses": "1.\tIn Section 4.2, the kNN and threshold-based methods for building new connections are highly sensitive to their parameters. This sensitivity greatly impacts the generation of new connections, making it difficult to control and optimize, thereby affecting the model's consistency and robustness.\n2.\tThe study is limited to datasets from Singapore and New York City; additional testing on more diverse datasets would enhance the findings' applicability.\n3.\tThere is no code or dataset provided.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your constructive comments and suggestions. We apologize for any confusion. We are pleased to inform you that all concerns have been addressed. Below are our responses to each comment.\n\nResponse to the Weaknesses:\n\n1. We have conducted the sensitivity test on the hyper-paramter $k$ of kNN graph, and we find our method is not sensitive to $k$. \n    - For implementation, we choose the kNN graph because of its high efficiency. \n    - For kNN graphs, the hyper-parameter is $k$. Therefore, we conducted comprehensive hyper-parameter sensitivity tests on various datasets and metrics, and the results are reported in Section 5.3 and Appendix C.6. The results show that the $k$ does **not** have a significant impact the performance of various downstream tasks. In other words, our model is not sensitive to the values of $k$. In our main experiments, we also use $k=6$ on all experiments, and this setting can produce much better results than all the baselines.\n\n2. Thanks so much for your suggestion. Currently, we only use those datasets because of the limited data sources. Specifically, street view images are very **expensive** and time-consuming to collect, and other sources of data (e.g., road function, and traffic speed) are unavailable in most cities. To mitigate the potential issues caused by data availability, we have considered diverse downstream real-world tasks, i.e., road function prediction, road traffic inference, and visual road retrieval, to comprehensively test the proposed method and other baselines. In the future, we will try to collect more datasets for evaluation.\n\n3. Sorry for the confusion, we have uploaded the code in the \"Supplementary Material\" under \"Abstract\" in this webpage.\n\n\n\nResponse to Questions:\n\n1. We achieve \"roads with dissimilar geographic configurations should have dissimilar representations.\" by negative sampling in the contrastive learning framework. In particular, contrastive learning requires positive samples and negative samples. Thus we design a negative graph $\\bar{\\mathcal{G}}^{[1]}$ whose edges mainly connect roads with dissimilar geographic configurations. By discriminating the negative sample and anchor, we can achieve \"roads with dissimilar geographic configurations should have dissimilar representations.\"\n\n2. Following the reviewer's suggestion, we conducted a case study comparing the First and Third Laws of Geography. The case study is included in the attached PDF under \"Author Rebuttal by Authors\" and will be added to the final version of the paper. \n    - We randomly selected an anchor road, computed its representation similarity with other roads (according to cosine similarity), and displayed the top 10 most similar roads. The anchor road is red, the top 10 similar roads by the First Law are blue, and those by both laws are orange. \n    - With only the First Law, similar roads are much closer to the anchor. With both laws, similar roads are farther but have similar geographic configurations, as shown by comparing street view images. This demonstrates that the Third Law ensures similar representations for roads with similar configurations, regardless of distance.\n\n3. For the GPU memory, the proposed method does not require more GPU memory as the number of roads (nodes) grows. Because we use a technique called subsampling (refer to **Sample** in Fig. 1 and the text description from line 207). In particular, for each iteration (forward and backward propagation), we only sample a subgraph with a fixed size of nodes (4000 nodes in our setting). We observe that the GPU memory usage is less than 10GB, and thus the proposed method can run on a single RTX 3090 GPU. In the implementation of graph learning (in a single graph), if the graph is not very large, we usually load the graph into the memory [1]. If the graph is extremely large and cannot be loaded into the memory, we can first sample the index of the nodes, and then read related edges and node features from the disk.\n\n4.  Thanks very much for raising this interesting question. In current literature on road network representation, the changes in road network itself have not been considered, because its changes are relatively slow, and usually require several months or years. We also follow their settings. Actually, graph neural networks can be trained on certain graphs and tested on other similar graphs, and maintain competitive results. (For example, the PPI datasets are several graphs of proteins, and learned GNN models are tested on unseen proteins to predict the label of nodes. [2,3]) Thus, if there are only some small changes, we do not need to re-train the model, we just need to update the input data and get the output representation with the same model. If there are significant changes in the road network, we can try to re-train the model, and re-train is not very time-consuming. We just need several hours to train the model on Tesla V100 GPU, which is even slower than on a single RTX 3090 GPU.\n\nResponse to Limitations:\n\n1. (Refer to \"Response to Weaknesses\", 2)\n2. (Refer to \"Response to Questions\", 4)\n\n---\n\n[1] https://docs.dgl.ai/generated/dgl.data.DGLDataset.html#dgl.data.DGLDataset\n\n[2] Inductive Representation Learning on Large Graphs. In NeurIPS.