Cross-City Latent Space Alignment for Consistency Region Embedding
Authors: Meng Chen
Hongwei Jia
Zechen Li
Wenzhen Jia
Kai Zhao
Hongjun Dai
Weiming Huang
Venue: ICML 2025 poster (2025)
Keywords: Consistency Region Embedding
Cross-City Knowledge Transfer
Latent Space Alignment
Human Mobility
Socioeconomic Indicators Prediction
Primary area: applications->social_sciences

Abstract: Learning urban region embeddings has substantially advanced urban analysis, but their typical focus on individual cities leads to disparate embedding spaces, hindering cross-city knowledge transfer and the reuse of downstream task predictors. To tackle this issue, we present Consistency Region Embedding (CoRE), a unified framework integrating region embedding learning with cross-city latent space alignment. CoRE first embeds regions from two cities into separate latent spaces, followed by the alignment of latent space manifolds and fine-grained individual regions from both cities. This ensures compatible and comparable embeddings within aligned latent spaces, enabling predictions of various socioeconomic indicators without ground truth labels by migrating knowledge from label-rich cities. Extensive experiments show CoRE outperforms competitive baselines, confirming its effectiveness for cross-city knowledge transfer via aligned latent spaces.

Cross-City Latent Space Alignment for Consistency Region Embedding
Meng Chen'
Hongwei Jia Zechen Li!
Wenzhen Jia
Kai Zhao
Hongjun Dai
Weiming Huang
Abstract
(Chen al., 2025a; Li et al., 2022; Ning et al., 2024; Zhang et al., 2023).
Learning urban region embeddings has substan- tially advanced urban analysis, but their typical focus on individual cities leads to disparate em- bedding spaces, hindering cross-city knowledge transfer and the reuse of downstream task predic- tors. To tackle this issue, we present Consistency Region Embedding (CoRE), unified framework integrating region embedding learning with cross- city latent space alignment. CoRE first embeds regions from two cities into separate latent spaces, followed by the alignment of latent space man- ifolds and fine-grained individual regions from both cities. This ensures compatible and com- parable embeddings within aligned latent spaces, enabling predictions of various socioeconomic in- dicators without ground truth labels by migrating knowledge from label-rich cities. Extensive ex- periments show CoRE outperforms competitive baselines, confirming its effecctivnness for cross- city knowledge transfer via aligned latent spaces.
From a holistic perspective, as illustrated in Figure (a)) learning region representations typically involves two stages: 1) regions from city X are projected into a latent space to generate representations (Z*), and 2) these representations are fed into downstream task predictors (decx) to produce analytical results. However, the second stage requires suffi- cient ground truth data to train decx, which is often difficult to acquire in practice. Many studies focus on cities like New York City, where ground truth labels are readily available with open data projects, while other cities remain understud- ied (Zhang et al., 2022).
To address this issue, we aim to answer the following ques- tion in the paper: can align the latent spaces between different cities so that we can leverage the knowledge from one city to facilitate the analysis in other cities? Technically, this hinges on whether the latent embedding spaces learned from urban sensory data in different cities are comparable. The straightforward answer that the latent spaces learned separately for different cities are typically incomparable and unaligned, making difficult to trans- fer knowledge through them. This incomparability issue is shown in Figure 2(a). where latent spaces learned by MVURE (Zhang et al., 2021) are projected onto the same 2D plane using t-Distributed Stochastic Neighbor Embed- ding (t-SNE (Maaten & Hinton, 2008). The triangles and dots represent regions in two cities (Chengdu and Xi' an), with yellow, green, and red indicating low, medium, and high GDP levels, respectively. The two spaces are clearly different, indicating meaningless direct comparison of two cities.
1. Introduction
Learning vector representations (embeddings) for small ur- ban units (regions) using various urban sensory data sources, including points of interest and human trajectories, has be- come a common practice in urban computing and analytics (Chen al., 2024; Huang et al., 2023; Li et al., 2023; Jia et al., 2024; Mai et al., 2023; Zhang et al., 2024; Chen et al., 2025b). These representations have been proven to be valuable for various urban downstream tasks, including regional land use analysis, crime rate prediction, and house price forecasting, demonstrating significant potential for real-world applications in urban planning and management
In this paper, we aim to achieve the knowledge transfer between cities by reusing task predictors (decx). These predictors, trained in label-rich city, can be reused in an- other city without ground truth labels, enabling cross-city predictions. Recent studies have realized this through unsu- pervised translation (Yabe et al., 2019; 2020; Haikal et al., 2022), where they transform region representations learned in one city to the other, similar to translating words across languages, as shown in Figure (bb). Specifically, they follow a two-stage paradigm: intra-city region embedding learning and cross-city translation. First, region embedding meth-
'School of Software, Shandong University, Jinan, China 2 Business School, Shandong Normal University. Jinan, China e "Walmart AI Lab, California. USA 'Department of Physical Ge- ography and Ecosystem Science, Lund University, Sweden. Cor- respondence to: Hongjun Dai <dahogn @ sdu. sdw.edu..nn.. Weiming Huang < Huann @ leeds.ac.uk>>
Proceedings of the 42nd International Conference Machine Learning, Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

---

Cross-City Latent Space Alignment for Consistency Region Embedding
(a)
(c)
Cross-City
Clayx
Region Embedding Medel
Region Embedding Model
Latent Space Alignment
z
decx
x
Latent Manifold Aligament
urbun regiets
Intent space of city
task predictors
latent space of city X
(triiiing)
decx
(b)
z (prediction)
Latent Individual Aligrmmet
Z Z
Iatent spaice translation
z
decx
Region Embedding Model
Z
task predictors
J(Z')
latent space of city Y
Intent space of city
task predictoons
latent space of city Y
Figure 1. Illustration of: (a) learning and using region representations within a single city, (b) existing latent space translation methods that requires direct mapping T from Z to Z and (c) CoRE method that integrates region embedding lcarning with cross-city alignment to produce compatible representations across cities, cnsuring that semantically similar regions lic close in the aligned spaces.
ods generate region representations (Z and Z") within individual cities (X and Y). where the two latent spaces are incompatible. Then they manually construct anchoring pairs of region representations across cities using fixed corre- spondence rules (e.g., urban hierarchical structures) learn transformation functions (Zx = T(Z")). This process translates the region representations of one city (Y) to the space of another (X), enabling the reuse of task predictors (decx) in city based on T.
(a) MVURE
(b) Our Proposed CoRE
Figure 2. Visualization of the pre-trained region embeddings. We project embeddings into 2D via t-SNE, where triangles and dots denote regions in Chengdu and Xi'an, an, respectively. Colors (yellow, green, red) indicate low, medium, and high GDP levels. Panel (a) shows the MVURE (Zhang et al., 2021) embeddings, with clearly separate city spaces, while panel (b) shows CoRE embeddings. where semantically similar regions are closely aligned.
While these methods have shown promise, they suffer from two major shortcomings:
1) Disconnected Embedding and Translation: In two- stage approaches, the decoupled learning paradigm creates fundamental limitation: the frozen pre-trained embeddings in the translation stage force cross-city mapping to operate on rigid latent spaces. This rigidity constrains the translation function to suboptimal linear projections between selected anchor pairs, failing to adapt the inherent non-linear man- ifold structures of urban feature spaces. Therefore, develop- ing one ste-stage method that jointly learns and aligns region embeddings through a synergistic optimization process is needed.
ment, and individual region alignment. Specifically, CoRE consists of three components. First, we employ a graph attention network as the encoder to generate city-specific region representations in distinct latent spaces using hu- man mobility data. Second, we construct virtual parallel common anchors in both spaces as bridges and align the data manifolds using the idea of relative representations. Third, we develop cross-city attention pipeline to transfer pairwise region correlations between two spaces, ensuring embedding consistency at the individual region level.
2) Reliance on Hand-Crafted Correspondence: Previous methods depend on fixed, hand-crafted correspondence (e.g., matching regions across cities by check-in in counts), which can be incomplete biased especially since user check- ins reflect social media biases (Wang et al., 2016; Li al., 2024). An adaptive cross-city alignment method free of manual rules is needed to address this limitation.
As illustrated in Figure 2(b), CoRE aligns the latent spaces of two cities such that semantically similar regions across cities are positioned closely. This makes CoRE useful for ur- ban embedding learning, which enables knowledge transfer between different cities trained on similar urban data types. The key contributions of this paper are as follows:
In this paper, we propose a one-stage Consistency Region Embedding method (CoRE), which integrates region em- bedding learning with cross-city latent space alignment to produce compatible and comparable region representations across cities, as shown in Figure I(c). Recognizing the challenge of achieving cross-city alignment without human- crafted rules and labels, CoRE accomplishes this through two mutually reinforcing pathways: latent manifold align-
We propose CoRE, a one-stage consistency region embed- ding method that integrates region embedding learning with cross-city latent space alignment a unified frame- work. This approach ensures compatibility and compara- bility of region representations from different cities within
2

