Block Diagonal Least Squares Regression for Subspace Clustering

Round 1

Reviewer 1 Report

A new clustering algorithm for high-dimensional data when the number of clusters are known is proposed (BDSLR). A computationally efficient algorithm is developed for its implementation, and conditions for its convergence to the solution are given (sec. 3). Its performance is evaluated on datasets where the actual clusters are known, and shown to be competitive with the best methods. The method has merit fills an important niche.  

Specific Comments
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* p. 4, line -3: Laplacian matrix for B is defined as L_B=Diag(B1)-B, but B1 is not defined.
* End of sec. 4.1 (p. 10): the choice of AC and NMI [25] as the evaluation criteria for quantitatively evaluating BDLSR should be better described, as ref. [25] is not easy to find.
* Algorithm 1: The proposed BDSLR requires input of 3 tuning parameters (lambda, alpha, gamma). Should these be chosen by doing some kind of cross-validation? I see that sec. 4.3 sheds some light on these choices, but this is done post-hoc on the selected datasets for which the clustering is known. Give a better discussion to give the user practical guidance.

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Reviewer 2 Report

In this work, Fan et al. explores BDLSR for subspace clustering. The manuscript is mostly well written. I am providing some comments below.

  1. I think the authors need to cite appropriate works such as this one. Please conduct a thorough literature survey Can-Yi Lu et al. Robust and Efficient Subspace Segmentation via Least Squares Regression
2. What are some of the potential drawbacks for the method? 3. Given your performance improvements elsewhere, why did BDLSR not perform well for the 3 motions (table 2)? 4. Have you conducted any ablation studies?

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

The authors have addressed comments adequately