\n\n[3] Simple and Deep Graph Convolutional Networks. In ICML.", "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": "", "extra_scores": {}}, {"review_id": "UFDMcJqLf6", "reviewer": "Reviewer_u7JA", "summary": "This paper introduces a novel framework for road network representation learning, with the key innovation being the incorporation of the Third Law of Geography. This concept is implemented through a tailored graph contrastive learning objective, featuring geographic configuration-aware graph augmentation and spectral negative sampling. To further preserve geographic proximity (the First Law of Geography), which has been proven crucial in existing literature, the authors further propose a dual contrastive learning strategy to accommodate both modeling perspectives. Experimental results on datasets from Singapore and New York City demonstrate significant improvements over several baseline methods in road function prediction, road traffic inference, and visual road retrieval tasks.", "questions": "1. Why is the spectral negative sampling strategy only applied to the contrastive learning task corresponding to the third law? How does the derivation of this strategy in section 4.5 relate to the mutual information maximization in equation (5)? Would it not be more intuitive to design an additional contrastive learning task to focus on encouraging the node representations of the augmented graph to satisfy both the third law and its inverse version?\n\n2. Why does the inverse version of the third law in section 4.5 hold? For instance, two roads with dissimilar geographic configurations might still exhibit spatial proximity, suggesting that their representations should remain similar.\n\n3. What proportion of roads in the dataset are associated with street view images? How does the model perform in geographic regions where (a) street view images are limited or of poor quality, or (b) the two geographic laws do not hold?\n\n4. Compared to widely used Points of Interest (POI) data, what are the unique advantages of street view images in this context?\n\n5. What are the specific experimental settings for the road traffic prediction task? If the objective is to predict future traffic variations, how do static road network representations contribute to this task without considering the dynamic correlations among road segments?", "limitations": "see weakness", "rating": 3, "confidence": 4, "soundness": 2, "presentation": 2, "contribution": 2, "strengths": "1. The paper addresses a significant problem in road network representation learning, which has important implications for real-world applications such as traffic management and urban planning.\n\n2. The core idea of the paper is grounded in established geographical theory, and the incorporation of street view images as a supplementary data source enhances the implementation of this concept.\n\n3. The authors demonstrate awareness of scalability issues and incorporate sampling techniques in their method design, enabling efficacy in large-scale road networks.\n\n4. The paper presents comprehensive experimental validations of the model's superiority over three downstream tasks.", "weaknesses": "1. The research challenges identified by the paper lack depth. In particular, the first challenge is insufficiently articulated, equivalent to stating that \"generating road representations that preserve the Third Law of Geography is challenging\".\n\n2. A significant weakness of the paper lies in the limited novelty of its ideas and methodological design:\n\n   a. While existing literature may not explicitly introduce the concept of the Third Law of Geography, several works have already considered the similarity of road segments in regions with similar functionalities [1,2,3]. Moreover, in the broader field of spatio-temporal data mining, several studies have considered the hierarchical structure of urban road networks [4,5].\n\n   b. The simple concatenation of street view image representations with other road features lacks sophistication. Images and other road attributes exist in different modalities, potentially introducing multi-modal data fusion issues that may impede the effective encoding of street view images into road representations.\n\n   c. The Simple Graph Convolution (SGC), its theoretical interpretation, and graph contrastive learning have already been well-developed in previous research.\n\n   d. The fusion of the third law and the first law is presented as one of the two major challenges the paper aims to address. However, the proposed solution merely combines two contrastive learning tasks without a thorough discussion of potential conflicts between them.\n\n   e. Although the paper considers scalability issues, the proposed sub-sampling solution is relatively straightforward.\n\n3. The paper lacks detailed discussions on the universality of the third law and the first law, particularly in large-scale road networks, raising concerns about the practical applicability of the method. Besides, merely mentioning this in the limitations section is insufficient.\n\n4. The second paragraph at the beginning of section 4 contains confusing notations that are not previously introduced.\n\n5. Experimental design:\n\n   a. As the paper's solution to improve scalability is straightforward, the baseline methods should also be equipped with the same graph sampling techniques to ensure a fair comparison.\n\n   b. The paper lacks case studies that demonstrate the effectiveness of integrating street view images. Relying solely on ablation studies is inadequate for this purpose.