Paper: URRL-IMVC: Unified and Robust Representation Learning for Incomplete Multi-View Clustering (ICLR-2024)

Reviewer comment (Novelty):
The biggest problem of this paper is the limited novelty in formulation of URRL-IMVC，which learns a unified embedding that captures the comprehensive representation. The differences between URRL-IMVC and the closely related works can be analyzed from different aspects.

Author response:
The key contribution of our paper lies in the novel approach of directly learning a unified and robust representation for the IMVC task.

**Unified**: In the DIMVC field, the prevailing framework is cross-view contrastive learning [2] [3] [4] [5]. However, this design primarily emphasizes the consensus information in multi-view data while neglecting the valuable complementary information. Therefore, our approach goes beyond the cross-view contrastive framework and instead learns a unified representation using a meticulously designed attention-based network that effectively leverages complementary information.

**Robust**: The primary approach for handling missing views in the DIMVC field is to first recover the missing views and then perform complete multi-view clustering [1] [2] [3] [4] [5]. However, the recovered views may be unreliable, and computational resources are wasted on repeatedly mapping between data and latent space [1]. To address this issue, we propose directly learning a latent embedding that is robust to view missing, without explicitly recovering the missing data. We have devised data augmentation and KNN imputation as preprocessing techniques, which, along with the unified representation learning framework, facilitate efficient and robust representation learning.

Overall, our paper introduces a novel approach that directly learns a unified and robust representation for the IMVC task, surpassing the limitations posed by existing approaches in the field.

Reviewer comment (Reproducibility):
The strategies including KNN imputation and data augmentation should be stated in details. Then the process of directly learning a robust representation capable of handling view-missing conditions without explicit missing view recovery is easily understood by the readers.

Author response:
A detailed description and formulation of the KNN imputation strategy is provided in Appendix B.5 and the data augmentation strategy in Appendix B.6. Given the length limitation of the conference paper (9 pages), we have to include most of the detailed formulations in the Appendix to ensure the paper's completeness. Additionally, in this revised version, we have added Algorithm 1 to describe the KNN imputation strategy, which we hope will facilitate easier interpretation. Regarding data augmentation, we believe that the formulation in equations 19 and 20 already provides sufficient detail.

Reviewer comment (Theory):
This paper asserts that cross-view contrastive learning may overlook complementary information, and contrasting the unified embedding has the potential to capture a more comprehensive representation. However, there is a lack of both theoretical and experimental evidence to support these claims from either perspective.

Author response:
The limitations of cross-view contrastive learning are intuitive and have been previously studied in existing literature. It is intuitive to understand that if the contrastive learning objective is achieved, the resulting embeddings from each view would be almost identical, thereby disregarding any view-specific or complementary information. Furthermore, a theoretical analysis conducted by [1] emphasizes that cross-view contrastive alignment can actually reduce the number of distinct clusters in the representation space, and this effect becomes more pronounced with an increasing number of views. Additionally, [2] mentions the inherent conflict between the reconstruction target and the cross-view contrastive target, as the former aims to preserve view-specific information while the latter attempts to ignore it.

In contrast, our unified design overcomed this drawback by learning unified representations. Although currently lacking theoretical evidence due to the black box nature of the unified embedding. However, we have made two experimental observations that provide circumstantial evidence of the preservation and utilization of both consensus and complementary information. Firstly, we noticed in our experiments that our approach outperforms cross-view contrastive learning-based methods on datasets that possess more complementary information. For instance, on the 100Leaves dataset where the two views represent the shape and texture of a leaf, our approach exhibits greater advantages. Secondly, we observed that the clustering performance of cross-view contrastive learning-based approaches declines when additional views are added, as theoretically analyzed in [1]. In contrast, our approach consistently benefits from the inclusion of more views in the dataset, thereby overcoming this drawback. The results of the second experiment have been included in the revised version of the paper as Table 7 in Appendix C.3.

