Global Context-aware Representation Learning for Spatially Resolved Transcriptomics

Thank you for taking the time to provide constructive feedback on our paper. To address your concerns, we have added tables and figures in this external link

Q1) Theoretical Justification

The similarity consistency loss in Equation (1) of our manuscript serves two key purposes: 1) explicitly guiding the embedding space to capture quantitative similarity relationships, and 2) encouraging the model to learn a global relational structure that spans all nodes.

In downstream tasks, we rely on cosine similarity between normalized embeddings. In other words, we treat the normalized embedding space as an Euclidean space, where distance serves as a proxy for semantic closeness. However, embeddings from GAE trained solely with the reconstruction loss are optimized for compression. As a result, the cosine similarity between embeddings lacks direct interpretability or consistency across different pairs. In an Euclidean space, the consistency loss equals zero ideally. Thus, the consistency loss serves as a regularizer that aligns the embedding space more closely with the desired geometry, making similarity values more meaningful and consistent.

Moreover, the limited receptive field of GNNs is problematic because downstream tasks involve comparing representations of distant nodes. The consistency loss helps mitigate this limitation by considering similarity relations between all node pairs. The reconstruction loss satisfies $\frac{\partial^2 \mathcal{L}_{\text{recon}}}{\partial \tilde{Z}_i \partial \tilde{Z'}_j} = 0$ for $i \neq j$, which implies that updates to each embedding do not depend on the others.

In contrast, the second derivative of the consistency loss, $\frac{\partial^2 \mathcal{L}_{\text{SC}}}{\partial \tilde{Z}_i \partial \tilde{Z'}_j}$, can have non-zero values, indicating that the update to each embedding depends on others as shown in our proof R1.1 in the external link.

In summary, the consistency loss not only enhances the quantitative interpretability of similarity in the learned space, but also provides a mechanism for global information flow, thus improving the utility of the representations for downstream tasks.

Q2) Scenarios where the global similarity assumption may not hold

We understand your concern that Spotscape could introduce noise, particularly when spots far from the anchor node but still within the same spatial domain are considered. However, we want to clarify that our method does not rely on any form of aggregation from global nodes. Instead, Spotscape is designed to learn the similarities between all spots, irrespective of their global or local relationships.

Our approach focuses on learning these similarities directly, without assuming that distant spots within the same spatial domain must always share meaningful information. Rather than aggregating information from any nodes, the model learns the relationships between spots through augmentation-based consistency, which expects that only meaningful relationships are captured. This avoids the risk of noise from distant spots and emphasizes learning the inherent semantic relationships between spots based on the data itself.

In summary, Spotscape prioritizes the direct learning of spot similarities and consistency across augmentations, without aggregating information from distant or global nodes, which could potentially introduce noise.

Q3) More baselines

We have updated our experiments to include these two latest SRT clustering methods, MAFN (TKDE'24) and stGCL (ACM MM'24), across all relevant tasks, including clustering and integration. The results are now reported in Tables 1, 2, and 3 in the external link.

Compared to these baselines, Spotscape still demonstrates superior performance, highlighting the effectiveness of our proposed method.

Q4) Trade-offs between performance gains and computational cost of the PCL scheme

To address your concern regarding the trade-offs between performance gains and computational costs associated with prototypical contrastive learning (PCL), we generated a synthetic dataset using scCube [1], with mouse embryo data as the reference, and reported the results in Figure 6 (external link). This analysis demonstrates that while PCL does require more training time, it leads to better performance. We argue that in practical scenarios, the decision to use PCL depends on the user's preference for balancing training time and performance. However, we emphasize that PCL does not lead to impractical training times, as it is not excessively slow, and can still be viable for real-world applications.

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[1] "Simulating multiple variability in spatially resolved transcriptomics with scCube," Nature Communications

Thank you for your constructive feedback. To address your concerns, we upload additional results in the external link.

