GTR: A General, Multi-View, and Dynamic Framework for Trajectory Representation Learning

We appreciate the positive comments and our responses are detailed below.

W1: Some parts of this paper are not explained very clearly, which could lead to misunderstandings and ambiguities. i) First, since there are many symbols, a symbol table is recommended for better following. ii) Besides, although the appendix includes detailed descriptions of relevant studies, the absence of citations of this "Section" in the main body may create the impression that the paper lacks a thorough discussion of prior studies. iii) In Table 1, does "Avg.Length" refer to the spatial length of the trajectory or the number of trajectory points?

We sincerely appreciate the reviewer’s valuable feedback regarding the clarity of our manuscript. We have addressed each point as follows. (i) We would like to include a notation table below to clearly define all mathematical symbols used throughout the paper. (ii) We will add explicit citations to the appendix’s related work section in the main text. (iii) The “Avg.Length” in Table 1 indeed refers to the average number of trajectory points.

W2: The experimental section can be optimized. i) For instance, including the percentage increase in experimental tables can indeed enhance the clarity and impact of the results. ii) The calculation processes of some evaluation metrics (e.g., PED for trajectory simplification task, Hausdorff/DTW for trajectory generation task, HR@x for trajectory similarity search task) are not provided.

Thanks for the suggestion. (i) In addition to the detailed performance values, we are happy to include the percentage increase, i.e., 15%–60% for trajectory imputation task, 1%–4% for trajectory classification task, 10%–90% for the travel time estimation (TTE) task, 5%–26% for trajectory simplification task, 4%–8% for trajectory similarity computation task, and 37%–81% for trajectory generation task. (ii) As these evaluation metrics are well-established in the field, we directly cited the related papers that introduced them in our manuscript. The definitions of these metrics can refer to the response to reviewer vfe9's.

W3: There are also some minor details that need attention. i) "we conduct extensive experiments on two real-world datasets demonstrate"->"we conduct extensive experiments on two real-world datasets to demonstrate". ii) "In this paper, we target perform"->"In this paper, we target performing". iii) "In classification task, there are two labels in beijing dataset"->"In classification task, there are two labels in the Beijing dataset". iv) "Mean Absolut Percentage Error (MAPE)"->"Mean Absolute Percentage Error (MAPE)"

We sincerely appreciate the reviewer's careful reading of our manuscript. We will correct all these minor issues in the revised version. We will carefully proofread the entire manuscript to improve its presentation.

We express our gratitude to the reviewer for providing constructive feedback on our paper, and we greatly appreciate the acknowledgement of our contributions. We have addressed the specific concerns raised by the reviewer as detailed below.

W1&Q1: The paper does not specify the value of the balancing parameter β in the combined loss function (LGTR), leaving ambiguity in how the MLM and triplet tasks are weighted during pre-training, which could affect reproducibility and performance interpretation.

Thanks for pointing this out. In our pre-training framework, the balancing parameter $\beta$ in the overall loss function is set to $0.7$, which was determined through empirical validation on the validation set to optimally weigh the MLM and triplet loss components. This configuration ensures a balanced contribution from both tasks while maximizing downstream performance.

W2&Q2: Some figures (e.g., 1 and 2) and tables (e.g. 5 and 8) in the paper are too small to be clearly legible.

Thanks for the comment. We will carefully fix these presentation issues in the revised manuscript.

Other Comments Or Suggestions: In table 5, the TTE task result MAPE in Porto 0.19186 should be bolded.

Thanks for pointing this out. We will fix this marking error in the revised manuscript.

Thanks for all the valuable comments.

Response to E1: Existing works (START, Trembr, ST2Vec, etc.) mainly use Beijing and Porto datasets, so we adopted them for fair comparison. Following the suggestion, we have added the larger Chengdu dataset (containing 2,140,129 trajectories). Due to space limitation, we specifically test the most computationally intensive trajectory similarity computation task. The results are shown in the anonymous link https://anonymous.4open.science/r/Rebuttal_GTR/ (Table 1 : Trajectory Similarity Computation on Chengdu Dataset). As expected, GTR maintains superior performance over baselines on this new dataset, confirming its robustness.

