Preference-Driven Spatial-Temporal Counting Process Models

W6: We summarize our response into following aspects:

• Are there specific sequential criminal events in the datasets? If so, does the proposed method successfully retrieve these sequences?: Specific sequential criminal events, such as repeated offenses by the same suspect, are rare in our crime dataset. However, the Mobike dataset documents multiple instances of bike rentals by the same user. The table below illustrates the mixture patterns adjusted by utility scores for different experts corresponding to 4 times bike rental records by the same user (user id 10344) on August 7, 2016, in Shanghai. The results indicate that under the same expert, the mixture patterns are similar, whereas they vary significantly across different experts. The mixture patterns generated by expert-1 exhibit obviously higher values compared to those produced by other experts. This demonstrates our model's ability to capture diverse user behaviors, underlying thinking processes, and sequential decision-making patterns in bike rental scenarios. | Time-Location Pair (time, (Lat., Lon.)) | Expert-1 | Expert-2 | Expert-3 | Expert-4 | |---|---|---|---|---| | 12h-16h, (31.185, 121.468) | 2.681e-2 | 1.481e-2 | 1.651e-2 | 1.631e-2 | | 16h-20h, (31.185, 121.468) | 3.251e-2 | 1.831e-2 | 1.921e-2 | 1.881e-2 | | 16h-20h, (31.185, 121.468) | 3.251e-2 | 1.831e-2 | 1.921e-2 | 1.881e-2 | | 20h-24h, (31.185, 121.468) | 2.401e-2 | 1.761e-2 | 1.961e-2 | 1.801e-2 |

• If each crime is independent, how are the datasets suitable for examining causal relationships?: We assume there are K latent mixtures, and each crime belongs to one of the mixtures independently. The causal relationships are revealed by the latent mixtures.

• How does the model demonstrate that its improvements are due to modeling the human decision process? Could simple statistics identify criminal hotspots at specific time slots to yield similar results to those in Fig. 2?: For Figure 2, simple statistics consider each time interval independently. However, our model jointly considers all the time intervals within a day and the interaction effects between time and location. To test the difference between the model performance of our model and statistical methods, we have added extra experiments. For statistical methods, we use the frequency of the previous day to predict the next day’s events. Seeing from the results shown in the table below, our model outperforms the statistical method on prediction tasks, indicating the incorporation of human decision processes of our proposed model indeed improves model performance.

Continuing with W6:

• For our claim of human decision process: In our experiment, we consider the severity of the crime, suspect race, and suspect gender as key categorical features. The utility score for each time-location pair is determined through regression analysis involving these features, with the coefficients reflecting the magnitude of impact on the utility score. For each expert, the utility score patterns are different, reflecting different preference patterns. We have taken the NYC Crime dataset as an example and the results are shown in heatmaps in Appendix G of our revised paper.

To illustrate the "human decision process" in a more clear way, we take an example for the top-5 crime event time location-pair for different races of expert-1 with largest utility score. The results are reported in the table below and the time-location pairs are recorded in "time, (Lat., Lon.)" format. From the results one can see that distinct patterns emerge based on the time and location of crime events across various racial groups. Black suspects tend to engage in criminal activities during the early morning or late night hours, while White Hispanic suspects are less active in criminal activities during the early morning hours. The timing of criminal activities among suspects of other races is more varied. At the regional level, the concentration areas for criminal activities among suspects of different races vary significantly. By incorporating social norms or individual information of suspects into the utility function, our approach better captures the role of individual differences and human decision-making processes in engaging in criminal activities.

W3: The matrices A and B encode the learnable embedded time-location information for all pairs across the various latent classes. The benefit of the intermediate matrix decomposition-based embedding is to capture the interaction impacts of different temporal spatial grids by utilizing the cross product of A and B. This approach enhances flexibility compared to merely combining A and B.

W4: Our sparse gating function generates a sparse vector, which consists of weights for each temporal-spatial grid. This vector retains only the top-k most significant choices with nonzero weights. The ranking of these weights reflects the preference order among choices. The probability for each temporal spatial grid depends on both the ranking and the utility. The ranking mechanism is used to reduce the dimension, i.e., from a high dimension choice set to a much smaller k dimension choice set. Since we aim to use our modeling framework to effectively represent the human decision-making process. The ranking mechanism delineates the initial step in the decision-making process — selecting a subset of candidates. The second step involves evaluating the utility of each choice. Although each event is treated independently, it emerges from underlying mixtures exhibiting diverse causal patterns.