---

Cross-City Latent Space Alignment for Consistency Region Embedding
an aligned latent space.
et al., 2024). To this end, we first construct base region embedding model for an individual city. This model cap- tures human mobility patterns between regions and derives latent region representations using a self-supervised graph embedding approach.
We achieve cross-city alignment of latent spaces through two intendependent pathways: latent manifold alignment and latent individual alignment, addressing both global and individual perspectives. Our method accounts for the complex interplay between cities without relying on explicit anchoring pains of region representations across cities based on human-crafted rules.
3.1.1. MOBILITY GRAPH CONSTRUCTION
Given a human mobility dataset M = {m1, my,....; } where each trip m, (For ra) represents movement from an origin region To to destination region ra- construct mobility graph & {V,E} for each city. Here, V = fri represents the N regions as nodes, and the edge weights ε = {wiy ] are derived from M. Specifi- cally, the transition frequency (edge weight) from region T; to region r, is calculated as:
We conduct comprehensive experiments across three downstream tasks using datasets from three cities. The results clearly show the advantages of CoRE over base- line methods. Data and source codes are available at: http://ggttbb.coo////Muaaaaaaa
2. PROBLEM FORMULATION
Definition 2.1 (Urban Region). A city is divided into n disjoint urban regions R = {r1, T2....; :.a) where each region r; is defined by a set of boundary points specified by their latitude and longitude coordinates.
May = count - rr)/ count(rs rk);
(1)
where count(r: - ry) denotes the number of trips from r; to ry. This normalization ensures that each edge weight reflects the proportion of trips from a given origin to each possible destination. Using this approach, we construct two separate mobility graphs, G and GY, for cities X and Y, respectively.
Definition 2.2 (Region Representations), For a region r:x in city X, its representation is encoded as a d-dimensional vector Z," The representations of all regions in city X are collectively represented as a (Nx x d) matrix z. where Nx denotes the number of regions in the city.
Definition 2.3 (Consistency Region Embedding across Cities). Our objective is to generate compatible region rep- resentations for cities X and Y by aligning their latent spaces. This alignment ensures that semantically similar regions from both cities are positioned closely within the shared latent space. Achieving consistent region embedding for cities X and Y makes their representations compatible and comparable. Thus, downstream task predictors trained with region representations in city X, where ample ground truth data is available, can be directly applied to make accu- rate predictions in city Y.
3.1.2. GRAPH EMBEDDING
Based on the mobility graph G, we employ a graph attention network (GAT) (Veličković et al., 2017) to learn the latent representation of each node (region). The input vectors for the N regions are initialized as {E, E R xd1 The GAT layer computes the feature representation Z, R Rixd for region r; follows:
Z:
Z
(N)
Z
Z
Σ MEN,
(b) d
E, w(n,
h=1
3. Method
(h) = exp(s!)) (k))
Σ exp(=!l))
(2)
ENN;
In this section, we first introduce the base region embedding model, which independently learns region representations for each city. We then propose cross-city latent manifold alignment component designed to align the data manifolds of two latent spaces without requiring external supervision. Finally, we present cross-city latent individual alignment component that enhances fine-grained alignment of individ- ual region representations through a self-supervised task.
(h) Lea w(()) E, w |wy, (
where W()) E Rdxd, (e E Rixd and (1) E RR1x3d are learnable parameters of the h-th attention head, H is the number of attention heads, || denotes concatenation, and Nf represents the neighbors of region ri.
3.1.3. INTRA-CITY REGION EMBEDDING LOsS
To effectively learn region representations, we utilize self- supervised task that reconstructs mobility patterns among regions within an individual city. Specifically, we predict the destination region given 72 using the region represen- tations Z. For specific region r;, the distribution of the
3.1. Base Region Embedding Model
Human mobility within a city reflects the relationships be- tween its different regions, making it a popular data source for learning region representations (Yao et al., 2018; Liu
3

---

Cross-City Latent Space Alignment for Consistency Region Embedding
latent space Z
relative representation
first relative space A%jl based on Z
relative representation
second relative space Apel based on A
2
72
2
A
A
A
simnje.
simnee,0
simte,a)
simte,
simne,,
stonje, o)
2
Ag
sinne 80
simie, an
Areto
Aimee
siim/e,
stimte,
Ag
simtooa
Arri
Latent Manifold Aligument Loss
A
A simnje, a)
A
A: sim((e.A)
sin((o.a)
Alst
ximte,,) e)
simnee o)
Ag sinIte.))
simie..)
simme. el
stinte.
simie,
23
A3
simito.)
simt(o.a)
Alrts
simto.a)
siim(o.
xim
relative space A7e based on z
second relative space Ayet based on A
latent space z"
relative representation
relative representation
virtual parallel common anchors
data points in latent space Z
data points in latent space 2
Figure 3. The framework of cross-city latent manifold alignment. Three common anchors A1, A2, and A3 (colored dots) are randomly generated both latent spaces, For given anchor A., we compute its similarity w.r.t. the region representations on the data manifold of z and ZV. yiclding vectors (A and Y.,,) of dimensionality 3 and respectively. Each dimension is treated as coefficients in coordinate system defined by all region representations, which are orthogonal in this example only for visualization purposes. Similarly, in the same coordinate system. Finally, we
compute the second relative representations A,a./ A w.t.A.A/ AA... /AAa which minimize the difference between A, X and A Yet to cnsure the alignment of the latent manifolds of Z and Z".
destination region ry is computed as:
3.2.1. RELATIVE REPRESENTATIONS OF PARALLEI. COMMON ANCHORS
(r, r2) exp(Z. 2, 2/ exp(Z. Zz ")
(3)
Due to the varying number of data points (regions) in each latent space, directly measuring the similarity between the data manifolds of two latent spaces is challenging. To ad- dress this, we propose using N₂, randomly generated virtual parallel anchor points, A IR xd which remain con- sistent across the latent spaces of different cities. These anchors serve as bridges for comparison, where N, is the number of anchors, and their dimensionality matches that of the region representations.
Using the human mobility data M, we define the intra-city region embedding (RE) loss as:
RR
Σ (MM-))EMM
logú (ry re).
(4)
M
This approach reconstructs actual mobility patterns based on the graph structure. enabling us derive the region representations Z and Y for both cities.
To represent the manifold of the latent space using these anchors, we adopt the concept of relative representations (Moschella al., 2023). Specifically, each anchor is rep- resented relative to all region representations in the la- tent space. We define generic similarity function sim Rd x Id + IR to capture the relationship between the an- chors and the region representations, yielding a scalar score Arel, = sim (A, Z,) for two absolute representations A, and Zj. Given the region representations Z," .... Z in the latent space z the relative representation of A; is
3.2. Cross-City Latent Manifold Alignment
The region embedding model in Section 3.1 generates city- specific region representations in distinct latent spaces. Aligning these separate latent spaces for cross-city com- parison poses significant challenges, particularly due to the absence of labeled paired data or correspondence annota- tions, as well as the differing numbers of regions across cities. To address these challenges, we propose a cross-city latent manifold alignment method. This method leverages the relative representations of virtual common anchors as shared reference system for both cities. By replacing the original absolute representations with relative reference system, defined by the similarity between region representa- tions and common anchor points, we ensure that the region representations of both cities are learned within a unified reference framework (see Figure 3).
A. (siin A., z sssnssnnn...... Zx )).
(5)
where cosine similarity is chosen the similarity function due to its invariance to imgl--preserve transformations. Similarly, the relative representation of A, with respect to the latent space Z is computed as:
A (sim(A,, ZY )... (A, Z
(6)
Based on Equations (5) and (6), we compute the relative

---

Cross-City Latent Space Alignment for Consistency Region Embedding
representations of all anchors in matrix form, projecting each anchor point A, Rd into the region sets R- Nx and Rxx IR-V in the latent spaces z and Z². This is formally represented as:
Isten srace 24
Chty-Spciific Painwis Region Cunclation
Attention based Cross City Correlation
Arto
Artn
Laieit
('mes-Spaoo Alteation
Individaal
Aliammest
Atto -1 Alts
Loss
A A A A.
where A E NN.N and Alel E NNN,, in which each entry quantifies the similarity between an anchor and a region within the city. The samples in A and A Y are rescaled to unit norm, capturing the intrinsic shape of the data by considering only the relative angles between points.
laneri space 2
City-peciffc Pairwise Region Curelatiin
Figure 4. Cross-city latent individual alignment.
from Z* to Z and vice versa. Specifically, if we can cycle through Z + Z - Z (or Z + z + z²) and ensure that the pairwise region correlations in the original and cycled spaces closely match, it indicates that the cross- city pairwise relations among regions are well preserved. This serves as strong evidence that the two latent spaces further aligned at the individual level.
We the parallel common anchors bridges and project A A and A AY into relative space based on the common anchor set A. Each sample is represented as a function of the common anchor set, computed as:
A A.D AND T A = A A
(8)
where AN E RNN.N and Ald E NN are also rescaled to unit norm. At this stage, through two rounds of relative representations, A X and Y are aligned within the same reference system.
This process is analogous to machine translation between two languages (e.g., English to Spanish). For instance, trans- lating words from English to Spanish and then back to En- glish should preserve the semantic relationships between the original English words. If these relationships remain consis- tent before and after translation,
3.2.2. LATENT MANIFOLD ALIGNMENT LOSS
can be confident that the translation process is reliable at the indivddul-woort level. Similarly, our cross-space attention mechanism ensures that the pairwise relationships between regions are preserved across cities, enhancing the alignment of individual region representations.
For well well-aligned latent spaces x and Z", the difference between A and A remains small, the latent mani- folds of the two spaces are similar. Conversely, significant discrepancies between the latent manifolds result in large differences in A and A To ensure the alignment of the latent manifolds, we minimize the difference between A and A and define the latent manifold alignment (LMA) loss as:
The proposed latent individual alignment method consists of several key steps, illustrated in Figure 4. First, we compute city-specific pairwise region correlations cre- ate ground truth labels. Next, we employ a cross-attention mechanism to generate cross-city correlation matrices from x to Z and from Z to Z Finally, we use these cross- city pairwise correlation matrices to reconstruct intra-city pairwise region correlations and minimize the reconstruc- tion differences based the ground truth signals.
LM
AX NZ
A
where || ll2 denotes the L2 norm. This difference is solely determined by the parallel common anchors in the latent spaces and is independent of the number of regions in each city. Moreover, the latent manifold alignment does not rely on human-defined rules for creating anchoring pairs of region representations across cities.
3. CITY-SPECIFIC PAIRWISE CORRELATIONS
Using the region representations in the latent spaces x and ZY, we compute the intra-city pairwise region corre- lation matrices Cor X-x E Nx XNx and Cor Y-Y
3.3. Cross-City Latent Individual Alignment
In addition to aligning the latent manifolds of two spaces, we aim to achieve more fine-grained alignment of individ- ual region representations. Effective alignment should bring semantically similar regions from different cities closer to- gether, which is crucial for cross-city knowledge transfer. To this end, we propose a self-supervised task that enhances alignment from an individual perspective. The core idea is to utilize cross- attention mechanisms to transfer pairwise region correlations between the two latent spaces:
R X as ground truth labels:
Cor x X = (Z* Y- z" (Z"))T (10)
3.3.2. ATTENTION-BASED CROSS-CITY PAIRWISE CORRELATION
To measure cross-city region correlations, we employ a cross-attention mechanism that facilitates interaction be-
5