Response to E2: We would like to emphasize that GTR extends task coverage compared to existing methods. As reported in Table 8 (Appendix A, lines 605--614), GTR is the first unified framework supporting all six fundamental trajectory tasks, whereas prior methods (including the state-of-the-art START, LightPath, JGRM) handle at most three tasks. Note that, our framework allows easy adaptation to additional tasks (e.g., next-location prediction, anomaly detection) through straightforward training strategy modifications. For anomaly detection specifically, our framework can learn discriminative trajectory representations through the MVE and STP modules. Based on that, we can learn representations of different trajectories and classify them as normal or abnormal.

Response to E3&References: We appreciate the reviewer's feedback regarding baseline selection. We would like to clarify that GTR is fundamentally a trajectory representation learning framework, rather than a task-specific model. Our primary objective is to learn robust trajectory embeddings that can effectively support multiple downstream tasks, which differs from specialized methods designed for individual tasks. This experimental design aligns with existing trajectory representation learning studies. Following the suggestion, we have now included comparisons with task-specific methods (AttnMove, MtrajRec, ControlTraj). The results are shown in the anonymous link https://anonymous.4open.science/r/Rebuttal_GTR/ (Table 2: Evaluationon on Trajectory Imputation Task; Table 3: Evaluationon on Trajectory Generation Task). As observed, GTR still achieves superior performance, further demonstrating the effectiveness. In the revised paper, we will include these results and cite these works.

Response to Methods And Evaluation Criteria: We appreciate the concerns about the technical contributions and novelty. GTR effectively and innovatively unified multi-view encoding, multi-task pre-training, and online adaptation, which have been recognized by the other reviewers (vfe9, Th6q, and nfbU).

(i) While multi-view learning is not new, our MVE is first to integrate Grid, POI, and road-network attributes to jointly model spatial, semantic, and structural features—unlike prior works that focus on only one or two views. The ablation studies (Tables 4 and 9) prove the effectiveness.

(ii) Our ST-MoE is not a trivial extension of standard MoE, as we introduces task-aware gating to dynamically adjust spatio-temporal feature fusion. This enables jointly optimizing multiple tasks while preserving inter-task correlations. Additionally, we employ dedicated spatial and temporal experts (rather than multiple experts) to ensure clear structural separation between spatial and temporal feature learning. This design mitigates the common issue of expert polarization, where only a subset of experts remains active.

(iii) Our online updating strategy is theoretically grounded in incremental learning [1]. We appreciate the opportunity to clarify the theoretical foundations, which combines layer-wise parameter freezing with Lyapunov stability analysis to ensure robust adaptation while preventing catastrophic forgetting.

Specifically, we freeze the first $L$ layers and update the last $N−L$ layers. The objective optimization function is: $\min\_{\theta^{L+1:N}}\mathbb{E}\_{(x, y)}\sim\mathcal{D}\_{\mathrm{new}}[\ell(f\_{\theta\_{\mathrm{pre}}^{1:L}}(x), y;\theta^{L+1:N})]$. With frozen lower-Layer parameters ($(\nabla_{\theta^{1:L}}\ell=0)$), old features remain unchanged, which guarantees that the old features are not forgotten.

The updating process can be modeled as a dynamic system: $\theta_{t+1}^{L+1:N} = \theta_t^{L+1:N} - \eta_t g_t$ , with a Lyapunov function: $V(\theta)=\mathcal{L}\_\mathrm{new}(\theta)+\gamma\|\theta^{1:L}-\theta_\mathrm{pre}^{1:L}\|^2$. As $\gamma\to\infty$, the system satifies: $\mathbb{E}[V(\theta\_{t+1})]\leq\mathbb{E}[V(\theta\_t)]-\eta\_t\|\nabla\mathcal{L}\_{\mathrm{new}}(\theta\_t)\|^2$. The monotonic decrease of $V(\theta)$ ensures stable updates. Freezing lower layers prevents cascading perturbations, balancing new feature learning with old feature retention.

