SlowGuess/NeurIPS_2023_OCR huggingface dataset:
Metrics. In this study, we evaluate all the methods using 10-fold cross-validation with the same partition of training and testing splits. Our evaluation metrics include classification accuracy (ACC), sensitivity (SEN), specificity (SPE), f1 score (F1) and ROC-AUC (AUC). Higher values for all metrics indicate better performance. We record the mean and standard deviation on 10 random runs with 10-fold cross-validation.
Implementation Details. For all experiments, we adopt Adam as the optimizer and StepLR (step_size=50, gamma=0.8) as the scheduler. The initial learning rate is set to 5e-4 and the dropout rate is set to 0.3. Also we utilize a early stop mechanism that 300 epochs patience in total 500 epochs. In the RH-BrainFS model, we set the k-hop in the subgraph sampling to 1, the number of bottlenecks  $N_{b}$  to 4, the number of attention heads in the Transformer to 4, and the total number of network layers to 2. All our experiments are implemented in PyTorch and trained on one NVIDIA 3090.
4.2 Comparison Experiments
In this section, we verify the performance of our RH-BrainFS against existing baselines on several datasets.
Baselines. We choose two categories of methods as comparison methods, both of which are methods for the direct study of SC and FC. The first category is unimodal methods, including FGDN [20] and BrainGNN [21], where FGDN uses a spectral graph convolution method to extract brain networks features, and BrainGNN proposes a ROI-aware graph convolution layer and uses pooling to extract brain networks features. In our experiments, SC and FC are used as inputs to the unimodal method, respectively. The second category is multimodal methods, including SVM, Random Forest, MGCN [29], GBDM [57], MMGNN [32] and AL-NEGAT [6], where SVM and Random Forest concatenate SC and FC as input, MGCN uses manifold-based regularization terms to consider inter-modality and intra-modality relationships, GBDM adopts weighted summation pattern to fuse multimodal brain networks, MMGNN utilises the concatenation method in multimodal tasks and AL-NEGAT combines multimodal information to construct edge feature maps and node feature maps. Code implementations of all baseline methods are taken from their respective original papers.
Table 1: Comparison experiments results (in percentage) on the all chosen datasets (only the accuracy is shown, the full results can be referred to the Appendix A). The best results are marked in bold. The suboptimal results are marked underlined.
Method	Modality	Datasets
HCP	Zhongda	Xinxiang	Two-site
FGDN	FC	67.56±3.02	65.67±3.26	67.91±3.27	59.34±2.78
FGDN	SC	63.42±4.79	64.02±3.49	65.89±5.15	68.91±2.53
BrainGNN	FC	66.41±6.44	69.18±3.39	73.46±4.33	69.55±3.23
BrainGNN	SC	67.37±5.89	70.73±2.07	73.66±3.60	69.51±2.58
SVM	SC,FC	74.49±2.97	63.21±2.09	71.73±1.99	66.06±1.56
Random Forest	SC,FC	68.24±2.94	61.45±2.80	62.78±1.63	62.43±2.19
MGCN	SC,FC	67.94±5.41	75.18±2.34	82.24±3.71	72.98±2.17
GBDM	SC,FC	71.02±4.39	74.81±2.44	80.71±2.83	72.48±1.91
MMGNN	SC,FC	73.33±2.82	60.69±3.61	68.21±4.44	59.72±3.18
AL-NEGAT	SC,FC	75.12±3.66	73.95±3.45	75.75±3.81	71.86±2.49
RH-BrainFS (ours)	SC,FC	78.63±4.36	80.64±1.58	90.27±2.00	78.48±1.43
Results. As shown in Tab. 1, our model significantly outperforms the other comparison methods on the all selected datasets. The results show that multimodal methods generally have better performance than unimodal methods because they capture more complementary information. Among the multimodal methods, our RH-BrainFS method achieves the best performance on the all the selected datasets (improvement of  $3.51\%$  on HCP,  $5.46\%$  on Zhongda hospital dataset,  $8.03\%$  on Xinxiang hospital dataset and  $5.50\%$  on two-site dataset). The reason for the performance improvement is that our RH-BrainFS method fully considers the issue of regional heterogeneity between SC and FC and proposes an appropriate solution strategy for this issue.
Figure 4: t-SNE visualisation of multimodal method on HCP dataset. Each dot denotes a test sample.