The results from Table 7 are as follows:
| Views | CPSPAN Acc(\%)               | CPSPAN NMI(\%)               | CPSPAN ARI(\%)               | URRL-IMVC (ours) Acc(\%)     | URRL-IMVC (ours) NMI(\%)     | URRL-IMVC (ours) ARI(\%)     |
| ------- | ------------------------------ | ------------------------------ | ------------------------------ | ------------------------------ | ------------------------------ | ------------------------------ |
| 2     | 50.88 $\pm$ 1.87              | 45.27 $\pm$ 2.50              | 35.79 $\pm$ 2.25              | 58.36 $\pm$ 3.01              | 47.16 $\pm$ 2.50              | 39.40 $\pm$ 2.71              |
| 3     | 73.17 $\pm$ 4.27              | 61.40 $\pm$ 4.29              | 55.37 $\pm$ 5.46              | 77.60 $\pm$ 0.88              | 67.61 $\pm$ 0.98              | 63.97 $\pm$ 1.33              |
| 4     | **84.89 $\pm$ 2.15**         | **75.37 $\pm$ 2.45**         | **71.79 $\pm$ 3.26**         | $\underline{91.73 \pm 0.47}$ | $\underline{83.57 \pm 0.68}$ | $\underline{83.26 \pm 0.76}$ |
| 5     | $\underline{77.62 \pm 4.74}$ | $\underline{69.70 \pm 4.04}$ | $\underline{63.23 \pm 5.51}$ | **92.95 $\pm$ 2.60**         | **86.29 $\pm$ 1.76**         | **86.02 $\pm$ 2.91**         |

Reviewer comment (Novelty):
The related work Section appears to be somewhat concise. Some recent works should be discussed.

Author response:
We acknowledge the importance of discussing recent works in our field. However, due to the length limitation of the paper, we had to move a portion of the related works section to Appendix A.1. This part provides an introduction to recent IMVC works that do not utilize deep neural networks. Additionally, in this revised version, we have included several more recent works in Appendix A.1 to ensure that we cover a broader range of relevant literature.

Reviewer comment (Experiments):
No evidence for the analysis on the computation cost and unreliability of explicit missing view recovery.

Author response:
Regarding the concern, we have added an ablation study in Table 12 to provide experimental evidence supporting our point of view. In this study, we adopted a similar framework to RecFormer [1] and constructed two identical networks. The first network was used to recover the missing views, while the second network was employed to cluster the recovered complete multi-view data. We achieved comparable results with this framework, which suggests that our robustness learning can effectively replace the role of a missing view recovery network while enjoying lower computational costs.

Furthermore, our experiments have shown that without the robustness objective, the performance of this framework can deteriorate. This observation suggests that missing views recovered with simple strategies may indeed be unreliable. We believe that these findings strengthen our argument and provide empirical support for the analysis of the computation cost and unreliability of explicit missing view recovery.

The results of Table 12 are as follows, in which RL represents Robustness Learning:
| Network 1 | Network 2 | Acc(\%)                      | NMI(\%)                      | ARI(\%)                      |
| ----------- | ----------- | ------------------------------ | ------------------------------ | ------------------------------ |
| -         | with RL   | **92.95 $\pm$ 2.60**         | **86.29 $\pm$ 1.76**         | **86.02 $\pm$ 2.91**         |
| with RL   | with RL   | $\underline{92.93 \pm 2.64}$ | $\underline{85.93 \pm 1.74}$ | $\underline{84.98 \pm 2.84}$ |
| with RL   | w/o RL    | 89.65 $\pm$ 4.65              | 83.34 $\pm$ 3.66              | 81.72 $\pm$ 5.38              |
| w/o RL    | w/o RL    | 87.23 $\pm$ 12.06             | 82.28 $\pm$ 6.62              | 79.96 $\pm$ 11.12             |

Reviewer comment (Presentation):
The writing of the methodology is not compact and unclear: Some related contents are far away from each other, for example, Eq. (5) and its details.

Author response:
Given the paper length limitation of this conference, we had to move some of the detailed formulations and ablation studies to the Appendix. This may have caused difficulty in finding relevant equations or contents. In this revision, we have made efforts to address this concern by adding more cross-references and highlighting relevant content or formulations. We hope this will make it easier for readers to locate the information they need.

Regarding the calculation of the KL divergence in Equation 23, it may appear abstract and difficult to follow due to a lack of reference to the Clustering Module section (Appendix B.4). We have included cross-references to help readers follow the calculation. 
We appreciate your valuable advice for improving this paper.

Reviewer comment (Theory):
Some essential details are missing, for example, the calculation of KL divergence in Eq. (23) is too abstract to follow.