W5: The method we applied in the paper for dividing time and regions is common practice, and the granularity of our time and region divisions is generally similar to methods used in other published works. ST-HSL [5] applies a 3 km by 3 km spatial grid unit to New York City and Chicago, resulting in the generation of 256 and 168 disjoint spatial regions, respectively, slightly more than our 100 disjoint spatial regions. SpatialRank [6] partitions the Chicago area into 500 m by 500 m square cells, while HintNet [7] divides the whole state of Iowa into 5 km by 5 km grids (the area closely aligns with our partitioning) and designates a single day as the appropriate time interval. Following the same approach, we partitioned the time horizon and regions in a similar manner.

We would like to highlight that, according to the official Mobike dataset documentation, the peak hours on workdays are specified as 16:00-20:00. To better capture the peak hour pattern, we designated this time frame as a distinct time slot, resulting in the division of the entire day into 6 time slots, each spanning 4 hours.

Moreover, we have also added more experiments to investigate the impact of spatial and temporal grid resolutions on both model performance and computational costs. Please refer to our responses for Reviewer v1uj and Reviewer VmVn, W3 & Q3. Detailed experiment results and corresponding analysis can also be found in Appendix F in our revised paper.

[5] Li, Z., Huang, C., Xia, L., Xu, Y., & Pei, J. (2022, May). Spatial-temporal hypergraph self-supervised learning for crime prediction. In 2022 IEEE 38th international conference on data engineering (ICDE) (pp. 2984-2996). IEEE.
[6] An, B., Zhou, X., Zhong, Y., & Yang, T. (2024). SpatialRank: urban event ranking with NDCG optimization on spatiotemporal data. Advances in Neural Information Processing Systems, 36.
[7] An, B., Vahedian, A., Zhou, X., Street, W. N., & Li, Y. (2022). Hintnet: Hierarchical knowledge transfer networks for traffic accident forecasting on heterogeneous spatio-temporal data. In Proceedings of the 2022 SIAM International Conference on Data Mining (SDM) (pp. 334-342). Society for Industrial and Applied Mathematics.

We first thank reviewer swpn for the insightful comments, especially for the questions about the details of our proposed model, which helped us to clarify our paper further. We would like to address the concerns one by one.

In response to your mentioned weaknesses:

W1: We summarize our response into following aspects:

• Explain more about spatial and positional embeddings: We treat spatial and position information for different embeddings as the work of [1]. In our approach, spatial information, akin to patch information in [1] which breaks down the image (area region in our problem) into smaller patches (blocks in our problem), treating them as individual tokens similar to words in text, allowing the embedding to capture spatial information. The position information provides information about the locations of patches (blocks) within the region, helping the model understand the relative positions of different patches (blocks) and enabling it to learn spatial dependencies across the image (area region).

• Which model does each expert use?: As indicated in Equation 5, we employ the same model architecture but utilize different parameters for each expert.

• Key individual features: Social norms and other pertinent factors are encapsulated within the utility function, formulated in a regression form. We have provided experiment fundings and detailed analysis in our response to W6. You can found our reply below.

[1] Dosovitskiy, A. (2020). An image is worth 16x16 words: Transformers for image recognition at scale. arXiv preprint arXiv:2010.11929.

W2: : Thanks for your suggestion about analyzing more related works. We will ensure to incorporate the reference you listed into the related work section of our paper. However, the codebases for the referenced methodologies have not been released. To ensure a fair comparison with state-of-the-art models, we have incorporated three more SOTA baseline models.

• HintNet [2]: It performs a multi-level spatial partitioning to separate sub-regions with different risks and learns a deep network model for each level using spatio-temporal and graph convolutions.
• STNSCM [3]: a causality-based interpretation model for the bike flow prediction.
• UniST [4]: a universal model designed for general urban spatio-temporal prediction across a wide range of scenarios.