Visualization. In order to intuitively display the performance of each multimodal method, we conduct visualization experiments on the HCP dataset. Specifically, we take the graph-level embedding output from the last layer of each multimodal method for t-SNE visualisation. As shown in Fig. 4, although the MGCN and GBDM all form two clusters, these two clusters do not distinguish the two types of samples well and there is still a lot of confusion. The MMGNN is loosely distributed and does not form good class boundary. It can be seen that the Al-NEGAT produces a similar distribution to our method, but there's still a lot of confusion at the class boundary. In contrast, our method eliminates the confusion at the class boundary, achieves a good classification effect, most of the samples can be accurately distinguished and only a small number of samples have errors.
In this section, we further perform ablation studies on the main modules and hyperparameters in the proposed RH-BrainFS method.
3Full results of hyperparameter experiments refer to Appendix B.
Table 2: Ablation study of the main modules in the RH-BrainFS method. The bold font indicates that the evaluation metric achieves the best performance in the ablation study.
Modules	ACC	SEN	SPE	F1	AUC
w/o BrainSubGNN Trans-Bottleneck	76.23±3.78	71.40±11.94	80.36±7.70	73.00±6.27	75.88±4.12
w/o BrainSubGNN	77.22±3.89	68.44±12.16	82.86±8.61	72.16±6.34	75.65±4.19
w/o Trans-Bottleneck	76.80±2.93	71.14±10.50	81.61±7.10	73.50±5.13	76.38±3.27
RH-BrainFS (ours)	78.63±4.36	75.59±6.75	81.25±6.04	76.49±4.91	78.42±4.38
(a)
Figure 5: The effect of varying hyperparameters. (a) and (c) are experiments on HCP datasets, (b) and (d) are experiments on Two-site datasets.
Effectiveness of Main Modules. First, we perform an ablation study on HCP dataset to validate effectiveness of the main modules, BrainSubGNN and Trans-Bottleneck. Specifically, we replace BrainSubGNN with normal GIN [52] (process on the whole brain network), and replace Trans-Bottleneck with a standard transformer (compute self-attention directly between two modalities, equal to direct interaction), respectively. As shown in Tab. 2, we can find that both BrainSubGNN and Trans-Bottleneck have a certain effect on the performance of the model (compare the first three rows in the table). Furthermore, we find that the two modules are compatible and complementary, as our RH-BrainFS method (combining the two modules) achieves the best performance among the ablation study.
Impact of Bottlenecks Number. We then investigate the impact of varying bottlenecks number. Specifically, we run experiments with # bottlenecks=2,4,6,8, respectively, with all other parameters unchanged. In order to ensure the credibility of the experiment, we perform experiments on two datasets (HCP dataset and Two-site dataset). As shown in Fig. 5, on both datasets, the performance of any number of bottlenecks exceeds the baselines. The main reason for this results is that the Trans-Bottleneck module takes into account the regional heterogeneity issue between SC and FC, and avoids the direct interaction of heterogeneous information, thus achieving good fusion performance. Such results demonstrate the importance of the regional heterogeneity issue in the modality fusion process of SC and FC. At the same time, we find that when # bottlenecks=4, the model performance reaches the best, which reflects that only a small number of bottlenecks is needed to achieve a good multi-modal fusion expression capability.
Impact of Subgraph Sampling Hops. Next, we investigate the impact of varying sampling hops of subgraph. In this experiment, we set the range of sampling hops of subgraph from 1 to 5. Likewise, we run experiments on HCP dataset and Two-site dataset. As shown in Fig. 5, it can clearly be seen that as the number of sampling hops increases, the performance of the model generally shows a downward trend, and when the sampling hops are too large, the model actually performs worse than the baselines. The reason for this results is that the brain network itself has strong regional characteristics, and too large sampling hops will cause the sampled subgraph to lose the local characteristics of the brain network and tend towards global characteristics.
Figure 6: The effect of varying thresholding values.
The results show that only 1 hop of subgraph sampling is needed to express the local characteristics of the brain network well.
Impact of Thresholding Values. Finally, in this paper, thresholding is used to obtain the adjacency matrix of the two modalities during data processing (thresholding  $X_{sc}$  and  $X_{fc}$  to obtain  $A_{sc}$  and  $A_{fc}$ , respectively). Thresholding value has been an important ablation study in neuroscience, and the same experiment was conducted in this paper. As shown in Fig. 6, we set the value range of thresholding to [0.02, 0.30], with 0.02 as a step, for a total of 15 thresholding experiments. From the experimental results, there is no clear trend between threshold values and model performance, but the model performs poorly when the threshold value is too high or too low, so in this paper we chose a threshold value of 0.12 as this is when the model performs best.