---

Cross-City Latent Space Alignment for Consistency Region Embedding
Tween region representations from the two latent spaces. The cross-attention module consists of two parallel attention op- erations:
4. Experiments
queries Q* and keys K- are derived from latent space z* while queries Q" and keys KY are derived from latent space z By computing the dot product of queries and keys, we obtain the attention-based cross-city pairwise region correlation matrices Attn E R XNy and Attn Attn y-x E N This process defined as:
In this section, we evaluate the proposed CoRE on three cross-city urban prediction tasks with real-world datasets and compare its performance against various baselines.
4.1. Data
We use real-world datasets from three cities: Xi'an (XA), Chengdu (CD), and Beijing (BJ). Each dataset comprises ur- ban sensory data (including region data and human mobility data) and downstream label data (i.e., urban socioeconomic indicator data). The details of each data type are introduced in Appendix A.
Attn x Q* (K /Va
Attn Y = Q" (K*)//vO,
(11)
Q" =z=="". w", Kt zz w'
Q" w", k" z²w*,
where 8 Rdxd and W e Rdxd are trainable parame- ters.
4.2. Experiment Settings
4.2.1. 1. MODEL PARAMETERS
3.3.3. LATENT INDIVIDUAL ALIGNMENT Loss
In the base region embedding model, we utilize a two-layer GAT as the encoder with an embedding dimension d set to 128 and the attention heads H set to 8. For cross-city latent manifold alignment, we initially generate 1000 anchors and further assess the impact of varying anchor counts in our experiments. The optimization of the model is conducted using the Adam optimizer, with learning rate configured at 1 x 10-3.
Using the two cross-city pairwise correlation matrices, we reconstruct the city-specific pairwise region correlations through a cyclical approach. We then minimize the recon- struction differences based on the ground truth city-specific pairwise region correlations and define the latent individual alignment (LIA) loss as:
C
Cor X Attn X-Y Attn x
X
4.2.2. BASELINES
(12)
Cor
Attn Y-X
Attn
x-Y
To evaluate CoRE, we compare against unsupervised trans- lation methods and domain adaptation techniques. Among the translation methods, we primarily benchmark against the approach proposed by Yabe et al. (2020). This method first generates city- region representations and then employs three strategies (rank-based, hierarchical stochastic, and hierarchical batch) to construct anchoring embedding matrices across cities. These matrices are aligned using Orthogonal Procrustes and Affine alignment techniques, resulting in six baselines: RP (Rank-based Procrustes), RA (Rank-based + Affine), HSP (Hierarchical Stochastic + Procrustes), HSA (Hierarchical Stochastic Affine), HBP (Hierarchical Batch + Procrustes), and HBA (Hierarchical Batch + Affine). Furthermore, we include MMD (Saito et al., 2018), Ady (Ganin et al., 2016), and CrossTReS (Jin et al., 2022) as domain adaptation baselines, along with CARPG (Yang et al., 2023) as knowledge transfer base- line. We also introduce lower-bound baseline, Individual, which generates city-specific region representations without any cross-city alignment. Detailed descriptions of these baselines are provided in Appendix A.2.
N2
By minimizing this loss, the pairwise relative positions of regions preserved. This holds true for both intra-city and inter-city region pairs, strongly indicating that the individual region representations from the two cities are positioned reasonably within the aligned latent spaces.
3.4. Model Training
Our proposed CoRE is one-stage approach that simul- taneously learns region representations for two cities and aligns their latent spaces. We combine the objectives into the overall loss function:
C = (cX + LBB) LMA + SCLIA
(13)
where CRE and CR denote the intra-city region embedding losses for cities and Y, respectively. The terms a and are hyperparameters that adjust the weights of the LMA loss and the LIA loss, respectively. This objective function can be optimized using stochastic gradient descent. Once optimized, the two latent spaces x and z are aligned within the same coordinate system, positioning semantically similar regions from different cities closer together. This alignment facilitates effective cross-city knowledge transfer and enables the reuse of task predictors across cities.
4.2.3. EVALUATION METRICS
We conduct cross-city region-level prediction of sociocco- nomic indicators using region representations in aligned
6

---

Cross-City Latent Space Alignment for Consistency Region Embedding
Table 1. Performance comparison on three downstream tasks with the XA and CD datascts, where the hest results are represented in bold and the performance improvements of CoRE are compared with the second best results marked by underlined.
XA(X (CD()
CD(X MXA(Y)
Method
GDP
Population
Carbon
GDP
Population
Carbon
MAE
МАPE
MAE
МАРE
MAE
МАРE
MAE
MAPE
MAE
MAPE
MAE
MAPE
Individual
475.84
20.39
1694.82
7.92
480.05
21.69
247.9
10.61
978.15
11.92
176.19
4.56
RP
189.75
11.91
664.31
3.62
145.11
10.51
191.44
6.19
672.58
5.39
148.11
2.53
RA
197.47
12.58
654.83
3.84
143.99
10.49
187.07
6.08
614.32
5.27
143.04
2.09
HSP
189.48
11.66
674.31
3.74
143.46
10.13
192.22
6.43
697.59
5.71
144.49
2.1
HSA
183.68
11.51
642.17
3,71
140.73
9.98
182.52
5.6
622.43
5.33
141.06
1.97
HBP
196.14
11,52
682.71
3.82
149.6
10.33
228.25
8.65
808.61
7.84
152.76
2.96
HBA
196.67
11.53
661.88
3.61
153.71
9.77
187.7
5.68
653.88
5.53
142.91
2.07
MMD
205.48
12.97
767.26
4.8
153.38
9.9
208.17
7.07
776.82
6.61
148.05
2.51
Adv
204.92
12.79
742.62
4.13
153.8
10.04
216.67
7.81
779.52
5.75
153.77
3.01
CrossTReS
201.06
12.71
698.49
3.98
164.81
11.21
195.13
6.81
689.83
5.69
142.96
2.08
CARPG
188.08
11.89
650.62
3.85
133.82
9.66
189.81
6.14
655,39
5,58
144.99
2.21
CoRE
178.93
11.4
620.15
3.42
127.45
9.42
170.25
5.06
580.98
4.88
136.56
1.77
Improvement (%)
2.59
0.96
3.43
5.26
4.76
2.48
6.72
9.64
5.43
7.4
3.19
10.15
latent spaces. The training data consists of region represen- tations (Zx) and socioeconomic indicator labels (ly:" ) including GDP, population, and carbon emissions, from the source city (X). The test data comprises region represen- tations (Z)) and corresponding labels ([y) D from the target city (Y). First, a downstream task predictor deex is trained using the source city's 's representations Z and so- cioeconomic labels {y: J The predictive performance is evaluated by applying the trained decx to the target city's s representations Z Ridge regression is employed as the task predictor. We use mean absolute error (MAE) and mean absolute percentage error (MAPE). Lower values of MAE and MAPE indicate higher predictive accuracy,
distributions and fail to adequately capture inter-region relationships. Additionally, disparities in the number of regions between cities further compromise their alignment effectiveness. The CARPG exhibits limited performance due to its inability to explicitly align feature distributions between citics. The Adv method also underperforms com- pared to other methods, which we attribute the limita- tions of unsupervised learning. In the absence of labeled data from the target city, the alignment process cannot be directly validated or optimized based on predictive per- formance, potentially leading to incomplete or inaccurate alignment.
Our proposed CoRE method achieves the best perfor- mance with two key contributions: 1) it aligns both the la- tent manifolds of embedding spaces and individual region representations across cities, and 2) the cross-city align- ment enhances the quality of region embedding learning. The superiority of CoRE is further validated by paired t-tests (Hull, 1993), which confirm that its improvements over the basclines are statistically significant (p-value < 0.01).
4.3. Performance Comparison with Baselines
Table I presents the cross-city socioeconomic indicator pre- diction performance of various methods on the XA and CD datasets, where X denotes the source city and Y denotes the target city. Each method is evaluated over five runs, and the average values of MAE and MAPE are reported. Additional results for other city pairs are provided in Appendix A.3. From these results, we have the following observations:
To further validate the effectiveness of approach, visualize the region representations learned by HBA and CoRE for two cities by projecting them onto 2D planes us- ing t-SNE (Maaten & Hinton, 2008). Detailed results are provided in Appendix A.4. The visualizations demonstrate that CoRE effectively aligns individual region representa- tions across cities, achieving fine-grained alignment of latent spaces from both global and local perspectives.
The Individual method performs the worst, as it fails to align latent spaces across cities. This underscores the necessity of cross-city aligmment to effectively reuse task predictors trained in data-rich cities. In contrast, the latent space translation methods (RP, RA, HSP, HSA. HBP, and HBA) achieve better performance. These methods lever- age urban hierarchical structures to construct effective correspondences between regions, enabling the transfor- mation of target city region representations into the source city's 's latent space.
We also investigate whether the cross-city alignment com- promises within-city prediction performance, and if so, to what extent. The detailed analysis in Appendix A.5 confirms that this compromise is minor. Therefore, CoRE maintains strong within-city predictive accuracy while successfully
The MMD and CrossTReS methods exhibit poor per- formance, as they primarily focus on aligning feature
7

---

Cross-City Latent Space Alignment for Consistency Region Embedding
350
Stage
850
We Clp--Saa LIA CokE
250
via LMA CoKE
250
XAAI CIEXA
700
XAXII
200
XAXI CBMA
weo LMA
MAE
MAB
MAR
250
Colli:
750
200
200
600
150
MAE
MAF
150
500
100
150
650
150
20th 6P um um (s00
20
eP (OP)) uP
2 g (0t) (000 (s09)
number
number
number
50 XXCD CDNA
550
XXCD
100 XXCD
(a) GDP
(b) Population
(c) Carbon
(a) GDP
(b) Population
(c) Carbon
Figure 6. Effect of the number of virtual parallel anchors.
Figure 5. Performance comparison of different variants.
enabling cross-city alignment.
12:00 180
680
MAR
(40
640
120
4.4. Ablation Study and Parameter Analysis
0.0
T00
100
not
G
P
4.4.1. STUDY OF DIFFERENT VARIANTS
(a) GDP
(b) Population
(c) Carbon
To evaluate the contribution of each component in CoRE, we conduct an ablation study by designing three variants: I) CoRE w/o One-Stage: The one-stage paradigm is separated into two stages. First, region representations z and z are learned using the intra-city region embedding loss. Then, z and z are projected into two vector spaces via affine layers and aligned using MLMA and L without updating the parameters of the base region embedding model. 2) CoRE w/o LMA: The cross-city latent manifold alignment component is removed, and only the losses C and CLIA are used. 3) CoRE w/o LIA: The cross-city latent individual alignment component is removed, and only the losses CRE and CLMA are used.
Figure 7, Effect of weights a and B.
that a larger number of anchors enhances the model's 's ability to align latent manifolds. However, further increasing Na beyond 1000 results in performance degradation, likely due to overfitting increased computational complexity.
The parameters a and / control the influence of different components in the total loss function. To investigate their impact, we vary their values within the range (0.01, 0.1, 1, 10, 1003. Figure 7 illustrates the MAE results for the XA/CD pair, demonstrating that CORE achieves optimal performance when both a and 3 are set to 1. Deviating from this balance, either by increasing decreasing a and B, leads to suboptimal performance.
The results of CoRE and its variants in terms of MAE for XA/CD and CD/XA pairs shown in Figure 5. Additional results for other city pairs are provided in Appendix A.6. We observe that both CoRE w/o LMA and CoRE w/o LIA underperform compared to CoRE. The former struggles to align embedding spaces from a global perspective, while the latter lacks the ability to finely align individual region representations across cities. Additionally, CoRE w/o One- Stage exhibits inferior performance due its inability to adaptively adjust region representations based on the effec- tiveness of cross-city latent space alignment.
5. Conclusion
In this paper, we introduce CoRE, a framework that in- tegrates region embedding learning with cross-city latent space alignment to produce compatible and comparable consistency region representations across cities. CoRE com- prises three key modules: 1) an intra-city region embedding module that generates city-specific region representations from human mobility data, 2) a latent manifold alignment module that aligns data manifolds of two spaces using rela- tive representations, 3) a latent individual alignment module that ensures precise alignment of individual regions across cities through cross-attention mechanism. Experimental results on data from three cities demonstrate that CoRE out- performs state-of-the-art methods in cross-city prediction tasks. Importantly, our approach eliminates the need for manual inter-city correspondence rules, making it broadly applicable to unsupervised latent space alignment tasks.
4.4.2. STUDY OF PARAMETER SENSITIVITY
The parameter N. represents the number of virtual parallel anchors used latent manifold alignment. To evaluate its impact on model performance, we vary N₂ from 200 to 2000 in increments of 200. Figure 6 presents the MAE results for the XA/CD and CD/XA pairs, with similar trends observed for the other four city pairs. Our analysis reveals that CoRE performs poorly when N. = 200, indicating that an insufficient number of anchors hinders effective manifold alignment. Increasing N. from 200 to 1000 leads to a significant improvement in performance, suggesting
8

