Laplacian Eigenmaps Dimensionality Reduction Based on Clustering-Adjusted Similarity
Round 1
Reviewer 1 Report
See the attached file.
Comments for author File: 
Comments.pdf
Author Response
Dear Reviewer:
Response to algorithms-569822 (Algorithms (ISSN 1999-4893))Laplacian Eigenmaps Dimensionality Reduction based on Clustering Adjusted Similarity
We appreciate the opportunity of responding to the your’ comments and submitting a revised version of our manuscript. In the following, we have included a point-by-point response letter to the comments made by you. To save space, the details are moved into the supplementary file. Please see the attachment.
We appreciate your efforts and suggestions, and we believe that the current manuscript has substantially benefited from their suggestions.
Regards,
Honghu Zhou, Jun Wang
28-Aug-2019
Author Response File: 
Author Response.docx
Reviewer 2 Report
The main motivation of this manuscript is apply a technique to minimize the distance between data from border among groups. For that, the authors have applyed LE-CAS, a proposed technique in this manuscript.
This problem also can be minimized by applying fuzzy sets theory, ie, membership degree to data. Thus, I suggest you compare both techniques. Which of them is the best? (You can propose it for future works).
What is the computational complexity of the LE-CAS? It seems to be very costly because the technique is based on graph, in comparison on fuzzy sets.
For the experiments (Table 2), it would be interesting increases the number of runs (30 times or more). As you can see, the mean obtained is close among techniques; for example:
Msplice, F-Measure; W1a, F-Measure; Soccer-sub1, all measures; and so on. Therefore, a statistical analysis must be applied.
The applied technique proposes minimize the distance between data, as depicted in Figure 1. How can we see this on measures applied (Table 2)?
Author Response
Dear Reviewer:
Response to algorithms-569822 (Algorithms (ISSN 1999-4893))Laplacian Eigenmaps Dimensionality Reduction based on Clustering Adjusted Similarity
We appreciate the opportunity of responding to the your’ comments and submitting a revised version of our manuscript. In the following, we have included a point-by-point response letter to the comments made by you. To save space, the details are moved into the supplementary file. Please see the attachment.
We appreciate your efforts and suggestions, and we believe that the current manuscript has substantially benefited from their suggestions.
Regards,
Honghu Zhou, Jun Wang
28-Aug-2019
Author Response File: Author Response.docx
Round 2
Reviewer 1 Report
I appreciate the authors' response. Most of my comments were satisfactorily addressed. However, my main concern (point 1) still remains. To clarify, I don't think that k-means or any other clustering algorithm is an issue here. To be more precise, the conceptual problem that I see with the method is that the authors aim to find a boundary between classes (i.e., a supervised-defined region according to some class labels) using an unsupervised clustering method. Different clustering methods can potentially result in different cluster assignments, which, depending on the class labels of interest, will change the accuracy of the Laplacian method proposed by the authors. See for example Luxburg et al. 2012 "Clustering: Science or Art?", JMLR 2012.
It then seems to me that the accuracy of the method proposed by the authors heavily depends on whether the clustering method used, either k-means or kernel k-means, is reflecting the boundaries of interest. As I illustrated in my previous review, in Figure 1 there is no clear clustering structure, but if class labels turn out to be according to having y>0 or y<0, then the similarities will be very different, and the method might fail in this case.
Having said that, I think that the algorithm might still be relevant, and the good performance in some data analyses suggests that this is the case. However, the authors will need to recognize and discuss the limitations of their method. What happens if the clusters identified by kernel k-means are not relevant for the true decision boundaries?
It might still be the case that even if the clusters obtained by kernel k-means are wrong and the boundary between the classes is not identified correctly, the resulting LE-CAS similarity is still accurate because of the following steps. In that case, I would expect a more thorough analysis, including simulations in which the ground truth is known.
Author Response
Dear Reviewer:
Response to Algorithms (ISSN 1999-4893)
Laplacian Eigenmaps Dimensionality Reduction based on Clustering Adjusted Similarity
We appreciate the opportunity of responding to the reviewers’ comments and submitting a revised version of our manuscript. In the following, we have included a point-by-point response letter to the comments made by the reviewers. To help review, we also attached a manuscript with changes tracked in red font. To save space and keep in the maximum allowed pages, we move the results and their analysis from the main text into the supplementary file. Please see the attachment for details.
We appreciate the reviewer' s efforts and suggestions, and we believe that the current manuscript has substantially benefited from their suggestions.
Author Response File: Author Response.pdf
Reviewer 2 Report
All recommendations have been performed.
Author Response
Dear Reviewer:
Response to Algorithms (ISSN 1999-4893)
Laplacian Eigenmaps Dimensionality Reduction based on Clustering Adjusted Similarity
We are very grateful to the reviewers for your patience and carefulness, we appreciate your efforts and suggestions, and we believe that the current manuscript has substantially benefited from your suggestions.
Thank you very much!
Round 3
Reviewer 1 Report
Thanks to the authors for responding to my concerns. My suggestions have been addressed and I don't have further comments to add.