Conclusion. In this paper, we introduce a brain subgraph networks and a transformer-based fusion bottleneck to alleviate the issue of regional heterogeneity between SC and FC, and propose a novel multimodal brain networks fusion strategy (RH-BrainFS). To the best of our knowledge, this is the first paper to explicitly state the issue of structural-functional modal regional heterogeneity and to propose a solution. We validate our method on a variety of downstream task datasets, achieving state-of-the-art performance.
Limitations and Future Work. Due to the scarcity and difficulty of collecting and processing data in neuroscience, the only datasets currently available are very limited, despite the fact that we have spent a great deal of manual effort in this area, and thus the research in this paper suffers from a number of possible data bias issues. In our future work, on the one hand, we will do more work on data to mitigate the problem of data bias. On the other hand, although this paper proposes the use of indirect rather than direct interaction, the two may not be mutually exclusive, and in the future we will investigate how to combine the two to achieve better research results.
Ethical Issues. With regard to possible ethical issues in data collection, the Human Connectome Project (HCP) dataset, as a publicly available dataset that has been used in numerous previous studies, is undoubtedly not ethically questionable. It is true that the hospital dataset is held in collaboration with our partner hospitals and is not yet publicly available, but the data is collected with the consent of the subjects who are clearly informed of the purpose of the sample collection, and all identifying information about the sample is hidden in the hospital dataset. Therefore, it does not adversely affect any individual, so there are no ethical or moral issues.
Possible Negative Social Impacts. As the research in this paper deals with the diagnosis of depression, it is necessary to elaborate here on the possible negative social impacts of this work, despite the fact that all the current work is at the stage of scientific research and has not been put to practical use. Including but not limited to:
- Incorrect diagnosis. AI methods must have the possibility of error, which cannot be avoided, but an incorrect diagnosis will have a significant impact on individuals and society. Therefore, AI tools can only be used as a diagnostic aid, not as a decision maker, and the final decision should still be made by the doctor.
- Leakage of privacy information. In depression dataset, the identity information of the subjects is highly private, and the leakage of identity information will also have unpredictable and significant impact on individuals and society. Therefore, in this work, we have completely hidden the subjects' identifying information (which is also not visible to the staff in the study group) as a way of preventing the leakage of private information.
This work is supported by 2022YFE0116700 National Key Research and Development Program of China, supported by 82271570, 31800825 and 31640028 National Natural Science Foundation of China, and also supported by the Big Data Computing Center of Southeast University. This work is partly supported by grant 2242023k30052 Central University Basic Research Fund of China. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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Appendix A: Full Results of Comparison Experiments
Due to the layout of the text and page limitations, only the experimental results for the ACC metric are presented in the main text. However, to ensure a comprehensive presentation of the results, the full results of the comparison experiments involving all four datasets, HCP, Zhongda Hospital, Xinxiang Hospital and Two-site, are presented in Tables 1 to 4. Four tables are presented detailing the mean and standard deviation values for each evaluation metric. The most exceptional results are shown in bold, while results below the optimal threshold are underlined for clarity and emphasis.
Analysis. Based on the results from the four tables, our RH-BrainFS method achieved excellent results in all four datasets. Specifically, we achieved the best results on three metrics in the HCP dataset, four metrics in both the Zhongda and Xinxiang Hospital datasets, and an impressive five metrics in the Two-site dataset. This demonstrates the strong performance of RH-BrainFS in effectively completing the fusion classification task for multimodal brain networks. Furthermore, we observe that on the hospital dataset, our RH-BrainFS method significantly outperforms most other methods in terms of bias in each metric, indicating higher stability. This improved stability contributes to the reliability and robustness of RH-BrainFS in fusion classification tasks.
Table 3: Comparison experiments results on the HCP dataset.