[1] A Comprehensive Survey of Continual Learning: Theory, Method and Application.

We thank the reviewer for offering the valuable feedback. We have addressed each of the concerns as outlined below.

W1: Limited details are provided on the online updating approach. 

We are happy to provide more details about the online updating approach. To process newly arrived trajectory data, we employ the validation set to simulate real-world online/streaming scenarios. The model undergoes single-epoch incremental model updates.

W2: Some experimental results did not meet expectations, such as those in Table 5 and Table 9. 

We appreciate the reviewer's careful examination of our experimental results. Here, we are happy to provide more detailed experimental discussions to alleviate your concerns.

Regarding Table 5 (travel time prediction task), our online method GTR* shows slightly reduced effectiveness compared with our offline method GTR. This can be attributed to the presence of outliers in short-duration trajectories. Due to the sensitivity of regression task to short-term anomalies, it tends to overfit newly arriving anomalous real-time data. Nevertheless, our methods (GTR and GTR*) perform better than the other comparative baselines.

Regarding Table 9's ablation results for travel time prediction, the complete model shows slightly higher MAPE due to a small number of long-duration outliers. MAPE is known to be more sensitive to errors in lower-value ranges, which might amplify the effect of these outliers.

W3: It is beneficial to provide definitions of the metrics and specify which metrics indicate good performance, for clarity.

These evaluation metrics are standard measures widely adopted in trajectory data processing research. In the interest of manuscript conciseness, we directly cited the related papers in our manuscript. Here, due to space limitations, we provide rough definitions of the metrics and specify which metrics indicate good performance. We acknowledge that providing more detailed computational formulations could enhance reproducibility, and we will include these in the revised manuscript's appendix to ensure full methodological transparency.

For trajectory simplification task, $PED$ computes the shortest perpendicular distance between a deleted point $p_i = (x_i, y_i)$ and the line segment connecting its neighboring points $p_s = (x_s, y_s)$ and $p_t =(x_t, y_t)$. Lower $PED$ indicates lower compression errors.

For trajectory imputation task, $Recall@x$ evaluates the model's ability to recover masked tokens by checking whether the ground truth appears in the top-x predicted candidates. Specifically, if the true value is contained within the top-x ranked predictions, $Recall@x$ is assigned 1 for that token; otherwise, it is assigned 0. The final metric is computed by averaging these binary outcomes across all masked tokens in the evaluation set. The MAP represents the probability of the precision, and higher $Recall@x$ and MAP indicate higher performance.

For travel time estimation task, we use Mean Absolute Error (MAE), Mean Absolute Percentage Error (MAPE), and Mean Square Error (MSE) metrics. Specifically, lower MAE, MAPE, and MSE indicate higher prediction accuracy.

For trajectory classification task, we use $ACC$, $F1-Score$, and $AUC$ metrics. Specifically, higher $ACC$, $F1-Score$, and $AUC$ indicate higher classification accuracy.

For trajectory generation task, we use Hausdorff and DTW distance metrics. Lower DTW and Hausdorff value indicate higher performance.

For trajectory similarity computation task, we use Mean Rank and $HR@k$ metrics. Lower MR value and a higher $HR@k$ value indicate better performance.

Suggestions: Both MLM and Triplet Training are pre-training methods. It is beneficial to list them in parallel in Section 3.2.2 for clarity.

Thanks for the suggestion. Such layout issues can be easily adjusted.

Questions: Would you provide a comparison of model parameters between the proposed GTR and the baselines?

A comparison of model parameters is shown below. While GTR has a higher parameter count due to its multi-view encoder (MVE) and spatio-temporal fusion pre-training (STP) modules, this increase is justified by two key advantages. (i) Enhanced Capability. The additional parameters enable GTR to support more downstream tasks effectively. (ii) Performance Gains. The trade-off in model size is offset by improvements in accuracy and robustness.