PCSY-D-23-00001

Measuring patterns separability in complex data and network community embedding through the travelling salesman path

PLOS Complex Systems

Dear Dr. Cannistraci,

Thank you for submitting your manuscript to PLOS Complex Systems. After careful consideration, we feel that it has merit but does not fully meet PLOS Complex Systems's publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.

Please submit your revised manuscript within 60 days Feb 11 2024 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at complexsystems@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pcsy/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

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If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

We look forward to receiving your revised manuscript.

Kind regards,

Aming Li, Ph.D.

Academic Editor

PLOS Complex Systems

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Additional Editor Comments (if provided):

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. Does this manuscript meet PLOS Complex Systems’s publication criteria? Is the manuscript technically sound, and do the data support the conclusions? The manuscript must describe methodologically and ethically rigorous research with conclusions that are appropriately drawn based on the data presented.

Reviewer #1: Partly

Reviewer #2: No

Reviewer #3: Yes

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2. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: N/A

Reviewer #2: I don't know

Reviewer #3: N/A

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3. Have the authors made all data underlying the findings in their manuscript fully available (please refer to the Data Availability Statement at the start of the manuscript PDF file)?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception. The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: No

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4. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS Complex Systems does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: No

Reviewer #3: Yes

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5. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: In this manuscript, the authors introduce a framework for the definition and measure of the geometric separability (linear and nonlinear) of mesoscale patterns in complex data visualization by solving the travelling salesman problem. They also offer experimental evidence in the evaluation of network community embedding. With the aim of assessing if a network embedding provides a correct low-dimensional representation of a network, they use three state-of-the art network embedding techniques including HOPE, ProNE, and Node2ve. After reading this work, I have found the topic of the study interesting. However, I do not see the innovation of the work, although I am not an expert in this field. It is unclear to me why the authors use the techniques of HOPE, ProNE, and Node2ve. I guess that there exist other embedding techniques. In addition, the authors can present more description about the contribution of this work.

Reviewer #2: In the present paper, the authors propose a computational framework with which they embed a network data into a low-dimensional space (which is a usual network embedding) and then calculate a measure (or measures? of "geometric separability" to detect (?) communities of the network. The paper is written in an overly didactic manner and also misses various important details, and I even do not see the aim of the paper clearly stated. It tells a lot of philosophy of the work but comparatively less about details and practicals. Also, the references cited are very biased to the authors' own work, which made it difficult for me to locate this manusript into a wider context. Network embedding followed by a subsequent task (including community detection) is a well studied topic in both network science and computer science, so I do not much see where the contribution is. I'm pretty sure that some of this is due to my oversight, but it is the authors' responsibility to make the paper as transparent as possible. On this basis, I recommend the rejection of the paper. A substantially rewritten paper, mostly for clarity and justification, rather than adding more computational work, can be comfortably submitted to any journal with a similar caliber to this journal. To clarify, I am sufficient expert on this type of topic at large. My feedback is as follows:

- p.1, the first sentence of Introduction: I advise against defining "physics" in this way. There are many branches of physics, and various physicists (and non-physicists) have different opinions on what physics is. This manuscript is full of this type of statements.

- p.1, line -5: "These patterns" are not well defined or articulated. As a network scientist, I do understand what the authors mean, but it is not clear from the text above.

- p.2, line 3: "However, when FIg. 1a...". This sentence does not parse.

- p.2, middle: "extent to which the embedding of a network in a two-dimensional space is able to produce a representation that unfolds its mesoscale community structure.". This is not new, and there are many work on this already. I understand that the authors are not claiming a novelty on this, but given tons of work in the field, I don't see the distinction between the background of the present work and the claim/novelty of this paper. Also, the text up to this point can be shrunk a lot without losing accessibility.

- p.2, line -12: "the first contribution of this study is conceptual". The authors have four contributions (first to the fourth), and repeat the whole set three times in the paper. I do not think it is a good idea to say "contribution" 12 times for this. Much text on this is repetitive across the manuscript.

- p.3, line 11: "The fourth contribution of this study is analytical". Vague. "analytical" means what? Usually, it means mathematical theory in math and physics, but apparently it is not the case here. By reading the several lines of the text (i.e., till the end of this paragraph) that follows, I do not understand what the main contributions are (despite the bullet points (i) and (ii)).