Method	Modality	HCP Dataset
ACC	SEN	SPE	F1	AUC
FGDN	FC	67.56±3.02	52.37±12.55	80.54±8.24	59.09±6.98	66.45±3.49
FGDN	SC	63.42±4.79	53.98±20.69	71.43±13.72	55.12±14.65	62.71±5.57
BrainGNN	FC	66.41±6.44	68.92±6.92	63.66±12.30	65.41±5.15	66.29±6.04
BrainGNN	SC	67.37±5.89	68.39±6.07	66.17±8.50	65.88±4.45	67.28±5.80
SVM	SC,FC	74.49±2.97	71.18±4.95	77.32±3.30	71.96±3.49	74.25±3.05
Random Forest	SC,FC	68.24±2.94	54.88±5.78	79.64±4.16	61.31±4.44	67.26±3.04
MGCN	SC,FC	67.94±5.41	74.53±8.20	62.32±7.76	68.10±5.59	68.42±5.41
GBDM	SC,FC	71.02±4.39	61.95±12.37	79.18±8.58	65.76±6.35	70.56±4.32
MMGNN	SC,FC	73.33±2.82	71.17±4.52	75.17±5.67	71.10±2.88	73.17±2.72
AL-NEGAT	SC,FC	75.12±3.66	72.86±7.74	84.46±5.05	76.13±4.70	78.66±3.81
RH-BrainFS (ours)	SC,FC	78.63±4.36	75.59±6.75	81.25±6.04	76.49±4.91	78.42±4.38
Table 4: Comparison experiments results on the Zhongda hospital dataset.
Method	Modality	Zhongda Dataset
ACC	SEN	SPE	F1	AUC
FGDN	FC	65.67±3.26	78.31±8.26	49.25±12.11	70.10±4.21	63.78±3.86
FGDN	SC	64.02±3.49	65.67±14.37	61.50±16.65	60.67±8.24	63.58±3.56
BrainGNN	FC	69.18±3.39	73.10±5.23	64.05±5.00	72.05±3.61	68.57±3.46
BrainGNN	SC	70.73±2.07	75.93±3.93	64.10±3.58	73.81±2.33	70.01±2.04
SVM	SC,FC	63.21±2.09	74.17±2.06	49.00±3.22	68.87±2.07	61.58±2.20
Random Forest	SC,FC	61.45±2.80	86.69±2.78	29.00±4.28	71.53±2.17	57.85±2.96
MGCN	SC,FC	75.18±2.34	88.52±3.99	57.10±8.06	80.15±1.91	72.81±2.96
GBDM	SC,FC	74.81±2.44	81.77±5.21	58.14±8.37	74.92±3.20	69.96±3.11
MMGNN	SC,FC	60.69±3.61	70.35±9.19	47.90±9.32	64.45±6.48	59.12±3.50
AL-NEGAT	SC,FC	73.95±3.45	90.71±7.24	52.05±7.69	79.00±4.79	71.38±3.54
RH-BrainFS (ours)	SC,FC	80.64±1.58	90.05±5.58	68.45±9.32	83.96±1.13	79.25±2.24
Table 5: Comparison experiments results on the Xinxiang hospital dataset.
Method	Modality	Xinxiang Dataset
ACC	SEN	SPE	F1	AUC
FGDN	FC	67.91±3.27	43.58±8.18	84.50±8.30	42.03±6.59	64.04±2.88
FGDN	SC	65.89±5.15	61.83±14.81	68.85±15.06	53.03±8.16	65.34±3.82
BrainGNN	FC	73.46±4.33	54.92±10.57	86.25±6.10	55.72±9.30	70.58±4.88
BrainGNN	SC	73.66±3.60	56.83±10.76	85.35±8.26	57.39±8.58	71.09±3.76
SVM	SC,FC	71.73±1.99	49.92±4.35	86.55±3.42	54.52±4.72	68.23±2.19
Random Forest	SC,FC	62.78±1.63	12.08±4.81	97.20±1.96	17.03±6.61	54.64±2.11
MGCN	SC,FC	82.24±3.71	74.16±6.62	87.45±3.45	76.15±5.88	80.80±4.15
GBDM	SC,FC	80.71±2.83	60.20±10.03	88.43±5.86	63.46±9.11	73.31±5.83
MMGNN	SC,FC	68.21±4.44	57.33±6.35	75.10±8.12	55.48±6.03	66.21±4.06
AL-NEGAT	SC,FC	75.75±3.81	56.42±14.80	88.50±6.35	61.19±10.80	72.46±5.34
RH-BrainFS (ours)	SC,FC	90.27±2.00	80.75±5.86	96.65±2.34	85.43±3.90	88.70±2.48
Table 6: Comparison experiments results on the Two-site dataset.