---

Cross-City Latent Space Alignment for Consistency Region Embedding
Impact Statement
Haikal, C., Alizadeh, P., Rodrigues, C., and Chongke, B. Place embedding across cities in location-based social networks. In Proceedings of the 37th ACM/SIGAPP Sym- posium on Applied Computing, Pp. 539-546, 2022.
Learning effective representations for urban regions (neigh- borhoods) has become an increasingly popular approach for various urban analyses, such as inferring land use and population distribution. These representations are typically learned in seff-supervise manner, without requiring task- specific ground truth data. However, making task-specific predictions still relies on ground truth data to train predic- tors, which is often scarce or unavailable in practice. In this work, we propose a cross-city latent space alignment method that enables the transfer of learned patterns across cities. This allows task predictors trained in city with ample ground truth data to be reused in another city with such data, making it possible to use region representations in fully label-free manner.
Huang, W., Zhang, D., Mai, G., Guo, X., and Cui, L.. Learn- ing urban region representations with pois and hierarchi- cal graph infomax. ISPRS Journal of Photogrammetry and Remote Sensing, 196: 196:134: 13-114,, 2023.
Hull, D. Using statistical testing in the evaluation of retrieval experiments. In Proceedings of the 16th Annual Interna- tional ACM SIGIR Conference on Research and Develop- ment in Information Retrieval, pp. 329-338, 1993.
Jia, H., Chen, M., Huang, W., Zhao, K., and Gong, Y. Learn- ing -rrraccy-enhanced poi category representations us- ing disentangled mobility sequences. In Proceedings of the Thirty International Joint Conference on Artifi- cial Intelligence, pp. 2098, 2024.
Acknowledgments
This work was supported in part by the National Natural Science Foundation of China under Grant No. 61906107 and 42101421, the Key Scientific and Technological In- novation Project of Shandong Province under Grant No. 2024CXGC0101 13 and 2024CXG010213, and the Young Scholars Program of Shandong University. W.H. was sup- ported by the Knut and Alice Wallenberg Foundation.
Jiang, J., Pan, D., Ren, H., Jiang, X., Li. C., and Wang. J. Self-supervised trajectory representation learning with temporal regularities and travel semantics. In 2023 IEEE 39th International Conference on Data Engineering, pp. 843 855. IEEE, 2023.
Jin, Y., Chen, K., and Yang. Q. Selective cross-city transfer learning for traffic prediction via souree city region re- weighting. In Proceedings of the 28th ACM SIGKDD Conference Knowledge Discovery and Data Mining, pp. 731-741, 2022.
References
Bondarenko, M., Kerr, D., Sorichetta, A., and Tatem, gridded population
A. htass/pooocctioondddagggegg datasets for 189 countries in 2020 using built-settlement growth model (bsgm) outputs. 2020.
Li, T.. Xin, S., Xi, Y., Tarkoma. S., Hui, P., and Li, Y. Pre- dicting multi-level socioeconomic indicators from struc- tural urban imagery. In Proceedings of the 31st ACM International Conference on Information & Knowledge Management, pp. 3282-3291, 2022.
Chen, M., Li, Z., Huang, W., Gong, Y., and Yin, Y. Profil- ing urban streets: A semi-supervised prediction model based on street view imagery and spatial topology. In Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pp. 319-328, 2024.
Li, Y., Huang, W., Cong, G., Wang, H., and Wang, Z. Urban region representation learning with openstreetmap build- ing footprints. In Proceedings of the 29th ACM SIGKDD Conference on Knowledge Discovery and Data Mining, pp. 1363-1373, 2023.
Chen, M., Li, Z., Jia, H., Shao, X., Zhao, J.. Gao, Q., Yang, M., and Yin, Y. Mgrl4re: A multi-grapt repre- sentation learning approach for urban region embedding. ACM Transactions on Intelligent Systems and Technology, 2025a.
Li, Z., Ning, H., Jing, F., and Lessani, M. N. Understanding the bias of mobile location data across spatial scales and over time: A comprehensive analysis of safegraph data in the united states. Plos one, (9(1)400,,, 2024.
Chen, Y., Huang, W., Zhao, K., Jiang, Y., and Cong, G. Self- supervised representation learning for geospatial objects: A survey. Information Fusion, pp. 103265, 2025b.
Liu, C., Zhang, H., Zhu, G., Guan, H., and Kwong, S. Ex- ploring trajectory embedding via spatial-temporal propa- gation for dynamic region representations. Information Sciences, 668: 120516, 2024.
Ganin, Y., Ustinova, E., Ajakan, H., Germain, P., Larochelle, H., Laviolette, F. March, M., and Lempitsky, V. Domain- adversarial training of neural networks. Journal of Ma- chine Learning Research, 17(59):1-35, 2016.
Maaten, L. v. d. and Hinton, G. Visualizing data using t-sne. Journal of Machine Learning Research, 9(Nov): 2579-2605, 2008
9

---

Cross-City Latent Space Alignment for Consistency Region Embedding
Mai, G., Lao, N., He, Y., Song, J., and Ermon, S. Csp: Self- supervised contrastive spatial pre-training for geospatial- visual representations. In International Conference Machine Learning, pp. 23498-23515. PMLR, 2023.
Yang, G., Zhang, Y., Hang, J., Feng, X., Xie, Z., Zhang, D., and Yang, Y. Carpg: Cross-city knowledge transfer for traffic accident prediction via attentive region-level parameter generation. In Proceedings of the 32nd ACM International Conference on Information and Knowledge Management, pp. 2939-2948, 2023.
Moschella, L., Maiorca, V., Fumero, M., Norelli, A., Lo- catello, F., and Rodolà, E. Relative representations enable zero-shot latent space communication. In The Eleventh International Conference on Learning Representations, 2023.
Yao, Z., Fu, Y., Liu, B., Hu, W., and Xiong, H. Representing urban functions through zone embedding with human mobility patterns. In Proceedings of the Twenty-eventh International Joint Conference on Artificial Intelligence, 2018.
Ning, Y., Liu, H., Wang. H., Zeng. Z., and Xiong, H. Uukg: Unified urban knowledge graph dataset for urban spa- tiotemporal prediction. Advances in Neural Information Processing Systems, 36, 2024.
Zhang, D., Chen, M., Huang, W., Gong, Y., and Zhao, K. Exploring urban semantics: a multimodal model for poi semantic annotation with street view images and place names. In Proceedings of the Thirty-Thire Inter- national Joint Conference on Artificial Intelligence, pp. 2533-2541 2024.
Oda, T., Maksyutov, S., and Andres, R. J. The open- source data inventory for anthropogenic co2, version 2016 (odiac2016) 6): A global monthly fossil fuel co2 gridded emissions data product for tracer transport simulations and surface flux inversions. Earth System Science Data, 10(1):87-107, 2018.
Zhang, L., Long, C., and Cong, G. Region embedding with intra and inter-view contrastive learning. IEEE Trans- actions on Knowledge & Data Engineering, (01):1-6, 2022.
Saito, K., Watanabe, K., Ushiku, Y., and Harada, T. Max- imum classifier discrepancy for unsupervised domain adaptation. In Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, pp. 3723- 3732, 2018.
Zhang, M., Li, T., Li, Y., and Hui, P. Multi-view joint graph representation learning for urban region embed- ding. In Proceedings of the Twenty-Ninh -inth International Conference on International Joint Conferences on Artifi- cial Intelligence, pp. 4431 4437, 2021.
Veličković, P., Cucurull, G., Casanova, A., Romero, A., Lio, P., and Bengio, Y. Graph attention networks. arXiv 2017.
Zhang, Q., Huang, C., Xia, L., Wang, Z., YIu, S. M., and Han, R. Spatial-temporal graph learning with adversarial contrastive adaptation. In International Conference on Machine Learning, pp. 11151-41166 PMLR, 2023.
preprint arXiv:1710.
Wang, G., Schoenebeck, S., Zheng, H., and Zhao, B. "will check-in for badges": Understanding bias and misbehav- ior on location- based social networks. In Proceedings of the International AAAI Conference Web and Social Media, volume 10, pp. 417-426, 2016.
Zhao, N., Liu, Y., Cao, G., Samson, E. L., and Zhang, J. Forecasting china's s gdp at the pixel level using nighttime lights time series and population images. GIScience & Remote Sensing, pp. 1-19, 2017.
Wang. H. and Li, 7. Region representation learning via mobility flow. In Proceedings of the 2017 ACM on Con- ference on Information and Knowledge Management, pp. 237-246 2017.
Yabe, T., Tsubouchi, K., Shimizu, T., Sekimoto, Y., and Ukkusuri, S. V. City2city: Translating place represen- tations across cities. In Proceedings of the 27th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems, pp. 412-415, 2019.
Yabe, T., Tsubouchi, K., Shimizu, T., Sekimoto, Y., and Ukkusuri, S. V. Unsupervised translation via hierarchical anchoring: Functional mapping of places across cities. In Proceedings of the 26th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, pp. 2841-2851 2020.
10