- p.3, the first paragraph of the Results section: It is difficult to understand why "separabiity line" is important.

- p.4, middle, the "The second contribution" paragraph: "To sum up, the separability curve is the geometrical entity". Honestly, I am completely lost around here. I don't pretend that I understand all the article.

- p.4, line -5: "projection separability theory". Where is the theory?

- p.5: This is a long paragraph. Hard to read.

- p.5, line -6: "fourth contribution". I am lost. Scenario of what? How are the performances measured? What methods are compared? Of course, it is fine to have many details in the Methods section below, but still the main text (without the Methods section) should be self-consistent and clear enough to convey what is going on.

- p.6, line 7: "report the results". I am afraid I don't understand the analysis or its aim. What is the perfromance measure?

- p.7, Discussion, first paragraph: I advise against repeating the cliche. We all know (or should know) what the community structure is, given a good explanation of it in the introduction section.

- p.8, lines 1-3: "In this study, we provide a framework ...". This is vague. E.g., "complex data" means "network data"? It does not have to be "complex" even. Does "mesoscale patterns" precisely mean community structure in this paper? Does "separability" mean the separation between different communities? If so, is what the authors does in this paper different from community detection? These questions also apply to the introduction section: I encourage the authors to work on the Introduction section to make it much clearer on these and other topics.

- p.11: If there are four indices, it is better to organize the CPS/LDPS section (why don't you separate this into two sections because the third and fourth ones get one section each?), GSI section, and TSPS section into four subsections of the "Community separability indices" section? Are the authors proposing the fourth one as a new index in this paper while the first three are previous work? While I may be wrong by saying this, even such an easy thing is not clear due to a poor presentation.

Reviewer #3: The manuscript titled "Measuring patterns separability in complex data and network community embedding through the travelling salesman path," submitted for publication at PLOS Complex Systems, presents an interesting framework for defining and measuring the geometric separability of mesoscale patterns in complex data and network community embedding. The approach involves solving the traveling salesman problem (TSP) to evaluate network community embedding. The authors apply this framework to both artificial and real network data, offering a fresh perspective in the field of complexity science. Some comments are given below which the authors might want to consider in revisions.

-- While the manuscript briefly touches upon existing network embedding methods, a more thorough and detailed comparison would greatly enhance the paper. It would be particularly beneficial to delineate how the proposed TSP-based method differs from, and potentially improves upon, current methodologies in network science. Such a comparison could involve a deeper discussion on the limitations of existing approaches and how the proposed framework addresses these gaps. Additionally, elaborating on the specific advantages in terms of accuracy, computational efficiency, or applicability to different types of network data would substantiate the novelty and significance of the research.

-- The inclusion of more detailed captions for figures and tables would significantly aid in comprehension. These captions should aim to be self-explanatory, providing sufficient context and explanation so that readers can understand the visualized data and its relevance to the study's findings even without referring back to the main text.

-- The manuscript could benefit from a more extensive discussion on the possible implications and applications of the research in various fields, such as biological networks, transportation systems, and more. In addition, the authors should consider discussing the potential of applying their framework to diverse datasets, particularly those related to social media network data as mentioned in PHYSICAL REVIEW X 10, 041042 (2020), and political network data as in R. Soc. open sci. 5: 181122 (2018). Such a discussion would not only demonstrate the versatility and adaptability of the approach but also its potential impact and utility in different real-world contexts. This could significantly enhance the robustness of the findings and underscore the broad applicability of the method in various complex systems.

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Reviewer #1: No

Reviewer #2: No

Reviewer #3: No

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PCSY-D-23-00001R1

Geometric separability of mesoscale patterns in embedding representation and visualization of multidimensional data and complex networks

PLOS Complex Systems

Dear Dr. Cannistraci,

Thank you for submitting your revised manuscript to PLOS Complex Systems. As you will see, a few issues remain to be addressed. Therefore, we invite you to submit a further revised version of the manuscript that addresses the remaining points raised during the review process.