Method	Modality	Two-site Dataset
ACC	SEN	SPE	F1	AUC
FGDN	FC	59.34±2.78	54.70±10.82	63.79±8.83	49.96±8.04	59.24±2.85
FGDN	SC	68.91±2.53	70.02±12.42	67.83±9.78	66.31±7.03	68.93±2.52
BrainGNN	FC	69.55±3.23	69.62±5.23	68.36±6.67	67.54±3.34	68.99±3.22
BrainGNN	SC	69.51±2.58	68.12±5.41	69.24±6.66	66.76±3.42	68.68±3.03
SVM	SC,FC	66.06±1.56	58.01±2.49	74.04±1.77	62.03±2.27	66.03±1.56
Random Forest	SC,FC	62.43±2.19	56.17±2.87	68.60±3.48	59.04±2.73	62.38±2.20
MGCN	SC,FC	72.98±2.17	74.02±7.03	73.74±4.05	72.45±4.48	73.88±2.22
GBDM	SC,FC	72.48±1.91	71.53±7.55	65.97±5.61	68.74±4.92	68.75±2.90
MMGNN	SC,FC	59.72±3.18	65.10±4.83	54.42±4.42	59.96±4.02	59.76±3.15
AL-NEGAT	SC,FC	71.86±2.49	75.26±3.62	68.12±6.19	72.16±2.24	71.69±2.56
RH-BrainFS (ours)	SC,FC	78.48±1.43	76.20±4.06	80.72±3.60	77.35±1.97	78.46±1.43
Appendix B: Full Results of Hyperparameter Experiments
In the main text, our hyperparameter experiments are performed on the HCP dataset and the Two-site dataset. We explore two key hyperparameters in RH-BrainFS: the number of bottlenecks and the number of subgraph sampling hops  $k$ . However, in the main text we have only presented visualisations of the results of the hyperparameter experiments without giving specific numerical values. Hence, we present here the complete experimental results in Tables 5 to 8.
Table 7: Hyperparameter experiments of varying bottlenecks number on HCP dataset.
# bottlenecks	HCP Dataset
ACC	SEN	SPE	F1	AUC
2	76.26±3.58	69.70±11.51	80.00±5.46	71.74±6.13	74.85±4.06
4	78.63±4.36	75.59±6.75	81.25±6.04	76.49±4.91	78.42±4.38
6	76.85±3.41	69.72±8.32	80.54±7.38	72.29±4.26	75.13±3.46
8	76.51±3.05	71.16±9.82	81.25±8.11	73.45±4.42	76.20±3.18
Table 8: Hyperparameter experiments of varying bottlenecks number on Two-site dataset.
# bottlenecks	Two-site Dataset
ACC	SEN	SPE	F1	AUC
2	76.21±1.17	68.88±4.98	83.61±4.56	73.21±2.33	76.24±1.15
4	78.48±1.43	76.20±4.06	80.72±3.60	77.35±1.97	78.46±1.43
6	76.35±1.43	70.39±3.82	82.10±4.18	73.80±2.06	76.24±1.48
8	76.71±1.32	73.68±5.34	79.71±4.83	74.97±2.28	76.69±1.31
Table 9: Hyperparameter experiments of varying subgraph sampling hops on HCP dataset.
k	HCP Dataset
ACC	SEN	SPE	F1	AUC
1	78.63±4.36	75.59±6.75	81.25±6.04	76.49±4.91	78.42±4.38
2	77.09±3.53	71.35±12.30	81.96±9.40	73.72±5.73	76.66±3.81
3	77.47±3.31	74.73±6.83	79.82±5.36	75.27±4.00	77.28±3.39
4	76.61±4.00	69.07±11.44	83.04±4.01	72.63±6.79	76.05±4.50
5	73.92±2.94	64.50±6.03	81.96±6.41	69.44±3.56	73.23±2.88
Table 10: Hyperparameter experiments of varying subgraph sampling hops on Two-site dataset.
k	Two-site Dataset
ACC	SEN	SPE	F1	AUC
1	78.48±1.43	76.20±4.06	80.72±3.60	77.35±1.97	78.46±1.43
2	73.99±1.32	69.49±2.88	78.42±3.04	71.53±2.04	73.96±1.32
3	74.37±1.81	72.47±5.79	76.26±3.42	72.66±3.37	74.36±1.79
4	74.55±1.64	73.13±6.88	75.92±6.98	72.96±2.68	74.53±1.63
5	74.14±1.25	70.41±5.73	77.79±4.62	71.70±3.15	74.10±1.28