\n\n   c. The paper does not use weighted average of the two contrastive learning tasks, which is important as the first law and the third law might conflict in certain scenarios. Along this line, experiments on the trade-off between the two contrastive learning tasks should also be conducted. \n\n[1] Pre-training Context and Time Aware Location Embeddings from Spatial-Temporal Trajectories for User Next Location Prediction. In AAAI 2021.\n\n[2] Pre-training local and non-local geographical influences with contrastive learning. Knowledge-Based Systems 2023.\n\n[3] Pre-training Contextual Location Embeddings in Personal Trajectories via Efficient Hierarchical Location Representations. In ECML-PKDD 2023.\n\n[4] Semi-Supervised Hierarchical Recurrent Graph Neural Network for City-Wide Parking Availability Prediction. In AAAI 2020.\n\n[5] GPT-ST- Generative Pre-Training of Spatio-Temporal  Graph Neural Networks. In NIPS 2023.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your detailed comments and suggestions. We apologize for any confusion. We are pleased to inform you that all concerns have been addressed. Below are our responses to each comment. As the reviewer has many concerns, we conduct more discussions to address them.\n\nResponse to Weaknesses:\n\n1. We analyze the meanings of the third Law and point out that incorporating it into the road network representation learning is very beneficial. This challenge is in contrast with the first Law, which emphasizes the importance of distance effect. The Third Law focuses on mapping between relationships for geographical configurations in geospatial entities (road segments) to relationships of target variables (representations). It is more challenging to learn the mapping of relationships than to learn the mapping of values. More explanations can be found in our response to \"Weakness 2\" below.\n\n2. We argue the **novelty** of our idea and method as follows. In general, the novelty of our papers is twofold: (1) we introduce the Third Law of Geography for road network representation learning; (2) we design novel methods to learn the third law in graph neural networks (GNNs). In particular, our **novel designs** include geographic configuration-aware graph augmentation and spectral negative sampling. The responses to the detailed questions are listed as follows.\n   - a. The term \"geographic configuration\" is not functionalities of regions, and the Third Law of Geography is not related to hierarchical structures in cities. In particular, the definition of \"geographic configuration\" in [1] is \"the makeup and the structure of geographic variables over some spatial **neighborhood** around a point.\", far beyond the functionalities of regions. The street view images (SVIs), which provide the visual features of a road, also include important descriptions of a road. For example, the surface condition of a road and the number of lanes in a road (, which is not available for the majority of OSM data,). Also, the geographic configuration includes descriptions of a point itself and its neighborhood. Street view images describe both the visual features of a road and its **neighborhood**, e.g., its surrounding buildings, regions etc. Thus we think the street view images are a good proxy, among various current data, to describe the geographic configuration of a road. Besides, our work is **not** related to hierarchical structures in a city. However, we would also like to add another paragraph in the \"Related Work\" section to discuss the literature that the reviewer mentions.\n\n   - b. For multi-view / modality fusion, our design is not a direct concatenation of different data. Our designs include: (1) projecting different data into another space with learnable parameters and then concatenating them (as illustrated in Section 4.1); (2) fusing information from multiple views with mutual information maximization. The first design (joint representation) is widely adopted in multi-modality fusion [8], while the second design is inspired by [9]. Both [8] and [9] demonstrate that information from different views can be fused properly in our method.\n\n   - c. Our main contributions, as listed at the end of the Introduction in the paper, are: (1) introduction of the **Third Law of Geography** to road network representation; (2) **geographic configuration-aware graph augmentation** and **spectral negative sampling** in the graph contrastive learning framework. Those are our **original** designs and have never appeared in previous literature. As our proposed method is based on graph contrastive learning and SGC, which are preliminaries of our method, we need to put the contents in the method for those who are not familiar with these topics. Besides, the theoretical interpretation of SGC is closely related to the implementation of the Third Law of Geography, and thus we discuss why SGC can achieve our goal in Section 4.3. We believe that bridging existing theories to real-world applications is also very important and can extend the scope of existing theories.\n\n   - d. We have two efforts on fusing the First and the Third Law (the tuning of weights are listed in the comments):\n\n       - The two losses have some sharing parameters (module $g_{\\theta_0}$), which can learn the consensus, while those modules ($g_{\\theta_1}$ and $g_{\\theta_2}$) that do not have sharing parameters learn the discrepancy (potential conflicts). The final representation is the aggregation of the outputs from the three modules.\n       - Train the two losses jointly. For joint training, in our preliminary experiments, we have tried some multi-objective optimization techniques to balance the two terms. Specifically, we have tried the Pareto optimum [1] in neural networks to adaptively choose proper weights to balance the two terms. However, we find that (1) with this technique, the results do not have significant improvement; (2) We find the optimal weights for the two terms vary from (0.4, 0.6) to (0.6, 0.4), very close to (0.5, 0.5). Those are the reasons why we do not tune the weights and state in the last paragraph of Section 4.6 that \"Therefore, we do not introduce additional hyper-parameters to adjust their weights.