Please submit your revised manuscript within 30 days Aug 17 2024 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at complexsystems@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pcsy/ and select the 'Submissions Needing Revision' folder to locate your manuscript file.

Please include the following items when submitting your revised manuscript:

* A rebuttal letter that responds to each point raised by the editor and reviewer(s). You should upload this letter as a separate file labeled 'Response to Reviewers'.

* A marked-up copy of your manuscript that highlights changes made to the original version. You should upload this as a separate file labeled 'Revised Manuscript with Track Changes'.

* An unmarked version of your revised paper without tracked changes. You should upload this as a separate file labeled 'Manuscript'.

If you would like to make changes to your financial disclosure, please include your updated statement in your cover letter. Guidelines for resubmitting your figure files are available below the reviewer comments at the end of this letter.

We look forward to receiving your revised manuscript.

Kind regards,

Aming Li, Ph.D.

Academic Editor

PLOS Complex Systems

Journal Requirements:

1. Please review your reference list to ensure that it is complete and correct. If you have cited papers that have been retracted, please include the rationale for doing so in the manuscript text, or remove these references and replace them with relevant current references. Any changes to the reference list should be mentioned in the rebuttal letter that accompanies your revised manuscript. If you need to cite a retracted article, indicate the article's retracted status in the References list and also include a citation and full reference for the retraction notice.

Additional Editor Comments (if provided):

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Reviewers' comments:

Reviewer's Responses to Questions

Comments to the Author

1. If the authors have adequately addressed your comments raised in a previous round of review and you feel that this manuscript is now acceptable for publication, you may indicate that here to bypass the “Comments to the Author” section, enter your conflict of interest statement in the “Confidential to Editor” section, and submit your "Accept" recommendation.

Reviewer #1: All comments have been addressed

Reviewer #2: All comments have been addressed

Reviewer #3: (No Response)

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2. Does this manuscript meet PLOS Complex Systems's publication criteria? Is the manuscript technically sound, and do the data support the conclusions? The manuscript must describe methodologically and ethically rigorous research with conclusions that are appropriately drawn based on the data presented.

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: (No Response)

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3. Has the statistical analysis been performed appropriately and rigorously?

Reviewer #1: Yes

Reviewer #2: N/A

Reviewer #3: (No Response)

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4. Have the authors made all data underlying the findings in their manuscript fully available (please refer to the Data Availability Statement at the start of the manuscript PDF file)?

The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception. The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: (No Response)

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5. Is the manuscript presented in an intelligible fashion and written in standard English?

PLOS Complex Systems does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.

Reviewer #1: Yes

Reviewer #2: Yes

Reviewer #3: (No Response)

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6. Review Comments to the Author

Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)

Reviewer #1: The authors have successfully addressed my concerns and I recommend the publication of the work.

Reviewer #2: The authors put serious effort to significantly improve the readability of the manuscript, including clarification of what is novel and what is done in this paper. As the authors pointed out, I missed to understand what novel work was done in this paper in the last version of the manuscript, although the other two reviewers got it right. With my new understanding of the present work, aided by the revised Introduction section mainly, I am now confident that the work is novel and merits publication in this journal. In short, the authors expanded their previous recent work (their ref 2) to the case of nonlinear separability, and defined new methods and measures of cluster separability (considering intra- and inter-cluster diversity of the data points carefully), in the two-dimensional embedding space, including the novel use of the (approximate) solution of traveling salesman problem in the two-dimensional embedding space as a tool for defining the clustering performance measures.

Now the Introduction and Discussion sections do a good job of articulating what was done before and what the novelty of the present work is. This was really needed and missing in the last version of the manuscript, so I appreciate the authors' effort. The only thing I request/suggest is that the Introduction section is overly long and would negatively overwhelm many readers. By the same token, some part of the Discussion section iterates the Introduction section. I am saying these for the authors' benefit, so I do not request these changes (detailed below) as a condition for publication, and I do not think I need to check the revised manuscript once again; this is already the second time I am *thoroughly* reading and evaluating the manuscript for this journal. Nonetheless, the authors may find the following suggestions useful.

The page numbers below concern those in the change-tracked main text.

- p.3, middle, "For instance: (1) the projection ..." Instance of what?