---

Cross-City Latent Space Alignment for Consistency Region Embedding
A. Appendix
A.1. Data
We use real-world datasets from three cities: Xi'an an (XA), Chengdu (CD), and Beijing (BJ). Each dataset comprises three types of data, namely region data, human mobility data and socioeconomic indicator data. The details of each data type are as follows:
1) Region data is obtained from Beijing City Lab'. Each city is segmented into various regions, which serve basic spatial units defined by the road network. The number of regions in XA, CD, and BJ datasets are 1306, 1056, and 1311, respectively.
2) Human mobility data includes one-month taxi trips from three cities, with each trip providing the latitude and longitude of both the origin and destination (Jiang et al., 2023). The XA, CD, and BJ datasets contain 559729, 384618, and 78945 trips, respectively.
3) Socioeconomic indicator data includes GDP data (Zhao et al., 2017), population data (Bondarenko et al., 2020), and carbon emission data (Oda et al., 2018) of the three cities, which are used in downstream tasks. Since the data types are raster and the regions are irregular, we first map the pixels to the regions and then use the sum values as the final socioeconomic indicators for those regions.
A.2. Description of Baselines
We compare our proposed CoRE with unsupervised latent space translation methods and domain adaptation techniques. Among the translation methods, we primarily benchmark against the approach proposed by (Yabe et al., 2020). This method first generates city-specific region representations and then employs three strategies (rank-based, hierarchical stochastic, and hierarchical batch) to construct anchoring embedding matrices across cities. These matrices are aligned using Orthogonal Procrustes and Affine alignment techniques, resulting in the following baselines:
RP (Rank-based Anchoring + Procrustes): Establishes one-to-one correspondences by sorting regional ranks within each city, forming anchoring pairs that are aligned using the Orthogonal Procrustes method.
RA bRank-based Anchoring + Affine): Similar to RP but employs Affine alignment instead of Orthogonal Procrustes.
HSP (Hierarchical Stochastic Anchoring Procrustes): Randomly selects anchoring pairs within each hierarchical level across cities and aligns them using the Orthogonal Procrustes method.
HSA (Hierarchical Stochastic Anchoring Affine): Uses Affine alignment instead of Orthogonal Procrustes, as in HSP.
HBP (Hierarchical Batch Anchoring + Procrustes): Computes mean vectors of region representations at each hierarchi- cal level, constructs anchoring matrices, and aligns them using the Orthogonal Procrustes method.
HBA (Hierarchical Batch Anchoring Affine): Replaces Orthogonal Procrustes with Affine alignment, differing from HBP.
Additionally, we include three domain adaptation methods and one knowledge transfer method for comparison:
MMD (Saito et al., 2018): Utilizes Maximum Mean Discrepancy (MMD) to minimize representation distribution disparities between source and target cities for effective alignment.
Adv (Ganin et al., 2016): Implements domain adversarial training to make region representations indistinguishable between cities, enabling distribution alignment through model parameter adjustments.
CrossTReS (Jin et al., 2022): Employs MMD to reduce the distribution discrepancies in representations between source and target cities. Furthermore, constructs edge embeddings by concatenating the features of paired regions. An edge classification task is implemented to enhance the alignment of feature distribution.
http://wwww.iiiiincchhh....ooare

---

Cross-City Latent Space Alignment for Consistency Region Embedding
Table Performance comparison on three downstream tasks, where the hest results represented in bold and the performance improvements of CoRE are compared with the second best results marked by underlined.
BI(XY)D(Y)
CD(XWBI()
Method
GDP
Population
Carbon
GDP
Population
Carbon
MAE
MAPE
MAE
МАРE
MAE
MАPE
MAE
MAPE
MAE
MAPE
MAE
MAPE
Individual
245.46
16.06
1170.74
9.89
361.29
25.57
321.48
12.63
997.96
6.62
240.71
6.56
RP
210.89
11,89
1065.99
8.81
253.03
15.53
187.07
8.15
803.38
6.24
198.69
3.79
173.46
8.5
720.68
5.58
189.94
13.84
161.96
6.98
731.01
5.48
181.74
3.09
HSP
198.11
1 11,45
1074.02
8,56
255.89
15.988
163.98
6.92
743.87
5.55
197.54
3.83
HSA
176.49
8.57
685.37
4.19
170.52
12.46
158.64
6.55
726.02
5.35
189.95
3.68
HBP
202.74
11.04
1092.02
8.82
250.42
14.86
187.39
8.13
843.17
6.53
187.69
3.63
HBA
152.18
6.63
707.67
4.2
182.68
13.62
184.49
7.18
759.61
5.68
186.49
3.49
MMD
179.28
8.58
904.79
6.75
230.04
14.4
199.39
8.66
873.23
6.64
197.82
3.82
Adv
227.23
13.92
940.57
7.27
330.95
23.53
193.39
8.39
825.77
6.33
186.31
3.45
CrossTReS
188.66
9.61
902.92
6.45
222.77
14.19
179.59
7.84
755.34
5.71
183.55
3.32
CARPG
173.24
8.07
813.84
6.56
195.91
14.18
191.25
8,54
741.44
5.53
187.13
3,58
CoRE
148.55
6.22
665.16
4.07
148.49
10.09
141.96
5.79
676.87
4.73
179.25
2.95
Improvement (%)
2.39
6.18
2.95
2.86
12.92
19.02
10.51
11.6
6.77
11.59
1.37
4.53
XA(X XA(X)/BI(() )/BI(Y)
BI(X WXA(Y)
Method
GDP
Population
Carbon
GDP
Population
Carbon
MAE
MAPE
MAE
MAPE
MAE
MAPE
MAE
MAPE
MAE
MAPE
MAE
MAPE
Individual
362.51
15.35
1102.51
6.84
374.34
8.71
500.1
18.28
1238.58
11.92
372.03
9.23
RP
230.14
7.96
699.15
3.51
215.86
3.81
224.03
7.01
795.08
7.38
213.86
6.04
RA
212.87
7.41
666.45
3.47
175.31
3.28
175.04
3.87
674.65
4.83
182.05
4.79
HSP
229.63
7.96
744.88
3.81
224.14 14
4.06
208.79
1042.84
10.06
306.32
8.25
HSA
167.41
5.88
630.88
3.21
186.08
3.62
188.86
5.33
735.32
6.57
227.79
6.03
HBP
264.14
8.29
905.45
4.81
261.15
5.81
207.27
6.85
963. 11
9.81
291.51
7.93
HBA
170.67
6.35
659.64
3,43
191.89
3.65
173.02
3.91
682.59
4.89
181.05
4.83
MMD
242.42
8.76
856.39
4.37
236.43
4.16
198.91
6.42
788.16
6.89
231.81
6.45
Adv
235.38
8.54
886.34
5.89
260.98
5.75
241.76
8.38
972.23
9.91
257.08
6.57
CrossTReS
187.07
7.27
674.28
3.53
196.13
3.71
188.99
4.99
740.94
6.83
217.4
6.12
CARPG
177.08
6.71
746.81
3.84
246.33
4.41
228.84
910.22
8.67
267.8
7.32
CoRE
154.85
5,45
608.66
2.94
173.82
3.12
164.96
3.65
623.92
4.66
176.25
4.38
Improvement (%)
7.31
7.31
3.52
8.41
0.85
4.88
4.66
5.68
7.52
3.52
2.65
8.56
CARPG (Yang et al., 2023): Facilitates cross-city knowledge transfer by constructing an inter-city region graph, where regions from the source and target cities are connected based on feature similarity. A reconstruction loss is incorporated to enable joint learning of region representations across both cities during the training stage.
Finally, we introduce a lower-bound baseline, Individual, which generates city-specific region representations without any cross-city alignment.
A.3. Performance Comparison with Baselines
Table 2 presents the cross-city socioeconomic indicator prediction performance of various methods across XA, BJ, and CD datasets, with X as the source city and as the target city. For the four city pairs (BJ/CD, CD/BJ, BJ/XA, and XA/BJ), our CoRE method also demonstrates the best performance.
12

---

Cross-City Latent Space Alignment for Consistency Region Embedding
A.4. Visualization of Region Representations
We visualize the region representations of two cities by projecting them onto 2D planes using t-SNE (Maaten & Hinton, 2008). The results from the XA and BJ datasets, including CoRE, CoRE w/o LIA (which represents the complete CoRE model excluding the cross-city latent individual aligmment component), and the baseline method (HBA), shown in Figure 8. In these plots, each point represents a region, with green squares for BJ regions and yellow triangles for XA regions. Figure 8 (a) indicates that the region representations from HBA are only partially aligned. Notably, as shown in Figure (b), CoRE w/o LIA exhibits a discemible trend that the overall distributions of region representations from the two cities are similar, suggesting that our latent manifold alignment method enhances the similarity between the data manifolds of the two latent spaces, while still falling short in individual- alignment. Figure 8 (c) shows that CoRE effectively aligns individual region representations across cities, demonstrating fine-grained alignment of latent spaces from global and local perspectives.
(a) HBA
(b) CoRE w/o LIA
(c) CoRE
Figure 8. Exhibition of region representations of two citics in 2D planes, with green squares denoting region representations from the BJ data and yellow triangles denoting region representations from XA data.
A.5. Within-City Performance
To investigate the potential trade-off between cross-city and within-city predictive performance, we conducted experiments evaluating CoRE on within-city prediction tasks. We compared CoRE against representative mobility- region embedding methods: HDGE (Wang & Li, 2017) constructs human mobility flow graphs and applies graph embedding to learn region representations; ZE-Mob (Yao et al., 2018) models co-oceurrence patterns between regions for representation learning. We also included variant of our model, CoRE w/o Alignment, which does not perform cross-city alignment and thus serves as city-specific embedding baseline. We evaluated within-city performance for three cities (XA, CD, BJ) on three downstream tasks: GDP estimation, population prediction, and carbon emission prediction. Results in terms of MAE and MAPE are shown in Table 3.
Table Within-ein city predictive performance on three tasks. "X/Y" denotes training and testing on the same city. The best results per column are in bold.
XA(XYXA(')
CD(XYCRY))
BEXYYRRY)
Method
GDP
Population
Carbon
GDP
Population
Carbon
GDP
Population
Carbon
MAE
MAPE
MAE
MAPE
MAE
MAPE
MAE
MAPE
MAE
MAPE
MAE
MAPE
MAE
MAPE
MAE
MAPE
MAE
MAPE
LIDGE
207.36
12.58
616.37
5.45
175.24
5.95
174.39
18.95
701.82
4.97
73.84
6.08
124.55
5.57
708.58
5.57
202.60
5.43
ZE Mob
199.09
11.82
597.54
5.35
169.06
5.78
173.09
20.72
687.44
4.90
72.56
6.07
122.46
5.16
695.64
5.45
198.39
5.31
CoRE wio Alignment
165.36
7.24
498.38
2.96
140.81
3.31
146.35
9.05
611.24
3,01
64.34
3.41
107.13
3.34
595.11
3.08
174.82
3.19
CoRl
172.91
10.11
508.78
3.51
143.53
3,36
148.31
10.09
621.58
3.05
65.38
4.35
107.82
3.44
608.95
3.38
176.29
3.36
As shown in Table 3, CoRE achieves strong within-city performance, consistently outperforming mobility-based baselines. CoRE exhibits a marginal compromise compared to its variant without cross-city alignment, which an expected trade-off for its cross-city alignment capabilities.
A.6. Ablation Study
The results of CoRE and its variants in terms of MAE and MAPE for the four city pairs (CD/BJ, BJ/CD, BJ/XA, XA/BJ) are shown in Figure 9. We observe that CoRE w/o LMA, CoRE w/o LIA and CoRE w/o One-Stage underperform compared to
13