Q1-1) Presentation of Figure 1

Figure 1 highlights the limitations of previous methods that address the issues present in the Vanilla GAE (b-1), particularly the problem where boundary spots receive noisy information from spots in different spatial domains.

While we describe the observation from Figure 1 in the second paragraph of our manuscript, we understand that the presentation of Figure 1 may have caused some confusion, as we did not clearly indicate which part of Figure 1 readers should focus on. The most important part of Figure 1 is the number of red dots, which represent Wrongly Clustered in Boundary and boundary CA. We will revise the manuscript to make this point more prominent.

Additionally, the spot colors in Figure 1 (a) and (b) are independent. Please refer to the legend at the top of the Figure 1 (a) of our manuscript.

Q1-2) Spotscape vs. GAE variation

Spotscape did not exceed GAE with oracle edges (b-3), which is connected with the same ground truth only, in terms of Total CA, which is not a real scenario. However, Spotscape does outperform the oracle setting in terms of boundary CA, demonstrating the effectiveness of our proposed method in addressing the boundary-related issues.

Q2) GNN for cell-type specific signals

Your concern arises from the fact that all of the datasets we used are annotated by spatial domains rather than cell types, and that our evaluations only focus on spatial domains. You may also have assumed that as our graph is primarily constructed based on spatial coordinates, this would be only effective for capturing spatial signals, while not as useful for encoding cell-type-specific signals.

To address this, we introduce a new dataset from the Postnatal Mouse Brain (PMB) (STOmicsDB ID: STDS0000004), annotated by cell types, and perform ablation studies with an MLP encoder. The clustering performance for PMB and DLPFC both is reported in Table 5 and 6 in the external link.

We observe that the GNN-based encoder is less beneficial in the PMB dataset (cell-type) than in the DLPFC dataset (spatial domain) clustering. This indeed aligns with your intuition that the spatial graph carries more information regarding spatial-specific signals rather than cell-type-specific signals. However, GNN still provides a performance gain in the PMB data since spatial regions also implicitly carry signals related to cell types because the same cell types tend to cluster together within tissues, reflecting their functional and structural organization, as well as their interactions within specific tissue regions [1]. In fact, the homophily ratio of both the SNN graph in the DLPFC and the PMB data is 0.92, demonstrating that spatial regions also carry cell-type-related signals.

Q3) Scalability

Please refer to Figure 10 in our manuscript about reasonable runtime up to 100,000 spots. To further address your concern, we conducted additional experiments using the Mouse Main Olfactory Bulb dataset (STOmicsDB ID: STDS0000142 - 1,792,797 spots in 39 slices). In Figure 5 in the external link, we present the runtime for different numbers of slices, demonstrating that Spotscape can handle large datasets without exponential runtime growth as the number of slices grows.

Q4-1) Hyper-parameters setting

Please refer to our rebuttal regarding Q4 to reviewer uFL9 due to the character limits.

Q4-2) More baselines

We have updated the baselines in the external link.

• PASTE2: Slice-to slice alignment using optimal transport in Table 4
• CAST: Integration and alignment using CCA-SSG in Table 3 (Heterogeneous integration), Figure 1 (UMAP for batch effect), Figure 3 (Trajectory inference), and Table 4 (Alignment)

Q5-1) Figure 6 UMAP & Trajectory of raw expression

We did not intend to show trajectory inference results in Figure 6. Our goal was to highlight the performance of the heterogeneous integration reducing batch effect.

To address your concern, we show that the scores based on the raw expression do not provide reliable information on trajectory. To evaluate this, we calculate the pseudo-Spatiotemporal Map and report its correlation with the ground-truth layer, adding the results in Figure 2 in the external link. These results indicate that raw expression alone performs the worst, demonstrating the necessity of additional representation learning methods.

Finally, we also conducted trajectory inference on this dataset and reported the results in Figure 3 and 4 in the external link. These results show that while Spotscape successfully captures the trajectory, the raw expression-based approach fails to do so.