Compared to the newly added baselines, our model surpasses all baselines in prediction tasks on the Chicago dataset. In the NYC dataset, our model demonstrates competitive performance with UniST and outperforms the other two models. The mean aRMSE and mean MAPE across three random runs of our model on the NYC dataset are 2.34 and 107.94, slightly higher than UniST's 2.26 and 105.23, respectively. However, our model exhibits a lower standard deviation, indicating better stability in our predictions. For the Mobike dataset, our model remains the second-best performing model, with a mean aRMSE and mean MAPE of 3.28 and 154.62, respectively, trailing only behind STNSCM with 3.12 and 152.38. Additionally, our model also exhibits lower standard deviation than the STNSCM model. Overall, our model significantly outperforms the models considered in our paper. Against the newly introduced state-of-the-art baselines, our model also achieves stable predictions and competitive results across all three datasets.

[2] An, B., Vahedian, A., Zhou, X., Street, W. N., & Li, Y. (2022). Hintnet: Hierarchical knowledge transfer networks for traffic accident forecasting on heterogeneous spatio-temporal data. In Proceedings of the 2022 SIAM International Conference on Data Mining (SDM) (pp. 334-342). Society for Industrial and Applied Mathematics.
[3] Deng, P., Zhao, Y., Liu, J., Jia, X., & Wang, M. (2023, June). Spatio-temporal neural structural causal models for bike flow prediction. In Proceedings of the AAAI conference on artificial intelligence (Vol. 37, No. 4, pp. 4242-4249).
[4] Yuan, Y., Ding, J., Feng, J., Jin, D., & Li, Y. (2024, August). Unist: a prompt-empowered universal model for urban spatio-temporal prediction. In Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (pp. 4095-4106).

In response to your questions:

Q1: We use training negative log-likelihood, test aRMSE, test MAPE, and training time cost as metric to select appropriate hyper-parameters. Taking NYC-crime dataset with 732 samples as an example. And we divide the time horizon and region into 4 time slots and 100 region blocks.

• Impact of Learning Rate | Learning Rate | 1e-4 | 5e-4 | 1e-3 | 5e-3 | 1e-2 | 5e-2 | |---|---|---|---|---|---|---| | Mean Neg. Log-likelihood | -4.980 | -5.112 | -5.059 | -4.839 | -4.854 | -5.010 | | aRMSE | 2.38 +/- 0.04 | 2.25 +/- 0.08 | 2.34 +/- 0.05 | 2.53 +/- 0.26 | 2.57 +/- 0.64 | 2.48 +/- 0.40 | | MAPE | 108.33 +/- 5.12 | 106.90 +/- 4.67 | 107.94 +/- 4.27 | 115.47 +/- 7.32 | 113.50 +/- 7.83 | 110.33 +/- 6.12 | | Time Cost (h) | 0.8354 | 0.7239 | 0.5859 | 0.5630 | 0.6239 | 0.5253 |

We vary the learning rate through grid search from 1e-4 to 5e-2 and our current choice is 1e-3. When using a relatively low learning rate like 1e-4, the mean converged negative log-likelihood (lower is better) and the predictive accuracy remains nearly the same as our current selection (1e-3), but with increased computational cost for convergence. With a larger learning rate, the model performance starts to become unstable. For instance, when the learning rate is set to 5e-2, the mean aRMSE and mean MAPE for the prediction task across three random runs increase to 2.48 and 110.33, respectively, with larger standard deviations of 0.40 and 6.12. And the mean converged negative log-likelihood is also larger than the result achieved by our current choice of learning rate. Meanwhile, the training time for the model to converge does not decrease significantly. Therefore, we opted for a learning rate of 1e-3 in our experiments.

• Impact of Number of Experts | Number of Experts | 1 | 2 | 3 | 4 | 5 | |---|---|---|---|---|---| | Mean Neg. Log-likelihood | -4.885 | -4.934 | -5.059 | -5.219 | -5.320 | | aRMSE | 2.52 +/- 0.08 | 2.46 +/- 0.10 | 2.34 +/- 0.05 | 2.25 +/- 0.12 | 2.28 +/- 0.08 | | MAPE | 113.85 +/- 5.23 | 110.54 +/- 5.67 | 107.94 +/- 4.27 | 105.83 +/- 4.50 | 104.73 +/- 4.75 | | Time Cost (h) | 0.4087 | 0.4860 | 0.5859 | 0.8216 | 1.2621 |

For the number of experts, we vary it from 1 to 5. As our current choice for the NYC dataset is 3, decreasing it would degrade the model performance. However, increasing the number of experts does not yield a substantial improvement in model effectiveness but notably escalates computational costs. For instance, raising the number of experts from 3 to 5 would extend the training time from 0.5859 hours to 1.2621 hours because of increased learnable model parameters, while the negative log-likelihood, aRMSE, and MAPE metrics only marginally shift from -5.059 to -5.320, 2.34 to 2.28, and 107.94 to 104.73, respectively. Hence, to strike a balance between model performance and training efficiency, we opt to maintain the number of experts at 3 for the NYC dataset. We also employed a similar strategy when selecting the number of experts for other datasets.

