Venue: NeurIPS 2022 Conference

Reviews:

final_score: rating: 8: Strong Accept: Technically strong paper, with novel ideas, excellent impact on at least one area, or high-to-excellent impact on multiple areas, with excellent evaluation, resources, and reproducibility, and no unaddressed ethical considerations.
review_content: summary: This paper proposes a new multi-view subspace clustering method to exploit a common affinity representation using self-expression property. The proposed model explores the implied data manifold by learning the topological relationship between data points. Then, the model integrates multiple affinity graphs into a consensus one with the topological relevance considered. Experimental results on seven benchmark datasets illustrate the effectiveness of the proposed model.
strengths_and_weaknesses: Strengths:
+ The theoretical basis is intuitive and sound, and the optimization algorithm is well designed.
+ The convergence of the corresponding algorithm is theoretically and empirically guaranteed.
+ The paper is well written and organized, and the code is available.
+ Extensive experiments are conducted, and the experimental results of the proposed method are promising.

Weaknesses:
- The computation complexity of the proposed model seems to be O(n^3). Hence this model is computationally slow on large data sets.
- The experiments section should be improved. More diverse experimental results, such as ablation analysis, should be available.

questions: 1) Since manifold learning requires a large amount of computational complexity, so how to handle large data sets with the proposed methods? Are there any speedup tricks?
2) The paper is well written but there are some grammatical errors and expression problems in the paper. It is suggested to conduct further inspections.
3) The detailed information about experimental settings is missing. Is there a significant difference in parameter settings for different datasets? And please provide different parameter settings for all datasets if possible.

limitations: Yes, the authors have addressed the limitations in Section 5.
review_title: null

final_score: rating: 7: Accept: Technically solid paper, with high impact on at least one sub-area, or moderate-to-high impact on more than one areas, with good-to-excellent evaluation, resources, reproducibility, and no unaddressed ethical considerations.
review_content: summary: To explore the implied data manifold by learning the topological relationship between data points, this paper proposes to integrate multiple affinity graphs into a consensus one with the topological relevance considered. And to get the discrete result directly, a connectivity constraint is included in the proposed model. Detailed analyses about the optimization and convergence are provided. Solid experimental results are shown to demonstrate the efficiency and stability of the proposed algorithm.
strengths_and_weaknesses: Strengths:
1.	This paper is well organized and the motivation is clear to understand.
2.	The proposed algorithm, the optimization procedure, and the corresponding analysis are convinced.
3.	The empirical evaluation shows significantly better results than existing related clustering algorithms.
Weaknesses:
1.	It could be better to analyze the properties and behaviors of the proposed algorithms.
2.	Introduction section, the motivation for the proposed algorithm is ambiguous.
3.	There are some writing problems in the current manuscript.


questions: 
1. Is there any assumption of the algorithm?
2. Why there is no synthetic dataset with topological clusters used to verify the performance of the proposed algorithm.
3. How to determine the range of parameters \alpha and \beta?
4. What are linear data and nonlinear data?
limitations: Yes, the authors have addressed the limitations.
review_title: null

final_score: rating: 5: Borderline accept: Technically solid paper where reasons to accept outweigh reasons to reject, e.g., limited evaluation. Please use sparingly.
review_content: summary: To explore the benefits of the topological structure in multi-view data, this paper is to integrate multiple affinity graphs into a consensus one with the topological manifold for multi-view subspace clustering. Experimental results on several benchmark datasets illustrate the effectiveness of the proposed model. 
strengths_and_weaknesses: Strengths:
1. This paper is well-written and is easy to follow.
2. This paper proposes a multi-view subspace clustering method based on topological manifold.
3. The proposed method achieves good performance compared to the state-of-the-art competitors over the clustering performance.

Weakness:
1. The novelty of the proposed method seems limited since it is simple to combine the multi-view learning formulation in Eq. (4) with the topological structure in Eq. (3). Moreover, Eq. (4) is popular in multi-view subspace clustering and Eq. (3) has been proposed in [17]. Which part is introduced in this paper?
2. In fact, Fig. 1 is same to the Fig. 2 of [17]. So, please cite this paper in the caption of Fig. 1.
3. Experiment on the topological manifold is missing. I suggest one experiment to show the topological manifold. 


questions: Please see the weaknesses.
limitations: The novelty of the proposed method seems limited
review_title: null

Meta-review: metareview: All reviewer agree that this paper is innovative and well-written, so I recommend to accept.
confidence: Certain
Decision: Accept