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[1] "An introduction to spatial transcriptomics for biomedical research," Genome Medicine

Thank you for your positive feedback regarding our manuscript. To address your concerns, we have added tables and figures in this external link.

W1) The scalability analysis is incomplete

In our manuscript, we initially focused on training time in Figure 10 because our performance improvements had already been demonstrated through various experiments. The scalability experiment was conducted using synthetic data without meaningful spot information, making it unsuitable for reporting performance metrics.

To provide a more comprehensive evaluation, we generated another synthetic dataset using scCube [1], with mouse embryo data as the reference. In Figure 6 in the external link, we demonstrate that Spotscape not only achieves fast inference but also maintains robust performance across varying numbers of spots and slices.

Q1) t-tests results

In the external link, we have conducted t-tests for all our experiments. We indicate statistical significance with ** for p-value < 0.01 and * for p-value < 0.05.

Q2) Comparison with domain-specific imputation methods

Most existing imputation methods in spatial transcriptomics, such as Tangram [2] and stDiff [3], rely on single-cell RNA sequencing data as a reference for improvement. However, this approach is not always applicable, as single-cell reference data is not always available, making these methods unsuitable as direct baselines for our study.

Given this limitation, we considered STAGATE, GraphST, SpaCAE, and SEDR as state-of-the-art baselines, as they denoise input expression data using decoded outputs and have also reported imputation results in their respective papers. To further address your concern, we additionally include stMCDI [4], which employs masked conditional diffusion strategies. To our knowledge, this is the most recent baseline that operates under the same setting as ours. Through this experiment in Figure 7 (external link), we demonstrate that Spotscape continues to achieve the best results.

Q3) Discussion on the theoretical underpinnings of the loss functions

As you pointed out in your review, our paper primarily focused on practical applications rather than theoretical analysis. However, to provide more clarity on the theoretical underpinnings of our approach, we would like to elaborate on the similarity consistency loss presented in Equation (1) of our manuscript. This loss function is a key contribution and one of the main components in Equation (8) of our manuscript. We discussed this loss in our rebuttal regarding Q1 for reviewer aaPZ due to character limits.

Meanwhile, outliers may potentially impact the embeddings of other nodes, as the loss considers global relationships, which could be a limitation. Despite these challenges, the consistency loss remains an effective tool for improving the model's global contextual understanding.

Q4) Guidance on the hyper-parameter tuning process

In lines 245-253 of our manuscript, we clarify that

To ensure fairness, we conduct a hyperparameter search for all baseline methods instead of using their default settings, as optimal hyperparameters may vary across datasets. The best-performing hyperparameters are determined based on NMI using the first seed. For Spotscape, only the learning rate is searched using the same criterion. Details of the selected hyperparameters and search spaces are provided in Appendix E.1 of our manuscript.

We ensure fairness in the comparison by conducting a broader hyperparameter search for the baseline methods compared to our proposed method, making the comparison as fair and consistent as possible. Specifically, in Appendix E.1 of our manuscript, we state that for Spotscape, we utilized default parameters across all datasets except for the learning rate. However, for the baseline methods, additional parameters, such as loss balancing, are also tuned along with the learning rate because some baselines are highly sensitive to them. In this section, we also provide the full search spaces for each baseline. To further address your concern, we have now added the final selected hyperparameters for all baseline methods across all datasets to our Anonymous Github, ensuring full transparency and reproducibility.

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[1] "Simulating multiple variability in spatially resolved transcriptomics with scCube," Nature Communnications
[2] "Deep learning and alignment of spatially resolved single-cell transcriptomes with Tangram," Nature Methods
[3] "stDiff: A diffusion model for imputing spatial transcriptomics through single-cell transcriptomic," Briefings in Bioinformatics
[4] "stMCDI: Masked Conditional Diffusion Model with Graph Neural Network for Spatial Transcriptomics Data Imputation," BIBM 2024