- p.3, lines -5 - -4: "CPS scales linearly with the number of samples only". It does so for any $D$, i.e., not only for $D=2$.

- p.4, line 1: "Finally, a projection separability ...". Are the authors talking about ref. 2? If so, I recommend explicitly citing ref. 2 in this sentence, too.

- p.4, 2nd last paragraph, i.e., the paragraph starting with "In recent decades,". I strongly recommend (but do not request) removing this paragraph. It is close to general nonsense, is non-specific, and the next paragraph can start as is without this paragraph.

- p.4, last paragraph, i.e., the paragraph starting with "The emergence of mesoscale...". I assume that there are many review papers talkiing about the importance of mesoscale patterns. I recommend that the authors cite them and shrink the length of this paragraph. Likewise, the next paragraph is excessively long. Mesoscopic structure being important and there are some such examples (such as network's community structure and swarms in mobile agent system) are the only important things, and I do not think it deserves 1.5 paragraphs (i.e., the entirety of the last paragraph on p.4, and the first half of the next paragraph).

- Fig. 3 appears before Fig. 2 in the main text? If so, swap them.

- p.6, line -12: "projection separability theory". Where is "theory"?

- p.7, lines 10-15, i.e., "According to this definition ... 1 (best result)." This is too much overlapping with the Introduction section.

- p.7, line 14: "as an overall measure". Measure of what? Goodness of community structure?

- p.7, middle: "The fourth innovation of this study is in multidimensional analysis". Why do the authors say "multidimensional"? I do not understand.

- p. 11, last paragraph (i.e., "In our previous study^2 ..."). This heavily overlaps with the Introduction section. The first paragraph of the Discussion section is acceptable because it is an executive summary of the results (I mean, even if there is overlap with the Introduction section). However, the rest of the Discussion section should talk about what was not discussed in the Introduction section, assuming that the readers have read the results section.

- p.12, the third paragraph (i.e., "The final innovation of ...") is again repetitive of the Introduction section.

Reviewer #3: It seems that the revisions are constructive and comprehensive, which I am happy with.

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7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files.

Do you want your identity to be public for this peer review? If you choose “no”, your identity will remain anonymous but your review may still be made public.

For information about this choice, including consent withdrawal, please see our Privacy Policy.

Reviewer #1: No

Reviewer #2: No

Reviewer #3: None

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[NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.]

While revising your submission, please upload your figure files to the Preflight Analysis and Conversion Engine (PACE) digital diagnostic tool, https://pacev2.apexcovantage.com/. PACE helps ensure that figures meet PLOS requirements. To use PACE, you must first register as a user. Registration is free. Then, login and navigate to the UPLOAD tab, where you will find detailed instructions on how to use the tool. If you encounter any issues or have any questions when using PACE, please email PLOS at figures@plos.org. Please note that Supporting Information files do not need this step.

Geometric separability of mesoscale patterns in embedding representation and visualization of multidimensional data and complex networks

PCSY-D-23-00001R2

Dear Professor Cannistraci,

We are pleased to inform you that your manuscript 'Geometric separability of mesoscale patterns in embedding representation and visualization of multidimensional data and complex networks' has been provisionally accepted for publication in PLOS Complex Systems.

Before your manuscript can be formally accepted you will need to complete some formatting changes, which you will receive in a follow-up email from a member of our team. 

Please note that your manuscript will not be scheduled for publication until you have made the required changes, so a swift response is appreciated.

IMPORTANT: The editorial review process is now complete. PLOS will only permit corrections to spelling, formatting or significant scientific errors from this point onwards. Requests for major changes, or any which affect the scientific understanding of your work, will cause delays to the publication date of your manuscript.

If your institution or institutions have a press office, please notify them about your upcoming paper to help maximize its impact. If they'll be preparing press materials, please inform our press team as soon as possible -- no later than 48 hours after receiving the formal acceptance. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact complexsystems@plos.org.

Thank you again for supporting Open Access publishing; we are looking forward to publishing your work in PLOS Complex Systems.

Best regards,

Aming Li, Ph.D.

Academic Editor

PLOS Complex Systems

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Reviewer Comments (if any, and for reference):