Q3: To ensure a model's stability and consistency, we can use k-fold cross-validation and out-of-sample testing. To implement K-Fold Cross-Validation, we need to split our crime or mobike datasets into k subsets and train the model on k-1 folds and validate on the remaining fold. We need to repeat this process k times, each time using a different fold as the validation set. After training the model using cross-validation like k-fold cross-validation, we can use out-of-sample testing to test it on entirely new, unseen data. In the prediction tasks detailed in our paper, we have employed both cross-validation and out-of-sample testing methodologies to validate and ensure the robustness of our model's performance.

We appreciate that reviewer cFeC has a positive impression of our work. To address your concerns about the our method, we provide point-wise responses as follows.

In response to your mentioned weaknesses:

W1: Take crime datasets for examples, we consider the suspect features such as severity of the crime event, suspect race, and suspect gender as key categorical features to build the utility functions. And the utility score for each time-location pair is determined through regression analysis involving these features, with the coefficients reflecting the magnitude of impact on the utility score. For each expert, the utility score patterns are different, reflecting different preference patterns. By doing this, our paper's claim regarding the interpretability of the human decision process can be effectively demonstrated, as distinct suspect features reveal varying crime preferences across different time-location pairs. In our response to Reviewer swpn, W6, we present the experimental results. Please refer to our response for a comprehensive view of the results and corresponding analysis.

W2 & Q2: Please refer to our responses for Reviewer v1uj. We have also incorporated detailed experiment results and corresponding analysis in Appendix E and Appendix F of our revised paper.

W3: Future research could integrate attention mechanisms into the gating function of choice model. This integration may enhance the model’s flexibility, enabling it to capture a broader range of and long-term information through neural networks. To improve the interpretability, we can also consider integrating the attention mechanisms into the utility function. These ideas serve as promising starting points which will be the future research direction to improve our work.

We are grateful for your careful reading and useful suggestions! Below, we will address your concerns one by one.

In response to your mentioned weaknesses and questions:

W1 & Q1: Thanks for your insightful suggestion! We have added a scalability experiment to test the performance of our proposed model in large-scale datasets. Please refer to our response for Reviewer v1uj for the complete results across all three dataset we used in our paper. We have also incorporated the scalability experiments in Appendix E in our revised paper. Here we provided the corresponding analysis to address your concerns.

Across all experiments, as the dataset sample size increases, both evaluation metrics, aRMSE and MAPE, generally decrease for the prediction task. For the NYC dataset, with an increase in data size from the current 732 samples to 5561 samples, mean aRMSE over three random runs decreases from 2.34 to 2.06, and mean MAPE decreases from 107.94 to 100.72. For the Chicago dataset, with an increase in data size from the current 861 samples to 5321 samples, mean aRMSE over three random runs decreases from 2.19 to 1.93, and mean MAPE decreases from 87.38 to 85.50. For the Mobike dataset, to obtain datasets with varying sample sizes while ensuring consistency in the differences between sample sizes across datasets, we reselected data from August 2, 2016, to August 6, 2016. The results indicate that with an increase in data size from 1457 samples (one day) to 8786 samples (five days), the mean aRMSE over three random runs sharply decreases from 4.27 to 2.88, and the mean MAPE decreases from 172.50 to 148.67.

The training time required for model convergence remains within acceptable ranges on the current computing infrastructure (details provided in Appendix D). For the large-scale NYC dataset with 5561 samples, the model converges in only 3.8970 hours. For the large-scale Chicago dataset with 5321 samples, the model converges in around 4.0410 hours. Even for the large-scale Mobike dataset with 8786 samples, our model converges and achieves good inference and prediction results after training for approximately 7.1056 hours, showcasing good scalability of our proposed model.