Author response:
Given the paper length limitation of this conference, we had to move some of the detailed formulations and ablation studies to the Appendix. This may have caused difficulty in finding relevant equations or contents. In this revision, we have made efforts to address this concern by adding more cross-references and highlighting relevant content or formulations. We hope this will make it easier for readers to locate the information they need.

Regarding the calculation of the KL divergence in Equation 23, it may appear abstract and difficult to follow due to a lack of reference to the Clustering Module section (Appendix B.4). We have included cross-references to help readers follow the calculation. 
We appreciate your valuable advice for improving this paper.

Reviewer comment (Presentation):
Most of the formulations are postponed to the appendix, making the main text hard to be understood and undermining the clarity.

Author response:
Given the paper length limitation of this conference, we had to move some of the detailed formulations and ablation studies to the Appendix. This may have caused difficulty in finding relevant equations or contents. In this revision, we have made efforts to address this concern by adding more cross-references and highlighting relevant content or formulations. We hope this will make it easier for readers to locate the information they need.

Regarding the calculation of the KL divergence in Equation 23, it may appear abstract and difficult to follow due to a lack of reference to the Clustering Module section (Appendix B.4). We have included cross-references to help readers follow the calculation. 
We appreciate your valuable advice for improving this paper.

Reviewer comment (Theory):
No solid theoretical guarantee is provided for the proposed method.

Author response:
We appreciate the reviewer's suggestion and acknowledge the importance of theoretical analysis about extracting or balancing consensus and complementary information in multi-view representation learning. Although we have some promising ideas, we have left them for future works due to the already extensive length and complexity of the paper.

Reviewer comment (Writing):
What is the first output of NDE module in the output choice of the proposed NDE?

Author response:
A1: In the Transformer Encoder, which is a sequence-to-sequence model, a sequence of vectors is provided as input and a corresponding sequence of vectors is generated as output. So the "first output" of the NDE module refers to the initial vector in the output vector sequence. It has a bias on the first vector in the input sequence, which is always the most reliable sample in KNN. To provide a more intuitive explanation of the output choice in the NDE and VDE, we have added Figure 5 in the revised manuscript. Additionally, we have updated equations 7 and 14 to incorporate the output choice procedure in the formulation.

Reviewer comment (Reproducibility):
How does the Siamese Encoder work in Figure 2? Do you mean the architectures of the upper and lower parts are identical with shared parameters?

Author response:
A2: Yes, the Siamese Encoder in Figure 2 utilizes identical architectures with shared weights for both the upper and lower parts. This design allows for the extraction of unified representations for both augmented and unaugmented input data. By further incorporating a robustness loss, the Encoder is trained to extract robust representations in the presence of augmentation, and also in the presence of real missing conditions.

Reviewer comment (Experiments):
How to determine the level of noise added to the original incomplete multi-view data?

Author response:
A3: In our approach, we employ three types of noise for data augmentation: (1) view dropout, (2) Gaussian noise, and (3) random dropout. For Gaussian noise and random dropout, we conducted a preliminary grid search to determine the optimal noise level. Since the input is normalized, we found that a fixed noise level of 0.05 yields good results for various datasets.
Regarding view dropout, we conducted an ablation study (Table 14) to determine the best noise level based on different missing rates. We designed Equation 25, which maps the missing rate to the desired noise level. This allows us to dynamically adjust the noise level depending on the missing rate of data.

The results from Table 14 are as follows:
| Parameter    | $\phi_1 = 0$    | $\phi_1 = 0.15$              | $\phi_1 = 0.3$               | $\phi_1 = 0.45$      | $\phi_1 = 0.6$               | Equation 25   |
| -------------- | ----------------- | ------------------------------ | ------------------------------ | ---------------------- | ------------------------------ | --------------- |
| $m_r$ = 0.00 | 89.30 $\pm$ 1.86 | $\underline{89.50 \pm 1.77}$ | 88.91 $\pm$ 1.89              | **89.71 $\pm$ 1.19** | 86.94 $\pm$ 2.12              | $\phi_1=0.15$ |
| $m_r$ = 0.25 | 86.15 $\pm$ 2.42 | $\underline{88.12 \pm$ 1.90}$ | **88.56 $\pm$ 1.55**         | 86.51 $\pm$ 3.33      | 83.57 $\pm$ 4.74              | $\phi_1=0.17$ |
| $m_r$ = 0.50 | 83.35 $\pm$ 1.94 | **86.12 $\pm$ 1.57**         | $\underline{85.61 \pm$ 2.08}$ | 83.25 $\pm$ 3.86      | 82.25 $\pm$ 4.82              | $\phi_1=0.23$ |
| $m_r$ = 0.75 | 81.41 $\pm$ 2.79 | $\underline{81.78 \pm$ 3.86}$ | **82.89 $\pm$ 4.51**         | 80.82 $\pm$ 3.58      | 77.17 $\pm$ 5.63              | $\phi_1=0.32$ |
| $m_r$ = 1.00 | 76.31 $\pm$ 3.00 | 77.53 $\pm$ 3.63              | 77.02 $\pm$ 3.91              | **80.21 $\pm$ 2.94** | $\underline{79.19 \pm$ 3.67}$ | $\phi_1=0.46$ |