---

Cross-City Latent Space Alignment for Consistency Region Embedding
the full CoRE model, which further validates the effectiveness of the newly designed cross-city alignment components and one-stage learning paradigm.
350
900
One-Stage
w/o LIA CORE
w/o One-Stage
w/o LIA
One-Stagel
LIA
250
200
MAE
MAE
MAE
150
700
150
600
100
30
15
30
w/o One-Stage
LIA
wlo One-Stage w/o LMA
w/o
W/o One-Stage
w/o CoRB
w/o LMA
CoRE
CoRB
w/a LMA
MAPE
20
MAPE
10
MAPE
20
10
10
CD3
BLCD
BEXA
XAIRI
CDA
BEXA
XAVII
BIXA
XARII
(a) GDP Prediction
(b) Population Prediction
(c) Carbon Emission Prediction
Figure 9, Performance comparison of different variants.
14


Reviews:
[{"review_id": "sQcn3yiGrc", "reviewer": "Reviewer_Hufa", "summary": "This paper tackles the challenge of transferring urban region embeddings across cities. Instead of the commonly used two-stage approach—first learning city-specific embeddings and then mapping among them—the authors propose a unified one-stage framework called CoRE. The idea is to learn region embeddings from human mobility data while aligning the latent spaces of different cities in one joint process. \n\nIn this paper, two key mechanisms are designed: one to embed regions from different cities into distinct latent spaces, and another to align their latent space manifolds while ensuring fine grained compatibility. Experiments conducted on datasets from three cities show that CoRE consistently outperforms several strong baselines on different downstream tasks.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Response to W1:** \nWe appreciate the reviewer's valuable suggestion regarding cross-country evaluation. To demonstrate the generalizability of our method, we conducted additional experiments using data from three cities of China and New York City (NYC) - cities with significantly different urban characteristics. Due to data availability constraints, we evaluated performance on carbon emission prediction (the only task with available ground truth in both cities). The results of CoRE and the two best baselines (HBA and HSA), measured by MAE and MAPE, are presented below:\n||XA / NYC||NYC / XA||\n|:-:|:-:|:-:|:-:|:-:|\n|Method|MAE|MAPE|MAE|MAPE|\n|HBA|358.82|4.01|1274.9|59.47|\n|HSA|441.67|4.7|1646.09|66.75|\n|**CoRE**|**279.69**|**2.43**|**514.49**|**16.53**|\n\n||BJ / NYC||NYC / BJ||\n|:-:|:-:|:-:|:-:|:-:|\n|Method|MAE|MAPE|MAE|MAPE|\n|HBA|325.18|3.64|531.04|19.52|\n|HSA|390.21|4.93|852.23|29.82|\n|**CoRE**|**220.83**|**1.44**|**356.71**|**7.65**|\n\n||CD / NYC||NYC / CD||\n|:-:|:-:|:-:|:-:|:-:|\n|Method|MAE|MAPE|MAE|MAPE|\n|HBA|239.23|1.39|398.92|38.19|\n|HSA|280.35|2.15|601.38|49.17|\n|**CoRE**|**211.42**|**0.99**|**269.82**|**22.17**|\n\nOur findings show that CoRE maintains strong performance even when transferring knowledge between these geographically and culturally distinct cities. This suggests our method's robustness in handling cross-country urban computing tasks. We acknowledge that further validation across more international city pairs would strengthen these conclusions, and we identify this as an important direction for future research.\n\n**Response to W2:** We thank the reviewer for the comment. Figure 3 shows how we align the hidden data spaces of two cities (like Chengdu and Xi’an) by using a few common anchor points as reference. Instead of comparing raw values directly, we compare how each data point relates to the anchors — like checking how far each region is from landmarks. First, we calculate these relative similarities in each city, and then use those to build a new space where everything is described based on those anchor relationships. We do this again to create a second, more refined version of that space. Finally, we align the two cities by minimizing the difference between their refined spaces, helping the model learn structural similarities even when the cities have different data distributions. I hope this comment can help you clarify the question. \n\n**Response to W3:** We thank the reviewer for the insightful comment. The reason the population results look different from GDP and carbon in Figure 6 is mostly because population patterns are naturally more uneven and complex across urban areas. People tend to live in places based on various personal and social factors—like job locations, housing affordability—which creates irregular and less predictable spatial distributions. GDP and carbon emissions usually reflect clearer, more structured patterns tied to specific economic or industrial areas. Because of this complexity, population prediction has relatively more fluctuation and benefits greatly at first from adding more anchors. In contrast, GDP and carbon emissions data don't need as many anchors to achieve stable predictions, which explains their relatively smoother performance trends when increasing N_a.\n\n**Response to minor questions:**\nWe thank the reviewer for pointing out areas that could benefit from further clarification. First, regarding how the graphs are constructed for each city: the mobility graphs are created using human mobility data, where each node represents a region within the city. Edges between nodes represent how frequently people travel from one region to another. These frequencies are normalized based on the total number of trips originating from each region. Second, in Section 3.1.3, the terms r_i and r_j refer to urban regions. Specifically, r_i is the origin region and r_j is the destination region in a recorded trip. The model is trained to predict how likely people are to travel from one region to another based on these patterns. Third, for the computation described in Equation 7, the transpose of the region data is calculated first. After that, the model performs a matrix multiplication with a set of common anchor points. This operation generates a table that shows how similar each anchor is to every region in the city, helping align data across different cities. We will revise the manuscript to clearly explain these parts, so future readers can understand them more easily.", "claims_and_evidence": "This paper has three major claims: the first is that a unified framework works better than previous two stages works, which ensures compatibility and comparability of region representations from different cities within aligned latent spaces; the second is that cross-city alignment of latent spaces can account for the complex interplay between cities without relying on explicit anchoring pairs of region representations across cities based on human-crafted rules; the third is that by properly aligning the latent spaces, task predictors trained in a data-rich city can be directly applied to another city with minimal degradation in performance.\n\nThis paper’s claims have been supported by very well designed and deployed experiments in my opinion. The experimental results clearly indicate that CoRE outperforms various baselines as shown in section 4.2.2, including methods based on hand-crafted anchoring pairs, unsupervised translation techniques, and standard domain adaptation approaches. The improvements in MAE and MAPE are not only consistent across city pairs but are also statistically significant (section 4.3). The ablation study proves that either the manifold alignment or the individual alignment module components are crucial for the overall performance (section 4.4). Visual analysis using t-SNE plots demonstrate that region embeddings from different cities become more tightly clustered and semantically consistent after alignment, which visually supports the authors’ claims (appendix A.4). The downstream tasks are not only on one issue, but on three very distinguished tasks, such as predicting GDP, population, and carbon emissions, showing the very strong capability of the paper applying on different domains for cross city knowledge transfer (Table 1 and Table 2). \n\nOverall, I am very positive with the claims that the authors claimed in the paper, and they have been shown very good evidence to support them. I am very satisfied with both the claims and evidence part.", "methods_and_evaluation_criteria": "The authors start by constructing a mobility graph using human mobility data and then apply a graph attention network (GAT) to learn the initial embeddings. This choice is well justified as GATs are effective at capturing complex relationships in spatial data (section 3.1.2). To bridge the gap between the latent spaces of different cities, the authors introduce a set of virtual parallel common anchors. By computing relative representations of each city’s region embeddings with respect to these anchors, they align the global structure of the latent spaces using an L2 loss (section 3.2). Beyond aligning the overall structure, the method also leverages a cross-attention mechanism to ensure that pairwise correlations between regions are maintained across cities (section 3.3). This cycle-consistency approach forces the fine-grained structure of the embeddings to be preserved.\n\nThe proposed CoRE is evaluated on predicting socioeconomic indicators (GDP, population, carbon emissions), which are realistic and meaningful tasks in urban analytics (Table 1 and Table 2).  The use of MAE and MAPE is standard and appropriate for regression problems like these. The authors compare CoRE against a variety of strong baselines, including rank-based methods, hierarchical approaches, and domain adaptation techniques (Section 4.2.2 and section 4.2.3). This comprehensive set of comparisons adds credibility to the results. The paper also includes experiments that explore the impact of the number of virtual anchors and the weights for the alignment losses (section 4.4.1 and section 4.4.2). This analysis helps demonstrate the robustness of the approach.\n\nOverall, I believe that authors have done well with the methods and the evaluation section. The evaluation sections support the claims from the methods in different ways and I think that it is good enough to support all the method claims.", "theoretical_claims": "Overall, I am satisfied with the theoretical part. Some minor questions: \n\n1. In equation 1, how the graphs of Gx and Gy are constructed in city x and y, this part is not clearly explained in the paper. One or two sentence explanation would be helpful for readers to understand this part. \n\n2. In section 3.3 the destination region rj given ri, what are the meanings of rj and ri here?\n\n3. How will equation 7 be calculated? Will the transpose be calculated first or later? \n\n4. Equation 11 is a commonly used attention mechanism, the authors do not need to spend time explaining this part", "experimental_designs_or_analyses": "I have explained my thoughts on experimental designs and analysis in both Claims and Evidence and Methods and Evaluation Criteria. Overall I believe the experiment section is good enough to support the claims of the paper. I am satisfied with this part.", "relation_to_broader_scientific_literature": "I can see the potential of the paper’s impact not only limited in the ML application domain, but in a broader machine learning domain especially on the questions related to Latent Space Alignment. Latent Space Alignment is a common problem in many fields, for example, in e-commerce recommendation of different categories. The paper’s proposed methods could be deployed in other ML application fields with similar backgrounds with ease.", "essential_references_not_discussed": "I think that the authors have provided enough references.", "other_strengths_and_weaknesses": "Overall, I think that this is a strong paper. The paper is well written, the algorithms are very well and thoroughly designed, and this paper is on a very interesting topic. I have been enjoying reading the paper. I have explained my thoughts in detail in my previous comments. \n\nSome further suggestions: \n\nThe paper used the data all from the cities in China. I am very curious to see how the algorithm would perform under cross-country cities (e.g., NYC to Beijing). Some experiments on this part would be very interesting. \n\nFigure 3 information is a bit too much, took me a lot time to understand this part. \n\nWhy in Figure 6, population results are different from GDP and carbon results? Some explanation is needed for this part.", "other_comments_or_suggestions": "See Other Strengths and Weaknesses", "questions_for_authors": "None", "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": "SuQhvrUwbN", "reviewer": "Reviewer_kYEv", "summary": "**Problem:**\n- This paper studies the region representation learning problem, with a special focus on cross-city learning\n- The cross-city representation learning problem is important because some cities have abundant labelled data, while many others do\n- Existing methods rely on heuristic translation functions to align disjoint embedding spaces\n    - These typically require hand-crafted rules and require the definition of similar pairs in the two cities, X and Y\n    - This is inherently a two-stage approach where translation is disconnected from learning\n\n**Solution:**\n- The authors propose CORE, which is a region embedding method that both learns and aligns semantic embedding space across cities\nCORE has three key modules:\n    - A self-supervised module to learn the primitive embedding spaces of city X and city Y.