W2 & Q2: Our approach aims to uncover the preference-driven decision-making processes. The mixture of experts is used to capture the thinking patterns of different latent groups. In addition to the Mixture of Experts module, our model incorporates choice theory and a sparse gating function to effectively capture the intricate patterns in spatial-temporal event data. Notably, for certain datasets, the mixture patterns may not be distinctly observable. Our model can capture these subtle differences and thus enhance the model performance. For instance, as illustrated in Figure 7 of the appendix, the first two mixtures from the Chicago dataset exhibit considerable similarity, while the third mixture contributes minimally with weight 0.1056. Guided by these complex mixtures, as demonstrated in Table 2, for the Chicago dataset, our model's performance significantly surpasses that of the baseline models.

W3 & Q3: Your concern about the resolution is constructive! Employing a finer resolution undoubtedly enhances the model's persuasiveness by capturing more detailed time-location patterns for event occurrences. But we want to emphasize that the method we applied in the paper for dividing time and regions is common practice, and the granularity of our time and region divisions is generally similar to methods used in other published works. ST-HSL [1] applies a 3 km by 3 km spatial grid unit to New York City and Chicago, resulting in the generation of 256 and 168 disjoint spatial regions, respectively, slightly more than our 100 disjoint spatial regions (as we reported in our paper). SpatialRank [2] partitions the Chicago area into 500 m × 500 m square cells, while HintNet [3] divides the whole state of Iowa into 5 km by 5 km grids (the area closely aligns with our partitioning) and divides a single day as the appropriate time interval.

Moreover, we have explored the impact of spatial and temporal grid resolutions on both model performance and computational costs. Please refer to our response for Reviewer v1uj for the complete experiment results. Detailed experiment results and corresponding analysis can also be found in Appendix F in our revised paper.

With finer resolutions for the time grid and region blocks, the model is expected to capture event patterns more accurately and with greater granularity in time and location. However, our experimental results indicate that increasing the fine-grained spatial and temporal resolution does not significantly enhance the model performance. For instance, when comparing Case-4 with Case-2 using a dataset of 2985 samples, despite Case-4 having finer resolution, the mean aRMSE (over three different runs) only decreases from 2.29 to 2.12, and the mean MAPE decreases from 104.43 to 101.30. This could be attributed to the overly detailed partitioning of time and space, leading to insufficient instances of events at each time-location pair, thereby impacting the model's effectiveness. Further validation of this observation is evident when varying the sample size within the same case. For Case-2, increasing the sample size from 2985 to 5561 results in a more significant improvement in model performance, with the mean aRMSE decreasing from 2.29 to 2.06 and the mean MAPE decreasing from 104.43 to 100.72. It addresses the substantial impact of increasing dataset size on model effectiveness. Therefore, the results presented in our paper reflect a trade-off in selecting resolution based on balancing model performance and the level of detail in capturing time-location pair patterns.

[1] Li, Z., Huang, C., Xia, L., Xu, Y., & Pei, J. (2022, May). Spatial-temporal hypergraph self-supervised learning for crime prediction. In 2022 IEEE 38th international conference on data engineering (ICDE) (pp. 2984-2996). IEEE.
[2] An, B., Zhou, X., Zhong, Y., & Yang, T. (2024). SpatialRank: urban event ranking with NDCG optimization on spatiotemporal data. Advances in Neural Information Processing Systems, 36.
[3] An, B., Vahedian, A., Zhou, X., Street, W. N., & Li, Y. (2022). Hintnet: Hierarchical knowledge transfer networks for traffic accident forecasting on heterogeneous spatio-temporal data. In Proceedings of the 2022 SIAM International Conference on Data Mining (SDM) (pp. 334-342). Society for Industrial and Applied Mathematics.

Additionally, we have explored the impact of spatial and temporal grid resolutions on both model performance and computational costs. The results are presented in the tables below and detailed experiment results and corresponding analysis can be found in Appendix F in the revised paper. We use NYC crime dataset with 2985 samples and 5561 samples across 4 cases, each case with different time grid length and resolution for region. The descriptions about these 4 cases and corresponding experiment results are as below:

• Case-1: 2 time grids (12 hour per grid), 25 region blocks (5 * 5)
• Case-2: 4 time grids (6 hour per grid), 100 region blocks (10 * 10)
• Case-3: 6 time grids (4 hour per grid), 225 region blocks (15 * 15)
• Case-4: 8 time grids (3 hour per grid), 400 region blocks (20 * 20)