Reviewer comment (Writing):
Do you consider the private information in each view? In addition to the consensus information, the complementary information is also essential, which has been indicated in this paper. However, I cannot understand what is the mechanism used to leverage the view-specific information in the proposed method. Please clarify this in details.

Author response:
A4: Our proposed method incorporates the preservation of complementary information by training an auto-encoder to reconstruct the input from the unified embedding. This design ensures that the unified embedding have to capture complete information from each view, in order to correctly reconstruction of the multi-view input. Consequently, both consensus and complementary information are retained within the unified embedding. Furthermore, since the unified embedding is directly used for clustering, both types of information are effectively leveraged in our approach.

For a more detailed discussion and evidence regarding the preservation of complementary information, we kindly refer you to our response R1 to Reviewer LBwN, where we provide additional insights and supporting evidence.

Reviewer comment (Experiments):
The experiments are not sufficient. Firstly, there are no experiments on large-scale datasets. Secondly, the authors only evaluate the method on the image datasets, where all views are extracted from the image.

Author response:
We would like to address the concerns regarding the experiments. 

Firstly, we would like to note that the largest datasets we used in our experiments are Reuters (18,758 samples) and ALOI_Deep (10,800 samples), which are roughly at the same scale as prior works such as RecFormer [1] (10,800 samples), SURE [2] (30,000 samples), and DSIMVC [3] (6,773 samples). We acknowledge that experiments on larger-scale datasets are important and we plan to explore them in future work due to limited time.

Secondly, we acknowledge the limitation of only evaluating our method on image datasets where all views are extracted from the image. To address this concern, we have made revisions to our manuscript. In this revision, we have included two textual datasets for comparison. The statistics of these datasets are summarized in Table 4, and the results of our approach with textual features are recorded in Table 5 in Appendix C.3. BDGP is a multi-modal dataset with 1,750-dimensional visual features and 79-dimensional textual features as two views, while Reuters is a multilingual dataset where English and French are used as two views. The results achieved by our approach with textual features demonstrate its competitive effectiveness in different modalities. The main results of Table 5 are as follows:


| Dataset\Metrics   | BDGP Acc(\%)                 | BDGP NMI(\%)                 | BDGP ARI(\%)                 | Reuters Acc(\%)              | Reuters NMI(\%)              | Reuters ARI(\%)              |
| ------------------ | ------------------------------ | ------------------------------ | ------------------------------ | ------------------------------ | ------------------------------ | ------------------------------ |
| Completer        | 58.37 $\pm$ 4.87 | 48.52 $\pm$ 4.34 | 25.13 $\pm$ 6.71 | 40.30 $\pm$ 7.32 | 22.86 $\pm$ 6.44 | 10.53 $\pm$ 8.25 |
| DSIMVC           | **95.71 $\pm$ 0.21**         | **87.08 $\pm$ 0.54**         | **89.62 $\pm$ 0.51**         | 48.39 $\pm$ 2.92 | **31.88 $\pm$ 2.27**         | **26.04 $\pm$ 2.27**         |
| SURE             | 63.27 $\pm$ 7.55 | 41.35 $\pm$ 7.70 | 36.51 $\pm$ 8.87 | $\underline{48.63 \pm 3.56}$ | 27.73 $\pm$ 2.46 | 22.46 $\pm$ 1.59 |
| DCP              | 55.82 $\pm$ 7.02 | 44.56 $\pm$ 8.92 | 20.08 $\pm$ 11.71 | 39.02 $\pm$ 3.16 | 22.47 $\pm$ 4.19 | 6.92 $\pm$ 3.34$              |
| CPSPAN           | 81.40 $\pm$ 8.64 | 66.19 $\pm$ 6.61 | 64.71 $\pm$ 9.89 | 39.35 $\pm$ 2.13 | 14.47 $\pm$ 2.01 | 12.37 $\pm$ 1.79 |
| RecFormer        | 49.76 $\pm$ 3.49 | 38.62 $\pm$ 3.30 | 19.01 $\pm$ 2.68 | 39.70 $\pm$ 5.14 | 17.27 $\pm$ 2.83 | 14.82 $\pm$ 3.19 |
| URRL-IMVC (ours) | $\underline{92.52 \pm 5.71}$ | $\underline{82.29 \pm 5.66}$ | $\underline{84.26 \pm 7.57}$ | **49.91 $\pm$ 2.44** | $\underline{29.49 \pm 1.38}$ | $\underline{25.71 \pm 2.08}$ |

