Noisy $ell^{0}$-Sparse Subspace Clustering on Dimensionality Reduced Data
High-dimensional data often lie in or close to low-dimensional subspaces. Sparse subspace clustering methods with sparsity induced by L0-norm, such as L0-Sparse Subspace Clustering (L0-SSC), are demonstrated to be more effective than its L1 counterpart such as Sparse Subspace Clustering (SSC). However, these L0-norm based subspace clustering methods are restricted to clean data that lie exactly in subspaces. Real data often suffer from noise and they may lie close to subspaces. We propose noisy L0-SSC to handle noisy data so as to improve the robustness. We show that the optimal solution to the optimization problem of noisy L0-SSC achieves subspace detection property (SDP), a key element with which data from different subspaces are separated, under deterministic and randomized models. Our results provide theoretical guarantee on the correctness of noisy L0-SSC in terms of SDP on noisy data. We further propose Noisy-DR-L0-SSC which provably recovers the subspaces on dimensionality reduced data. Noisy-DR-L0-SSC first projects the data onto a lower dimensional space by linear transformation, then performs noisy L0-SSC on the dimensionality reduced data so as to improve the efficiency. The experimental results demonstrate the effectiveness of noisy L0-SSC and Noisy-DR-L0-SSC.
This paper propose noisy -SSC and Noisy-DR- -SSC to handle noisy data and dimensionality reduced data so as to improve the robustness of sparse subspace clustering methods. The authors conduct a complete and detailed theoretical analysis, and the results provide theoretical guarantee on the correctness in terms of SDP on noisy data. Positive: (1) Under both deterministic model and randomized models, this paper presents noisy -SSC , which enhances -SSC by theoretical guarantee on the correctness of clustering on noisy data. (2) Moreover, this paper presents Noisy-DR- -SSC, the method improves the efficiency of the basic algorithm, and provably recovers the underlying subspace structure in the original data from the dimensionality reduced data under deterministic model. Negative: (1) The authors conduct a complete and detailed theoretical analysis, but the description of the algorithm is not clear and the optimization process is not detailed enough. It is very difficult to understand it. (2) This paper proposes a noise model based on Yang et.al (2016), the objective function and the optimization process are already available, therefore, its innovation is not clear in this paper. (3) The results of experiments demonstrate the effectiveness of noisy -SSC and Noisy-DR- -SSC, but this paper not only lacks the description of experimental data, but also lacks the large-scale experimental data. In addition, the experiment is inadequate in this paper, it is suggested to add experiments to analyze the influence of noise ratio on the experimental results. It is hoped that the author will give the parameter analysis and convergence analysis of the algorithm in an experimental way.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Noisy $ell^{0}$-Sparse Subspace Clustering on Dimensionality Reduced Data
High-dimensional data often lie in or close to low-dimensional subspaces. Sparse subspace clustering methods with sparsity induced by L0-norm, such as L0-Sparse Subspace Clustering (L0-SSC), are demonstrated to be more effective than its L1 counterpart such as Sparse Subspace Clustering (SSC). However, these L0-norm based subspace clustering methods are restricted to clean data that lie exactly in subspaces. Real data often suffer from noise and they may lie close to subspaces. We propose noisy L0-SSC to handle noisy data so as to improve the robustness. We show that the optimal solution to the optimization problem of noisy L0-SSC achieves subspace detection property (SDP), a key element with which data from different subspaces are separated, under deterministic and randomized models. Our results provide theoretical guarantee on the correctness of noisy L0-SSC in terms of SDP on noisy data. We further propose Noisy-DR-L0-SSC which provably recovers the subspaces on dimensionality reduced data. Noisy-DR-L0-SSC first projects the data onto a lower dimensional space by linear transformation, then performs noisy L0-SSC on the dimensionality reduced data so as to improve the efficiency. The experimental results demonstrate the effectiveness of noisy L0-SSC and Noisy-DR-L0-SSC.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



This paper propose noisy -SSC and Noisy-DR- -SSC to handle noisy data and dimensionality reduced data so as to improve the robustness of sparse subspace clustering methods. The authors conduct a complete and detailed theoretical analysis, and the results provide theoretical guarantee on the correctness in terms of SDP on noisy data. Positive: (1) Under both deterministic model and randomized models, this paper presents noisy -SSC , which enhances -SSC by theoretical guarantee on the correctness of clustering on noisy data. (2) Moreover, this paper presents Noisy-DR- -SSC, the method improves the efficiency of the basic algorithm, and provably recovers the underlying subspace structure in the original data from the dimensionality reduced data under deterministic model. Negative: (1) The authors conduct a complete and detailed theoretical analysis, but the description of the algorithm is not clear and the optimization process is not detailed enough. It is very difficult to understand it. (2) This paper proposes a noise model based on Yang et.al (2016), the objective function and the optimization process are already available, therefore, its innovation is not clear in this paper. (3) The results of experiments demonstrate the effectiveness of noisy -SSC and Noisy-DR- -SSC, but this paper not only lacks the description of experimental data, but also lacks the large-scale experimental data. In addition, the experiment is inadequate in this paper, it is suggested to add experiments to analyze the influence of noise ratio on the experimental results. It is hoped that the author will give the parameter analysis and convergence analysis of the algorithm in an experimental way.
assistant
This paper propose noisy -SSC and Noisy-DR- -SSC to handle noisy data and dimensionality reduced data so as to improve the robustness of sparse subspace clustering methods. The authors conduct a complete and detailed theoretical analysis, and the results provide theoretical guarantee on the correctness in terms of SDP on noisy data. Positive: (1) Under both deterministic model and randomized models, this paper presents noisy -SSC , which enhances -SSC by theoretical guarantee on the correctness of clustering on noisy data. (2) Moreover, this paper presents Noisy-DR- -SSC, the method improves the efficiency of the basic algorithm, and provably recovers the underlying subspace structure in the original data from the dimensionality reduced data under deterministic model. Negative: (1) The authors conduct a complete and detailed theoretical analysis, but the description of the algorithm is not clear and the optimization process is not detailed enough. It is very difficult to understand it. (2) This paper proposes a noise model based on Yang et.al (2016), the objective function and the optimization process are already available, therefore, its innovation is not clear in this paper. (3) The results of experiments demonstrate the effectiveness of noisy -SSC and Noisy-DR- -SSC, but this paper not only lacks the description of experimental data, but also lacks the large-scale experimental data. In addition, the experiment is inadequate in this paper, it is suggested to add experiments to analyze the influence of noise ratio on the experimental results. It is hoped that the author will give the parameter analysis and convergence analysis of the algorithm in an experimental way.