\n    - A latent manifold alignment module that aligns the entire representation space across X and Y using anchor points and reconstruction loss\n    - A latent individual alignment module that tries to align the represents of semantically similar regions across X and Y. They do this through cross attention (X→Y and Y→ X) and reconstruction of the empirical covariance of the region embeddings: $Z^X (Z^X)^T$.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Response to Q1\\&W1:**  We appreciate the reviewer raising this question about the trade-off between cross-city and within-city performance. To thoroughly investigate this aspect, we conducted new experiments comparing CoRE's within-city performance against established region embedding methods using human mobility data: HDGE [1] constructs flow graphs and applies graph embedding to learn region representations; ZE-Mob [2] models co-occurrence patterns between regions to learn representations. While we acknowledge that some recent methods incorporate multi-source data (e.g., POIs, imagery), we focused our comparison on mobility-based approaches due to data availability constraints in our experimental setup. We tested within-city performance (XA→XA, CD→CD, BJ→BJ) with three down-tasks. We also included our proposed preliminary region embedding model (named CoRE w/o Alignment, Section 3.1). The results in terms of MAE are presented below:\n\n|||XA/XA|||CD/CD|||BJ/BJ||\n|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|:-:|\n|Method|GDP|Population|Carbon|GDP|Population|Carbon|GDP|Population|Carbon|\n|HDGE|207.36|616.37|175.24|174.39|701.82|73.84|124.55|708.58|202.60|\n|ZE-Mob|199.09|597.54|169.06|173.49|687.44|72.56|122.46|695.64|198.39|\n|CoRE w/o Alignment|165.36|498.38|140.81|146.35|611.24|64.34|107.13|595.11|174.82|\n|CoRE|172.91|508.78|143.53|148.31|621.58|65.88|107.82|608.95|176.29|\n\nThe experimental results demonstrate that CoRE maintains strong within-city performance, with only marginal performance degradation compared to city-specific embeddings (CoRE w/o Alignment). Additionally, CoRE outperforms mobility-based baselines. More importantly, although it is true that adding the alignment module comes with a marginal sacrifice of within-city performance, the gain of our CoRE alignment method is something that cannot be overstated. It tackles a fundamental challenge in region representation that the embeddings are of little use without task-specific ground truth data. CoRE tackles this problem by aligning the embeddings across multiple cities, and thus enabling predictor reuse. \n\n[1] Region representation learning via mobility flow, CIKM.\n\n[2] Representing urban functions through zone embedding with human mobility patterns, IJCAI.\n\n**Response to Q2:** In Figure 2, we refer to regional GDP levels, not income. These GDP estimates are derived from a high-resolution dataset [3] that provides GDP values at a 1km × 1km grid scale. To adapt this data to our study: we mapped the gridded GDP values to our regions, aggregated the values by proportionally summing GDP within each region, and classified regions into three economic tiers based on these aggregated values. This approach allows us to analyze GDP variations at a finer spatial resolution than traditional state- or national-level metrics. \n\n[3] Forecasting China’s GDP at the pixel level using nighttime lights time series and population images. GIScience \\& Remote Sensing. \n\n**Response to Q3:** We appreciate the reviewer's question regarding our statistical analysis. We did indeed calculate standard deviations for all metrics. For instance, the MAE standard deviations of our CoRE for the CD/XA pair were 6.03, 19.72, and 3.34 across the three tasks. Due to space constraints in the table layout, we chose not to include these values in the original submission.\n\nThe paired t-tests were conducted as follows: 1) Computing performance differences between our method and each baseline for each of the 5 trials, 2) Performing two-tailed significance tests on these differences, 3) Testing the hypothesis that the mean difference equals zero [4]. The consistently significant results (p < 0.01) across all comparisons provide strong evidence that CoRE's improvements are statistically meaningful, not due to random variation. We will add these details to the revised manuscript.\n\n[4] Hull, David. Using statistical testing in the evaluation of retrieval experiments. SIGIR.\n\n**Response to W2:** We additionally conducted comparisons with CrossTReS and CARPG. While we considered the approach by Yao et al., we found it unsuitable for our unsupervised setting as it requires labeled data in both source and target cities. The results of CrossTReS, CARPG, and CoRE in terms of MAE are presented below:\n\n|||XA / CD|||CD / XA||\n|:-:|:-:|:-:|:-:|:-:|:-:|:-:|\n|Method|GDP|Population|Carbon|GDP|Population|Carbon|\n|CrossTReS|205.48|767.26|153.38|208.17|776.82|148.05|\n|CARPG|190.41|653.27|136.02|186.83|641.94|143.88|\n|**CoRE**|**178.93**|**620.15**|**127.45**|**170.25**|**580.98**|**136.56**|\n\nThe experimental results demonstrate that CoRE outperforms these baselines. Similar results are observed in the other four city pairs. These extensive comparisons further validate CoRE's effectiveness in cross-city knowledge transfer. We will incorporate these results into the revised manuscript.\n\n**Response to W3:** We will replace 3D barcharts with heatmaps in the revision.", "claims_and_evidence": "The authors primarily make claims around improved cross-city alignment. They construct experiments to test this hypothesis. Additionally, the authors perform an ablation to study to verify the marginal contribution of each of the components they introduce.", "methods_and_evaluation_criteria": "As mentioned above, the authors perform experiments to test the cross-city alignment hypothesis. They compare primarily to different variants of Yabe et al. 2020, which constitutes the majority of the baselines. Additionally, they compare to a few domain adaptation methods.\n\nI believe that other baselines should probably be included in their evaluation. Here are some recent examples:\n\n- Yang, Guang, et al. \"CARPG: Cross-City Knowledge Transfer for Traffic Accident Prediction via Attentive Region-Level Parameter Generation.\" Proceedings of the 32nd ACM International Conference on Information and Knowledge Management. 2023.\n- Jin, Yilun, Kai Chen, and Qiang Yang. \"Selective cross-city transfer learning for traffic prediction via source city region re-weighting.\" Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. 2022.\n\n\nOther cross-city learning methods that do require representation learning could also be considered:\n- Yao, Huaxiu, et al. \"Learning from multiple cities: A meta-learning approach for spatial-temporal prediction.\" The world wide web conference. 2019.", "theoretical_claims": "No theoretical claims", "experimental_designs_or_analyses": "Yes, discussed above. Missing baselines", "relation_to_broader_scientific_literature": "The spatial data sparsity issue likely has many applications to areas of social science, civil engineering or environmental science", "essential_references_not_discussed": "In addition to the missing baselines above, the authors could consider discussing other early works on region embeddings:\n\n- Jenkins, Porter, et al. \"Unsupervised representation learning of spatial data via multimodal embedding.\" Proceedings of the 28th ACM international conference on information and knowledge management. 2019.", "other_strengths_and_weaknesses": "**Strengths:**\n- The alignment modules are well explained and are well motivated\n- The ablation study is very useful for evaluating marginal impact\n- The improvement over the baselines studied indicates efficacy\n\n**Weaknesses:**\n- The authors test whether or not CORE can effectively perform cross-city prediction. However, I do think an obvious question is if this comes at the expense of within-city predictive performance. See below for additional thoughts/questions\n- Missing baselines\n- Figure 7 is not useful. The 3D barchart is very difficult to read or detect differences between hyperparameter settings. I would suggest using heatmaps instead", "other_comments_or_suggestions": "See thoughts about figure 7. I'm happy to see hyperparameter study but this figure is not useful.", "questions_for_authors": "The authors test whether or not CORE can effectively perform cross-city prediction. However, I do think an obvious question is if this comes at the expense of within-city predictive performance. For example, in Table 1, the authors test the cross-city prediction setting of XA(X) → CD(Y) and CD(X) → XA(Y). The performance on this task is quite good (although there are likely additional baselines to try). My biggest concern is what happens to the individual city representations when predicting on data within that same city. For example, after using CORE, what is the predictive performance of GDP_X using Z_X and GDP_Y using Z_Y. Do these representations degrade? How do they compare to the larger body of region representation research?  This is an important question and would warrant further study.\n\nFigure 2: Do you really mean GDP or do you mean income levels? Usually GDP is computed at state or national levels and is not tracked at low levels of spatial resolution. \n\nTable 1: The authors perform five trials and compute average MAE and MAPE over those trials. Why do they not present estimates of the standard deviations of these same statistics? I see they do some type of t-test; it would be helpful to get more details on how that t-test is constructed.", "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": "ioR2SxWUwz", "reviewer": "Reviewer_bm5L", "summary": "This paper addresses a critical question in urban computing: Can we align the latent spaces of different cities to leverage knowledge from one city for analyzing others? To tackle this issue, the authors introduce a one-stage Consistency Region Embedding method (CoRE), which combines region embedding learning with cross-city latent space alignment to generate compatible and comparable region representations. Additionally, they achieve cross-city alignment via two interdependent pathways: latent manifold alignment and latent individual alignment, which address both global and individual perspectives. Finally, the authors present comprehensive experiments across three downstream tasks using datasets from three cities.