Reviewer comment (Evaluation):
Efficiency and computational complexity are also the very important metric to evaluate the method. However, these are ignored.

Author response:
Thank you for bringing this to our attention. We have now included an analysis of model parameters and computational costs (Multiply-Adds, MACs) in Table 8 of Appendix C.3. The results demonstrate that our model surpasses other state-of-the-art DIMVC methods in terms of both model size and computational cost. It is worth mentioning that our network hyperparameters, such as the dimensions of the feed-forward networks, were roughly chosen similarly to prior DIMVC methods, and we maintained the same configuration (except for the input layers) across all datasets. However, we acknowledge that there is still room for improvement in carefully designing the network architecture tailored to different datasets. The main results of Table 8 are as follows:


| Approach         | MACs (M)           | Parameters (M)     |
| ------------------ | -------------------- | -------------------- |
| Completer        | 8.98               | 6.82               |
| DSIMVC           | 9.89               | 9.33               |
| SURE             | 8.24               | 8.24               |
| DCP              | 9.02               | 9.01               |
| CPSPAN           | $\underline{4.92}$ | $\underline{4.93}$ |
| RecFormer        | 12.08              | 6.09               |
| URRL-IMVC (ours) | **1.54**           | **1.01**           |

Reviewer comment (Novelty):
The novelty of the method seems not strong but the method seems very complex. Imputation the missing views for incomplete multi-view clustering is not new and has many related works. For example, the work ‘Deep safe incomplete multi-view clustering: Theorem and algorithm’ also exploits the KNN imputation for missing views. The method used Augmentation and KNN imputation to fill the missing views. However, the authors do not visualize the imputed missing views. This is not reasonable. In many existing works, such as ‘Dual contrastive prediction for incomplete multi-view representation learning’, the imputed missing views can be visualized to make the approach look more credible. However, just using ablation experiments is not convincing enough.

Author response:
We appreciate the reviewer's comments and we would like to clarify certain points. Although KNN Imputation is widely used in prior IMVC approaches, its utilization in our framework and the way to further process the imputation is different. 

In contrast to previous approaches like DSIMVC [3] and CPSPAN [4], where KNN Imputation is used as a missing view recovery strategy in the latent space, our framework is recovery-free, as mentioned in the paper (page 3, contribution 2). KNN Imputation serves as a preprocessing strategy in the data space, providing hints for learning a robust representation. **While the KNN Imputation algorithm itself is not novel, its utilization in our framework is different**.

Additionally, unlike prior works that use naive strategies to fuse searched KNNs, we retain the noisy raw KNN data and fuse it with well-designed attention-based Encoders (Neighbor Dimensional Encoder, NDE). **This approach is distinctive and explains why we did not visualize the imputed missing views, as they are raw data from the dataset**.

**Finally, KNN Imputation is just a component of our novel framework**, which directly learns a unified and robust representation for the IMVC task, surpassing the limitations posed by existing approaches in the field.

**Unified**: In the DIMVC field, the prevailing framework is cross-view contrastive learning. However, this design primarily emphasizes the consensus information in multi-view data while neglecting the valuable complementary information. Therefore, our approach goes beyond the cross-view contrastive framework and instead learns a unified representation using a meticulously designed attention-based network that effectively leverages complementary information.

**Robust**: The primary approach for handling missing views in the DIMVC field is to first recover the missing views and then perform complete multi-view clustering. However, the recovered views may be unreliable, and computational resources are wasted on repeatedly mapping between data and latent space [1]. To address this issue, we propose directly learning a latent embedding that is robust to view missing, without explicitly recovering the missing data. We have devised data augmentation and KNN imputation as preprocessing techniques, which, along with the unified representation learning framework, facilitate efficient and robust representation learning.


