Unsupervised Machine Learning for Improved Delaunay Triangulation

Round 1

Reviewer 1 Report

In this manuscript, the authors apply a clustering algorithm to reduce the number of narrow triangles in unstructured grid. The analysis of obtained results for three illustrative examples (global ocean, small sea area and South China Sea) shows the usefulness of the proposed methodology.

 

My remarks are as follows:

The benefits of the proposed algorithm for global ocean triangulation are not argumented well.

The visualization of Algorithm 1 and Algorithm 2 is doubled – pseudo-code (Table 1 and  Table 2) and flowchart (Figure 2 and Figure 5 respectively). Please, remove one of these two alternatives.

The meaning of Figure 8 is unclear. This figure is not mentioned in the text and could be omitted.

The three examples could be described more concisely without repetitions.

In “4. Results and analysis” section, a comparison with results from previous similar studies is missing.

 

Technical remarks:

Figure 1, Figure 3 and Figure 4 are not mentioned in the text. Please, edit this.

l. 204, 238: The captions “Table 1. Overview of preliminary optimization algorithms for unstructured grids.” and “Table 2. Overview of further optimization methods for unstructured lattices based on K-Means clustering.” could be omitted. Actually, these elements are not tables.

The manuscript’s title could be edited in order to correspond better to the content, for example “Unsupervised Machine Learning for Improved Delaunay Triangulation”.

Author Response

Response to Reviewer 1 Comments

1. The benefits of the proposed algorithm for global ocean triangulation are not argumented well.

Thank you for your comment. The benefits of the proposed algorithm for global ocean triangulation are in the first and second paragraphs of the conclusion. I have also described it in more detail in it. The benefit of unstructured mesh optimization is to improve the quality of the mesh by making the triangles in the mesh more closely resemble equilateral triangles and reducing narrow triangles. A higher quality unstructured grid can better fit the complex shoreline boundaries of the study area, which can reduce the errors in the numerical ocean calculations and improve the computational accuracy.

2. The visualization of Algorithm 1 and Algorithm 2 is doubled – pseudo-code (Table 1 and  Table 2) and flowchart (Figure 2 and Figure 5 respectively). Please, remove one of these two alternatives.

Thank you for your suggestion, the flowchart has been removed.

3. The meaning of Figure 8 is unclear. This figure is not mentioned in the text and could be omitted.

Thank you for your kind reminding. Changes have been made in the text. All image labels have been updated.

4. The three examples could be described more concisely without repetitions.

We sincerely thank you for your suggestion. I have made changes in the text to remove some repetitive descriptions and express more concisely.

5. In “4. Results and analysis” section, a comparison with results from previous similar studies is missing.

 Thank you for your suggestion. In the "4. Results and Analysis" section, the results of this paper are not compared with the results of other studies, because the results of this paper may not achieve the best results in the field and the results may not be as good as the results of other articles. In the conclusion, I mentioned the limitations of the study and analyzed the reasons. Maybe the algorithm proposed in this paper cannot achieve the best results in the field, but it cannot be ignored that this paper presents a new idea about unstructured mesh generation and optimization, which may be inspiring and perhaps can be used as part of other unstructured mesh optimization methods.

Technical remarks:

6. Figure 1, Figure 3 and Figure 4 are not mentioned in the text. Please, edit this.

Thank you for your kind reminding. In the revised manuscript, the numbering of all figures has been updated and each figure is mentioned in the text.

7. l. 204, 238: The captions “Table 1. Overview of preliminary optimization algorithms for unstructured grids.” and “Table 2. Overview of further optimization methods for unstructured lattices based on K-Means clustering.” could be omitted. Actually, these elements are not tables.

We sincerely thank you for your suggestion. In the revised manuscript, these two sentences have been removed.

8. The manuscript’s title could be edited in order to correspond better to the content, for example “Unsupervised Machine Learning for Improved Delaunay Triangulation”.

Thank you for your suggestion, the title has been modified.

 

Thank you for your valuable comments on revisions to my manuscript, which will help me improve my manuscript to a great extent. I have also embellished the entire manuscript.

Author Response File: Author Response.pdf

Reviewer 2 Report

I notice that the manuscript has undergone significant improvements. The added material allowed to clarify and improve the scientific content. 

In fact, this version of the manuscript is actually more informative and methodologically clearer by including more explanatory material such as appropriate algorithms and flowcharts.

As the authors themselves state, the proposed methodology does not claim to obtain better results than others, and therefore no comparative tests were performed. It is, in fact, a new methodology relatively easy to implement and capable of improving  Delaunay's classical triangulation.

Therefore, globally, this manuscript contains scientific content and may meet the key requirements for possible publication. However, it must be checked carefully. There are some flaws and inaccuracies that must be overcome in a second review; essentially they are:

- As a rule, all Figures and Tables must be mentioned/cited and properly framed before their appearances throughout the text. However, most of the Figures and Tables are not even mentioned throughout the text. These are the cases of Figures 1, 2, 3, 4, 6, 7, 8, 11, and 12. As far as it seems, Figure 7 is inappropriately mentioned in line 301. Figure 5 is the only one duly mentioned. All other figures, in addition to those indicated, are only mentioned after appearing throughout the text. 

