Cross-City Latent Space Alignment for Consistency Region Embedding

Response to W1: We 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.

To 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:

The 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.

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.

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:

As 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.

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:

The 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.

[1] Region representation learning via mobility flow, CIKM.

[2] Representing urban functions through zone embedding with human mobility patterns, IJCAI.

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.

[3] Forecasting China’s GDP at the pixel level using nighttime lights time series and population images. GIScience & Remote Sensing.

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.

The 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.

[4] Hull, David. Using statistical testing in the evaluation of retrieval experiments. SIGIR.

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:

The 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.

Response to W3: We will replace 3D barcharts with heatmaps in the revision.

Response to W1: We 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:

Our 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.

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.

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.

Response to minor questions: We 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.