\"\n       - We also conduct some empirical results on tuning the weights of the two losses, and the results on the road function prediction task are listed as follows. We introduce another hyper-parameter $\\beta$ to balance the loss of the third law ($\\mathcal{L}_1$) and the first law ($\\mathcal{L}_2$) : $\\mathcal{L} = \\beta \\mathcal{L}_1 + (1 - \\beta) \\mathcal{L}_2$ . The results show that the learning performance is not sensitive to the weight $\\beta$.\n   - e. Our paper does not focus on scalability issues in road network representation learning, and we do not claim our contribution on the scalability issue neither. We provide a sub-sampling trick in our implementation, which works well within our framework.", "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": "", "extra_scores": {}}, {"review_id": "Tke0g9ix0f", "reviewer": "Reviewer_cFij", "summary": "This paper proposes a novel framework for learning road network representations. Different from previous approaches, the proposed framework leverages a particularly designed graph contrastive learning method to integrate the Third Law of Geography into the process of road network representation learning, which can significantly alleviate the current shortcomings. In both classical and newly identified downstream tasks of road representation learning, the proposed framework achieves significant improvements compared with other state-of-the-art approaches.", "questions": "As stated in “Weaknesses,” I have the following questions.\n\nQ1. Are there more detailed explanations or examples that can show the significance of the Third Law of Geography in road network representation learning?\n\nQ2. Are there more easy-to-understand descriptions/explanations of the proposed spectral negative sampling method?\n\nQ3. Are there case studies or discussions in the experiments that can show the implication of the Third Law of Geography in road network representation learning?\n\nQ4. Since this work is based on the Third Law of Geography, it seems it is similar to context-aware spatiotemporal learning. It is encouraged for authors to discuss the correlations and distinguishment between context-based ST learning and Third Law of Geography based learning.", "limitations": "The authors have discussed the potential limitations but not much sufficient.", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 2, "contribution": 3, "strengths": "S1. Novelty: The idea of integrating the Third Law of Geography in learning road network representations for urban computing tasks is novel. \n\nS2. Technical solidity: The geographical law considered by the authors is mathematically modeled in the forms of graph augmentation and negative sampling, which is then integrated into the learning process of road network representation through a particularly designed graph contrastive learning framework. The proposal of this computational method lies in a non-trivial theoretical background.\n\nS3. Comprehensiveness: The empirical validations of the proposed approach are comprehensive. Besides of verifying the proposed approach with classical tasks of urban computing, new learning tasks closely related to real scenarios are further identified by the authors and used in the experiments. \n\nS4. Effectiveness: Compared with existing approaches, the proposed method achieves significant improvements on all downstream tasks.", "weaknesses": "W1. This paper lacks detailed explanations of using the Third Law of Geography in road network representation learning. The authors are suggested to give more explanations or examples to show the significance of using the Third Law.\n\nW2. The spectral negative sampling is effective but may not be easy to understand for non-experts. The authors are encouraged to provide more explanations of this technique.\n\nW3. In experiments, this paper only presents improvements in metrics, without more intuitive results. The authors are encouraged to give more discussions or empirical analysis of the implication of the third law on representations.\n\nW4. The presentation can be improved. Also, there are some typos in the paper.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your constructive comments and suggestions. We apologize for any confusion. We are pleased to inform you that all concerns have been addressed. Below are our responses to each comment.\n\nResponses to Weaknesses:\n\n1. To illustrate the Third Law of Geography, consider two roads surrounded by residential buildings. Even though two roads are located very far apart, according to the third law, as they have very similar geographic configurations, they should still have similar representations. We will include these discussions in the final version of the paper to provide readers with easy understandings of the proposed method.\n2. In the \"Spectral Negative Sampling\" section, we design a negative sample compared with the positive sample (the augmented graph from the third law of geography) for better contrastive learning. The positive sample connects nodes with very similar geographic configurations. Thus if we design a negative sample which mainly connects roads with dissimilar geographic configurations, then by discriminating the anchors (the original graph) from the negative sample, we can enhance the representations and achieve that \"roads with dissimilar geographic configurations should have dissimilar representations\". Then we design the specific form of the negative sample, which is inspired by the sparsest cut problem (Equation 8). In particular, it could be a complete graph with a proper graph encoder (as in Section 4.5). However, leveraging the complete graph as the negative sample is very time and space consuming (, even with subgraph sampling). Then we apply spectral graph sparsification to effectively approximate the complete graph, which results in a d-regular graph. Finally, we design a d-regular graph as the negative sample, with a properly designed graph encoder.