With finer resolutions for the time grid and region blocks, the model is expected to capture event patterns more accurately and with greater granularity in time and location. However, our experimental results indicate that increasing the fine-grained spatial and temporal resolution does not significantly enhance the model performance. For instance, when comparing Case-4 with Case-2 using a dataset of 2985 samples, despite Case-4 having finer resolution, the mean aRMSE (over three different seed) only decreases from 2.29 to 2.12, and the mean MAPE decreases from 104.43 to 101.30. This could be attributed to the overly detailed partitioning of time and space, leading to insufficient instances of events at each time-location pair, thereby impacting the model's effectiveness. Further validation of this observation is evident when varying the sample size within the same case. For Case-2, increasing the sample size from 2985 to 5561 results in a more significant improvement in model performance, with the aRMSE decreasing from 2.29 to 2.06 and the MAPE decreasing from 104.43 to 100.72. This underscores the substantial impact of increasing dataset size on model effectiveness. Hence, the results presented in our paper reflect a trade-off in selecting resolution based on balancing model performance and the level of detail in capturing time-location pair patterns.

We thank the reviewer for your careful reading and insightful comments! In response to the reviewers' suggestion, we have expanded our evaluation to include multiple datasets with varying sample sizes to test the scalability of our proposed model. Detailed experiment results and corresponding analysis can be found in Appendix E in the revised paper.

• Scalability experiments on NYC Crime Dataset | Sample Size | 732 | 1840 | 2985 | 4016 | 5561 | |---|---|---|---|---|---| | aRMSE | 2.34 +/- 0.05 | 2.25 +/- 0.06 | 2.29 +/- 0.13 | 2.10 +/- 0.08 | 2.06 +/- 0.10 | | MAPE | 107.94 +/- 4.83 | 103.32 +/- 4.67 | 104.43 +/- 5.33 | 101.83 +/- 4.33 | 100.72 +/- 5.67 | | Time Cost (h) | 0.5859 | 1.3252 | 1.7971 | 2.5254 | 3.8970 |

• Scalability experiments on Chicago Crime Dataset | Sample Size | 861 | 2434 | 3207 | 4578 | 5321 | |---|---|---|---|---|---| | aRMSE | 2.19 +/- 0.04 | 2.56 +/- 0.08 | 2.12 +/- 0.12 | 2.25 +/- 0.08 | 1.93 +/- 0.10 | | MAPE | 87.38 +/- 3.12 | 94.67 +/- 3.83 | 86.23 +/- 5.22 | 90.94 +/- 4.95 | 85.50 +/- 4.12 | | Time Cost (h) | 0.7785 | 1.6995 | 2.2787 | 3.2730 | 4.0410 |

• Scalability experiments on Shanghai Mobike Dataset | Sample Size | 1457 | 3347 | 5054 | 6602 | 8786 | |---|---|---|---|---|---| | aRMSE | 4.27 +/- 0.12 | 3.57 +/- 0.08 | 3.06 +/- 0.12 | 2.85 +/- 0.12 | 2.88 +/- 0.67 | | MAPE | 172.50 +/- 8.48 | 158.33 +/- 8.25 | 151.54 +/- 7.33 | 148.34 +/- 7.50 | 148.67 +/- 8.19 | | Time Cost (h) | 1.4245 | 2.4924 | 3.8226 | 5.5305 | 7.1056 |

For NYC dataset, the date time was divided into four time slots, and the New York area was segmented into 100 small area blocks based on longitude and latitude. We use the same temporal and spatial resolution for Chicago dataset. For Shanghai Mobike, we divide the date time into 6 time grids and divide the Shanghai area into 100 area blocks. Across all experiments, as the sample size increases, both evaluation metrics, aRMSE and MAPE, decrease for the prediction task. Taking the NYC dataset as an example, with an increase in data size from the current 732 samples to 5561 samples, mean aRMSE (over three different seeds) decreases to 2.06, and MAPE decreases to 100.72. The training time required for model convergence remains within acceptable limits on the current computing infrastructure (details provided in Appendix D). For the NYC dataset with 5561 samples, the model converges in only 3.8970 hours. Even for the large-scale Mobike dataset with 8786 samples, our model converges and achieves good inference and prediction results after training for approximately 7.1056 hours. For all these datasets, the model's prediction accuracy increases with larger sample size, requiring more training time, yet within reasonable range.