- Tables 3, 4, and 5 are also not properly framed before appearing in the text.

- The equation (line 358) should be numbered and must also be mentioned/cited. 

- Some problems with English syntax and grammatical constructions throughout the manuscript are also notorious and must be properly overcome. Therefore, a careful review of English should be done, probably by a native English speaker. 

Author Response

Response to Reviewer 2 Comments

1. As a rule, all Figures and Tables must be mentioned/cited and properly framed before their appearances throughout the text. However, most of the Figures and Tables are not even mentioned throughout the text. These are the cases of Figures 1, 2, 3, 4, 6, 7, 8, 11, and 12. As far as it seems, Figure 7 is inappropriately mentioned in line 301. Figure 5 is the only one duly mentioned. All other figures, in addition to those indicated, are only mentioned after appearing throughout the text. 

Thank you for your suggestion. In the revised manuscript, all figures and tables are mentioned, and the figures and tables appear before the text. The numbering of all figures and tables has been updated.

2. Tables 3, 4, and 5 are also not properly framed before appearing in the text.

We sincerely thank you for your suggestions. In the revised manuscript, Tables 3,4,5 were renamed to Tables 1,2,3, all of which are mentioned below, and the tables all appear before the text.

3. The equation (line 358) should be numbered and must also be mentioned/cited. 

Thanks to your suggestion, the equation has been numbered in the revised manuscript and has been mentioned below.

4. Some problems with English syntax and grammatical constructions throughout the manuscript are also notorious and must be properly overcome. Therefore, a careful review of English should be done, probably by a native English speaker. 

We sincerely thank you for your suggestions. The entire manuscript has been touched up.

 

 

 

Thank you for your valuable comments on revisions to my manuscript, which will help me improve my manuscript to a great extent.

Round 2

Reviewer 1 Report

The quality of jmse-1500002 “Unsupervised Machine Learning for Improved Delaunay Triangulation” has been improved and the manuscript now meets the journal's requirements.

My recommendation is “Accept as is”.

This manuscript is a resubmission of an earlier submission. The following is a list of the peer review reports and author responses from that submission.

Round 1

Reviewer 1 Report

In this manuscript, the authors employ clustering algorithm to reduce the number of narrow triangles in the triangular mesh. The analysis of obtained results for global ocean, small sea area and South China Sea shows the efficiency and efficacy of proposed methodology.

My remarks are as follows:

The drawback of the manuscript is the poor description of proposed methodology, so the reader is unable to repeat the experiments. Please, describe the methodology in detail, step-by-step. It is desirable to include a flowchart and pseudo-code of proposed algorithm and an illustrative example.

Please describe your datasets in detail. Links to the datasets are missing. The implementation details (platform, software, libraries and/or source code details) are also missing.

In “4. Results and analysis” section, a comparison with results from previous similar studies should be added. The “Conclusions” part should be extended – study’s limitations are missing.

Technical remarks:

l. 22, 109: “in less than 30 seconds” – Please, edit this fragment. You should add some details about your dataset and computer platform used.

l. 76, 77-78: “the trained neural network can replace” – Please, edit this paragraph to avoid the repetitions.

l. 88: “SOM” is undefined.

l. 105: “triangular mesh can be more homogeneous and standardized.” – Please, edit.

l. 144-145: “each object belongs” – Please, edit this paragraph to avoid the repetitions.

l. 167: “square triangle” – Please, clarify. The triangle ABD is an equilateral triangle.

l. 175: “? points” and l. 141: “? objects” – Please, use different variable name in order to avoid confusing the reader.

l. 220: “After performing Delaunay triangulation is performed” – Please, edit.

Figure 13, Figure 15 and Figure 17: The font size should be enlarged.

Reviewer 2 Report

This manuscript aims to optimize unstructured triangular meshes formed by Delaunay triangulation using machine learning methods. It is structured in two dimensions (1) optimization of unstructured grids integrating machine learning, and (2) use of geometric principles for unstructured optimization and a new method of evaluating grid quality.

Overall, this manuscript raises some concerns.
The Introduction section does not cover the state-of-art with sufficient clarity and depth. Many other important references that address mesh optimization methods with different methodologies and very acceptable performances are not mentioned/cited.

This is, in fact, an already well-researched subject and to which this manuscript adds little; it doesn't really seem to contribute significantly, if at all, to the literature.

Literature is rich in unstructured mesh optimization methods and several commercial and freeware models are available in the market. Note that these models can also be used for comparison purposes of meshes optimized by the proposed method.

The authors claim that they propose a new method that goes through two optimization steps, claiming the application of geometric mathematical principles in the first step, without these principles being specified. In the second step, they suggest using the algorithm based on clustering K-means, without the methodology being comprehensively detailed and without any supporting references.

Indeed, based on Delaunay's classical triangulation, like most optimization methodologies, the contribution of this manuscript to the optimization of unstructured triangular meshes is unclear. Nor do the meshes supposedly optimized by the proposed new method seem to be of great quality, as the authors claim.

Throughout the manuscript, and especially in the 'Data Experiments' and 'Results and Analysis' sections, various statements and concepts are repeated. Furthermore, English style and syntax don't help, and the manuscript structure is neither motivating nor enlightening enough for JMSE readers.