**Reference:**
- [1]. Chengliang Liu, Jie Wen, Zhihao Wu, Xiaoling Luo, Chao Huang, and Yong Xu. Information recovery-driven deep incomplete multiview clustering network. IEEE Transactions on Neural Networks and Learning Systems, pp. 1–11, 2023. doi: 10.1109/TNNLS.2023.3286918.
- [2]. Mouxing Yang, Yunfan Li, Peng Hu, Jinfeng Bai, Jiancheng Lv, and Xi Peng. Robust multi-view clustering with incomplete information. IEEE Transactions on Pattern Analysis and Machine Intelligence, 45(1):1055–1069, 2023b. doi: 10.1109/TPAMI.2022.3155499.
- [3]. Huayi Tang and Yong Liu. Deep safe incomplete multi-view clustering: Theorem and algorithm. In Kamalika Chaudhuri, Stefanie Jegelka, Le Song, Csaba Szepesvari, Gang Niu, and Sivan Sabato (eds.), Proceedings of the 39th International Conference on Machine Learning, volume 162 of Proceedings of Machine Learning Research, pp. 21090–21110. PMLR, 17–23 Jul 2022.
- [4]. Jiaqi Jin, Siwei Wang, Zhibin Dong, Xinwang Liu, and En Zhu. Deep incomplete multi-view clustering with cross-view partial sample and prototype alignment. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 11600–11609, June 2023.

Reviewer comment (Evaluation):
How to validate the robustness as a robust method proposed in the paper?

Author response:
A1: We believe that the robustness of our proposed method can be explained from three aspects. 

Firstly, its stability has been validated through multiple runs of the same experiment. Table 2 presents the results of 10 runs, showing that our approach achieved a relatively low standard deviation. This indicates the reliability and consistency of our method.

Secondly, the robustness of our method has been examined under different view-missing conditions. Figure 3 demonstrates that our approach exhibits a smaller decline in performance compared to other state-of-the-art methods even when the missing rate reaches 0.75. This suggests that our method is more robust in handling missing data.

Finally, the robustness of our approach is determined by experiments on various datasets, including image-based and text-based. Our approach consistently achieves state-of-the-art performance, proving its robustness to different data types. 

It is also worth noting that when we use the term "robust" in the title, we specifically refer to the robustness of the embeddings generated by our method. This refers to the ability of the unified embedding to remain consistent even under different missing conditions. To ensure this robustness, we have incorporated a robustness loss and an augmentation strategy during the training process. These mechanisms work together to enhance the stability and consistency of the embeddings, ultimately resulting in a more robust method.

Reviewer comment (Experiments):
K-Nearest-Neighbor (KNN) imputation is introduced in the paper. Is the method sensitive to the nearest neighbor numbers?

Author response:
A2: According to current observations, near-optimal results can be achieved with k>=4. The related Ablation study has been presented in Table 15. The result is unimodal with the best k = 4, and larger k values tend to provide more stable results (smaller standard deviation). The main results of Table 15 are as follows:

| k=1 | k=2 | k=4 | k=8 | k=16 |
| --- | --- | --- | --- | --- |
| 83.84 $\pm$ 3.38 | 84.84 $\pm$ 2.82 | **87.31 $\pm$ 2.01** | $\underline{87.00 \pm 2.46}$ | 86.01 $\pm$ 1.28 |

Reviewer comment (Experiments):
From Table 1, the feature dimensions of the datasets are not large, even very small. For example, one feature dimension of handwritten datasets is just 6. Is it necessary to use deep neural networks even Transformer to extract its features again?

Author response:
A3: It is important to consider the use of deep neural networks, or even Transformers, to extract features again for datasets with small feature dimensions, such as the handwritten datasets mentioned in Table 1. While it may seem unnecessary at first glance, there are several reasons why we believe it can be beneficial for the IMVC task.

Firstly, raw data often lack sufficient clustering characteristics. For instance, in the case of the Handwritten dataset, simply concatenating the data and performing clustering does not lead to satisfactory results, as demonstrated in RecFormer [1]. This highlights the need for additional feature extraction methods to capture more meaningful representations.