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Response to Q1:** We acknowledge that evaluating the proposed method across additional tasks would further strengthen its empirical validation. Following your suggestion, we conducted supplementary experiments on traffic flow prediction, using datasets from Xi'an (XA) and Chengdu (CD). Specifically, we trained the predictor using labeled data (i.e., region visit counts derived from taxi trajectories) and pre-trained region representations from one city (XA or CD). The trained predictor was then directly applied to predict traffic flow in the other city (CD or XA). The results are summarized below:\n\n||XA / CD||CD / XA||\n|:-:|:-:|:-:|:-:|:-:|\n|Method|MAE|MAPE|MAE|MAPE|\n|HBA|148.62|6.42|155.53|11.47|\n|HSA|150.01|5.96|149.18|10.18|\n|**CoRE**|**143.79**|**5.12**|**127.59**|**8.46**|\n\nAs shown, CoRE consistently outperforms the baselines, reinforcing its effectiveness. While we recognize that no single study can comprehensively demonstrate superiority across all urban computing scenarios, we believe the three primary tasks in our paper, along with this additional cross-city traffic prediction experiment, provide substantial evidence of our method's robustness.", "claims_and_evidence": "They claim that the proposed CoRE method ensures compatibility and comparability of region representations from different cities within aligned latent spaces. The experimental results provide evidence to support their claims.", "methods_and_evaluation_criteria": "They achieve cross-city alignment of latent spaces through two interdependent pathways: latent manifold alignment and latent individual alignment. In the latent manifold alignment component, they create virtual parallel common anchors in both spaces, serving as bridges to align the data manifolds based on relative representations. Meanwhile, in the latent individual alignment component, they implement a cross-city attention pipeline that transfers pairwise region correlations between the two spaces, ensuring embedding consistency at the individual region level. The proposed method is not only innovative but also effectively addresses the challenges of cross-city alignment, demonstrating its value and potential in urban computing.", "theoretical_claims": "I have reviewed them and found no obvious errors.", "experimental_designs_or_analyses": "This paper evaluates the proposed CoRE model across three cross-city urban prediction tasks using real-world datasets and compares its performance to various baselines. Table 1 and Figure 5 present the performance comparison results for the CA and CD datasets, along with findings from the ablation study and parameter analysis. The results are comprehensive and effectively support the authors' claims.", "relation_to_broader_scientific_literature": "This paper addresses the challenge of aligning latent spaces across cities. On one hand, they align data manifolds of two spaces using the idea of relative representations; on the other hand,  they ensure precise alignment of individual regions across cities through a cross-attention mechanism. The proposed approach eliminates the need for manual inter-city correspondence rules, enhancing its applicability to unsupervised latent space alignment tasks.", "essential_references_not_discussed": "Related works are enough.", "other_strengths_and_weaknesses": "Strengths:\n1)\tThe paper introduces CoRE, a novel framework that integrates region embedding learning with cross-city latent space alignment. This approach addresses the limitations of existing methods by enabling knowledge transfer across cities without relying on hand-crafted correspondence rules, which is a significant advancement in urban computing.\n2)\tThe authors conduct extensive experiments across three downstream tasks (GDP, population, and carbon emissions prediction) using real-world datasets from three cities. The results demonstrate that CoRE outperforms state-of-the-art baselines, showcasing its effectiveness in cross-city prediction tasks.\n3)\tThe paper not only provides a theoretical foundation for cross-city latent space alignment but also offers practical insights by eliminating the need for manual inter-city correspondence rules. This makes the method broadly applicable to unsupervised latent space alignment tasks in urban analytics.\nWeaknesses:\n1) The paper focuses on socioeconomic predictions using three metrics (GDP, population, and carbon emissions). Expanding the evaluation to include more diverse benchmarks, such as traffic prediction or land use analysis, across different urban science settings would further demonstrate the robustness of the proposed method.", "other_comments_or_suggestions": "See strengths and weaknesses.", "questions_for_authors": "Could you extend the evaluation of CoRE to other urban science tasks, such as traffic prediction, beyond the current focus on socioeconomic indicators (GDP, population, and carbon emissions)? If not, explain the reason.", "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": "lx2ApTVQhF", "reviewer": "Reviewer_WP7Z", "summary": "This paper deals with a critical issue in the popular trend in urban computing, namely the cross-city latent space alignment problem in region representation learning, which  extracts useful features from different types of urban data for many urban prediction tasks. The issue is that although the pre-training process is free from labels of tasks, doing the actual predictions still need a substantial amount of labels. Oftentimes the labels are not really accessible, so this erodes the principle motivation of region representation. \nThe paper developed a method that can work without labels, by migrating patterns accumulated from another city to a city with no labels. A fundamental idea here is that the latent embedding spaces of the two cities for pre-trained can be aligned in an unsupervised way without ground truth and rules. The work achieved this by looking at both the overall distribution alignment and pairwise relationship preservation. This is overall an interesting and novel idea to address the critical issue in urban computing.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "**Response to W1:**\nWe appreciate the reviewer’s insightful question regarding the suitability of city pairs for knowledge transfer. At this stage of research in unsupervised cross-city alignment, we acknowledge that quantitatively defining the ideal criteria for city pair selection remains an open challenge. Testing numerous city pairs to identify patterns is non-trivial, and quantitatively characterizing a city’s traits—given the multidimensional nature of urban data—adds further complexity. While such analysis is beyond the scope of this paper, we agree it is a valuable direction for future work.\n\nTo demonstrate the robustness of our method even when transferring knowledge between highly dissimilar cities, we conducted additional experiments using three cities of China and New York City (NYC). Due to data availability, we evaluated carbon emission prediction (the only task with ground truth in both cities), with results of CoRE and the two best baselines  (HBA and HSA) summarized below:\n\n\n||XA / NYC||NYC / XA||\n|:-:|:-:|:-:|:-:|:-:|\n|Method|MAE|MAPE|MAE|MAPE|\n|HBA|358.82|4.01|1274.9|59.47|\n|HSA|441.67|4.7|1646.09|66.75|\n|**CoRE**|**279.69**|**2.43**|**514.49**|**16.53**|\n\n||BJ / NYC||NYC / BJ||\n|:-:|:-:|:-:|:-:|:-:|\n|Method|MAE|MAPE|MAE|MAPE|\n|HBA|325.18|3.64|531.04|19.52|\n|HSA|390.21|4.93|852.23|29.82|\n|**CoRE**|**220.83**|**1.44**|**356.71**|**7.65**|\n\n||CD / NYC||NYC / CD||\n|:-:|:-:|:-:|:-:|:-:|\n|Method|MAE|MAPE|MAE|MAPE|\n|HBA|239.23|1.39|398.92|38.19|\n|HSA|280.35|2.15|601.38|49.17|\n|**CoRE**|**211.42**|**0.99**|**269.82**|**22.17**|\n\nThe results show that CoRE maintains strong performance despite significant differences between cities of China and NYC, reinforcing its adaptability across diverse urban contexts. We acknowledge that further validation across more international city pairs would strengthen these conclusions, and we identify this as an important direction for future research.\n\n**Response to W2:** We sincerely appreciate the reviewer’s careful reading and valuable feedback. We will perform a round of grammar and consistency checks to further improve the clarity and readability of the paper in the revision.", "claims_and_evidence": "The overarching claim is the proposed one-stage method for both region representation learning and cross-city alignment can transfer the knowledge learned from a data-rich city to another one where labels are unavailable. The evidence is ample for this claim, including experimental results in multiple tasks, cities as well as baselines. The ablation such as “without one-stage” is convincing. \nThe other claim is that only looking at embedding distributions rather than using human developed rules are sufficient. This claim is well backed by the experiments too, and it is encouraging to see the advantages of this method with little intervention. \nThe figure8 for visually presenting the aligned and unaligned latent spaces is useful.", "methods_and_evaluation_criteria": "The method is novel and can be one of the first unsupervised methods on this topic. The method simultaneously learns city-specific region embeddings, cross-city distribution matching and individual level matching. The idea is intriguing and solid.\nThe evaluation criteria uses public datasets and well established metrics for this problem at hand.", "theoretical_claims": "The theoretical foundation of the paper primarily lies in the one-stage method where three components are simultaneously learnt – city-specific region embeddings, cross-city distribution matching and individual level matching. The theories underlying are solid. I have checked mathematical expressions of the model and training objective and found they are error free.", "experimental_designs_or_analyses": "The experiments are sound with valid tasks, datasets and evaluation metrics. The ablation is well designed with key components replaced or abandoned. For example, abandoning one-stage strategy yields less performance. Parameter sensitivity test is generally well done and makes sense.", "relation_to_broader_scientific_literature": "In an even broader sense, there are increasing works in self-supervised pre-training in urban contexts. Some of them claim to be foundation models. Nonetheless, it is obvious that many of them only focus on specific cities - pre-training in multiple cities is scarce. This submission then ushers an interesting path: overpasses can be established for sharing the knowledge accumulated in different cities. This is interesting in a broader  foundation model sense.", "essential_references_not_discussed": "I do not find such related works.", "other_strengths_and_weaknesses": "1) A promising and sound method is proposed for overcoming a critical challenge in urban computing, which has not been fully explored.\n2) The unsupervised method is novel without the need for data pairs in different cities and manual rules. \n3) Solid experiments across cities and tasks.\nA point that is missing in the paper is what forms a good pair of cities for alignment. If the two cities are extremely different, will this method still work? This is worth further discussing.", "other_comments_or_suggestions": "There are some typos in the paper, and it needs carefully proofreading.", "questions_for_authors": "Refer to weakness.", "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": {}}]

Author rebuttal:

Meta-review: The paper proposes a method to align latent representations between different cities in an unsupervised manner within a unified framework, enabling cross-city knowledge transfer. The method learns representations for each city and then aligns their latent spaces to ensure both global and local consistency. This alignment allows representations to be reused across cities for downstream tasks, which is validated through experiments showing that the proposed method outperforms related approaches.

The reviewers agree that the paper makes a significant contribution to urban modeling, noting that: 1) the core idea is clever and solid, addressing limitations of previous work; 2) the experiments are well-designed, sound, and convincingly support the claims, and 3) the paper is well-written, clearly explaining all aspects. A few concerns were addressed in the rebuttal. I therefore recommend acceptance and encourage the authors to consider the feedback and update the final version of the paper accordingly.
Decision: Accept (poster)