\n\n3. Following the reviewer's suggestion, we conducted a case study comparing the First and Third Laws of Geography. The case study is included in the attached PDF under \"Author Rebuttal by Authors\" and will be added to the final version of the paper. \n    - We randomly selected an anchor road, computed its representation similarity with other roads (according to cosine similarity), and displayed the top 10 most similar roads. The anchor road is red, the top 10 similar roads by the First Law are blue, and those by both laws are orange. \n    - With only the First Law, similar roads are much closer to the anchor. With both laws, similar roads are farther but have similar geographic configurations, as shown by comparing street view images. This demonstrates that the Third Law ensures similar representations for roads with similar configurations, regardless of distance.\n\n4. Thanks for your suggestion. We will polish and double-check the writing.\n\n\n\nResponse to the Questions:\n\n1. (Refer to response to weakness 1)\n1. (Refer to response to weakness 2)\n1. (Refer to response to weakness 3)\n4. Following the suggestion of the reviewer, we discuss the correlations and differences between: (1) context and geographic configuration; and (2) context-aware spatiotemporal learning and the Third Law of Geography.\n   - (1) **Context** is usually defined as the some contents or attributes of a spatial entity, such as the spatial context of a road segment in [1] and the context of a POI [3], where the spatial context is still some attributes of a road. \"**Geographic configuration**\" is defined as \"the makeup and the structure of geographic variables over some spatial **neighborhood** around a point,\" in A-Xing Zhu's paper [2] on the Third Law of Geography. In our problem, the geographic configuration of a road segment includes both its features and the features of its **neighborhood**, e.g., its surrounding buildings, natural environments, regions, etc. And street view images are very good proxies to describe those. In a word, the major difference is that the term context, in the literature of spatiotemporal learning, focuses only on a spatial entity itself, while **geographic configuration** concerns both the attributes of the spatial entity itself and its spatial neighborhood. \n   - (2) **Context aware learning**, inspired by word2vec [4], encourages entities within a context to have similar representations, which is more similar to the First Law of Geography, \"everything is related to everything else, but near things are more related than distant things\". In contrast, the **Third Law of Geography** states that \"The more similar geographic configurations of two points (areas), the more similar the values (processes) of the target variable at these two points (areas).\" It maps the similarity relationship of the geographic configurations to the similarity relationship of the target variable (i.e., road representation in our paper).\n\n   We will include the above discussions in the final version of the paper.\n\n\n---\n\n[1] Robust Road Network Representation Learning: When Traffic Patterns Meet Traveling Semantics. In CIKM '21.\n\n[2] Spatial prediction based on Third Law of Geography. Annals of GIS, 2018.\n\n[3] How is the Third Law of Geography different? Annals of GIS, 2022.\n\n[4] Distributed representations of words and phrases and their compositionality. 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Author rebuttal:
We would like to express our sincere gratitude to all the reviewers for their careful review and constructive comments. Here, we briefly summarize our response to all the comments.
1. A case study can be found in the uploaded PDF file.
2. More ablation studies and concrete examples have been provided to demonstrate the critical role of the Third law of Geography in road network representation learning and clarify the motivations of the proposed approach.
3. As suggested by the reviewers, more clarifications on the modules of the proposed methods have been provided to make the proposed method easy to understand. In addition, sensitivity tests and more ablation studies have been conducted to show the peculiarities of the proposed approach. 
4. Experimental settings are clarified to make the experiments in this work convincing. 
5. As suggested by the reviewers, we have conducted discussions to distinguish the proposed approach from other related works, thus enhancing the novelty and contributions of the paper. 
6. How we will improve the paper according to all the reviewers' suggestions has been illustrated.

Again, we thank all the reviewers, and we will carefully revise the paper following all the suggestions raised.

Meta-review: This paper introduces a novel framework, Garner, which leverages graph contrastive learning to integrate the Third Law of Geography into road network representation learning. The method is technically sound, and the authors provide comprehensive empirical validation, showing significant improvements across several downstream tasks. While the paper is strong in novelty and effectiveness, it would benefit from clearer explanations of the Third Law's role, additional discussion of spectral negative sampling, and improved presentation. Despite these minor issues, the paper's contributions are significant, and I recommend acceptance with revisions for clarity.
Decision: Accept (poster)