Secondly, deep neural networks and Transformers not only extract features but also possess the capability to store learned knowledge, such as data correlation and distribution. These learned representations are crucial for handling complex cross-view correlations and missing data conditions. 

Finally, in our specific case, Transformers are employed to fuse information from multiple views and incorporate knowledge from nearest neighbors.

Reviewer comment (Experiments):
What is the impact of the design of deep neural network layers and the selection of dimensions for each layer on clustering results?

Author response:
A4: We performed an ablation study to investigate the impact of the design of deep neural network layers and the selection of dimensions. The results of this study are presented in Table 13 in Appendix C.6.

Our findings suggest that larger models do not necessarily lead to better clustering accuracy. In fact, the best results were obtained with a balanced setting, where there were 2 Transformer blocks in both the NDE and VDE, and the FFN and embedding dimensions were set to 256.

This observation can be explained by the fact that small models may struggle to learn the complex fusion mapping between raw data and unified embedding, while larger models can easily overfit and weaken the relationship between the latent space and data space.

It is worth noting that the design of deep neural network layers and the selection of dimensions have not been a primary focus in prior works. For example, some previous studies have used simplistic designs such as 3-layer MLPs. Therefore, the network hyperparameters in our approach were not finely tuned, and the same setting was applied to all datasets. 

The main results of Table 16 are as follows:
| Transformer Blocks | FFN Dimension | Embedding Dimension | MACs | Parameters | Accuracy |
| ------------------ | ------------- | --------------------- | ---- | ---------- | -------- |
| 1 | 128 | 128 | 29.73 | 12.07 | 91.86 $\pm$ 1.80 |
| 2 | 128 | 128 | 33.65 | 13.03 | 91.29 $\pm$ 3.24 |
| 2 | 256 | 128 | 43.04 | 16.69 | 90.33 $\pm$ 5.26 |
| 2 | 256 | 256 | 43.98 | 17.13 | **92.95 $\pm$ 2.60** |
| 4 | 256 | 256 | 60.08 | 21.07 | $\underline{91.92 \pm 2.57}$ |
| 4 | 512 | 256 | 97.05 | 34.14 | 89.31 $\pm$ 5.11 |
| 4 | 512 | 512 | 103.34 | 36.39 | 90.02 $\pm$ 3.29 |

Reviewer comment (Experiments):
For the experimental results, why are the experimental results you provided lower than the original papers? For example, DCP on the Scene 15 dataset is much lower than the published papers. In addition, how were the experimental results of Completer obtained? The original Completer is proposed for two view data which cannot be applied on the datasets you exploited in the paper directly.

Author response:
A5: It is common to observe differences in experimental results compared to original papers due to various factors such as dataset settings, view missing conditions, randomness, and adapting strategies. For example, the Handwritten dataset used in RecFormer [1] has 5 views, while CPSPAN [2] used a variant with 6 views. There is also a discrepancy in the number of samples in the Caltech7 dataset reported by these two methods (1474 vs 1400), and their reported results have a 35% difference in accuracy (86% vs 51%) on this dataset.

To ensure a fair comparison, we aligned the results of prior works with our dataset settings as described in Section 4.1 and Appendix C.2. For all methods compared in Table 2, we reproduced their results on our chosen dataset and used the same missing conditions. In Table 4, we adapted our method to match the settings in MPC [3]. However, some prior works are challenging to adapt to different numbers of views, which can hinder real-world applications. For example, the Completer method can only handle 2-view datasets, and the DCP method requires extensive modifications to handle datasets with more than 3 views. In such cases, we randomly select views to evaluate on datasets with a higher number of views. We have provided detailed experimental information in Appendix C.2 for a clearer understanding of our experimental setup.

The reported lower result for DCP compared to the original paper is due to the difference in the number of views. Our Scene-15 dataset has only 2 views, whereas the DCP paper considered 3 views. Previously, an incorrect adaptation from the 3-view implementation to the 2-view dataset was used. We have now reproduced the result using the correct setup and updated it in Table 2. The result now is slightly lower than the original paper, which may be due to the randomness or the difference in the number of views.

For Completer, we randomly select 2 views for evaluation on datasets with more than 2 views since the method is challenging to adapt to a higher number of views.

Besides, we have carefully checked the experimental settings of reproduced methods and found that the experimental results are consistent with the original papers. We hope this revised response addresses your concerns. Thank you for your valuable feedback.