Temporal Network Link Prediction Based on the Optimized Exponential Smoothing Model and Node Interaction Entropy

Round 1

Reviewer 1 Report

The manuscript titled "Temporal network link prediction based on the optimized exponential smoothing model and node interaction entropy" has been submitted to the MDPI Symmetry journal to be considered for publication. The authors of the manuscript propose a temporal network link prediction method based on the optimized exponential smoothing model and node interaction entropy to mine fine-grained interaction information among nodes within snapshots, called OESMNIE.

I have the following comments:

1) Abbreviations should be explained at the first occurrence, for example, WSN, GR, ARIMA, SAM, and AUC.  (In addition, it is possible to add a list of Abbreviations at the end of the paper.)

2) You should define all the central concepts you are using. For example, similarity matrix, eigenvector centrality, entropy, reference score, and single/multi-layer sequence. (Also, in lines 282-283, the sentence is not clear, please check).

3) You have mentioned Granovetter's "Weak ties." Maybe you should check Stephen P. Borgatti's article (On Network Theory, Organisation Science doi:10.1287/orsc.1110.0641, 2011) and his interpretation of the concept of "Weak ties.". You say: "The theory believes weak ties are easier to traverse different social groups than strong ties. In other words, nodes with weak ties are more likely to have connections with others." Lines 230-232: "For example, supermarket promoters can spread what they know to a wider audience in a short time because the spread breadth is usually more important than the number of contacts." Are these consistent with the original ideas of Granovetter? (This is just my comment)

4) I suggest that you add a list of variables at the end of the paper. Now, all definitions are not clear in the text. For example, on line 187. It is difficult to find where is the definition of the quantity.

5) In your numerical example Section 3.5 you have mixed both numbers and variables. You should explain with numerical values how all the variables are calculated, for example, Eq. (13) first line. Also, I think that Figures 4 and 5 need more explanation, for example, ((1,2,1), (1,4,1),...)?

6) Line 398-399. Check the instructions for authors on how to provide this information.

7) Line 400. The word "superior" in this sentence is not justified. You should specify the context of your statements.

8) You should explain the limitations of your method and model. Does it work only for unweighted and undirected links?

9) In Table 2 you mention other indicators. You should have a short summary of these other methods and explain why you think that they are representative. What are the main differences with your method? Provide references (also) in the table. Line 549: "The experimental results demonstrate the superiority of our proposed method over other methods". Is this universally true or compared to the selected methods (see item 7)?

10) You have used only three example networks. You should explain why you think that they are representative or provide more experiments.

11) All figures have too small fonts or too small fonts in the figure captions. Figure 2 colour should be changed because it is impossible to see what it represents. Also, Figure 2 left and right figures need some explanation.

A) The English language needs "polishing". For example, you have used the verb "believe" but in some places "assume", "conclude", or "observe" may be what you mean. Line 351: "We use the Equation 5 and the Equation 6" should be "We use Equation 5 and Equation 6" and so on. Please check the English language throughout the text.

B) Line 211: "weak". Please, check the wording.

C) Please check lines 312-313, 322-323, 271.

D) "Snap interaction number". Do you mean the number of interactions? 

Author Response

Thank you very much for your comments and suggestions on our paper. We would like to provide the following responses to your feedback:

1. We have provided explanations for the abbreviations used for the first time in the manuscript and added an abbreviation list at the end of the article. Please refer to line 619 for more details.
2. We have provided explanations for the central concepts mentioned in the manuscript, including: multi-layer network model (lines 159-161), eigenvector centrality (lines 218-230), information entropy (lines 200-216), reference weights (lines 341-345), and made modifications to the sentence in lines 282-283 (lines 313-316). Please refer to the respective lines in the article for more details.
3. According to the paper you provided, we have revised the examples in the manuscript to align with the concept of weak ties and the ideas presented in this paper. This has been very helpful to us. We kindly request permission to cite the article you provided. Please refer to lines 178-182 in the manuscript for further details.
4. We have added a variable list at the end of the paper to ensure that our definitions can be easily referenced. We have also provided brief explanations of the variables in the manuscript, including the one mentioned in your feedback at line 187. Please refer to lines 196-199 and 637-667 for more details.
5. In response to your mention of the mixed use of numbers and variables in Section 3.5, we have performed numerical computations for all the variables and provided explanations for Figures 4 and 5. Please refer to formulas 14, 15, 17, and 18, as well as lines 368-375 and 376-383, for more details.
6. Since the selected datasets are readily available on various network data websites, we consider that this section should be shortened and used to explain the reasons for choosing this type of network data.
7. We have revised the inappropriate wording mentioned in line 400 and clarified the contextual continuity. Please refer to line 445 for more details.
8. We have explained the limitations of our method and presented them as a separate section. Please refer to line 576 for more details.
9. We have provided a brief summary of other indicators as mentioned by you (refer to line 75) and explained the reasons for considering them representative (refer to lines 482-486). We have also highlighted the key differences of our method (refer to lines 102-114). In terms of presenting the experimental results, we have conducted a thorough proofreading (refer to line 599).
10. We have provided a comprehensive description of the networks used, covering their interaction characteristics, time span, and data storage aspects (refer to lines 428-444).
11. We have made modifications to the captions of the figures in the manuscript and adjusted the colors of Figure 2. We have also provided explanations for the left and right subfigures of Figure 2 (refer to lines 163-169).
12. We have corrected the grammar errors and proofread the manuscript for improvement.

Thank you for your valuable feedback and suggestions on our paper. We have made revisions based on the questions and suggestions you provided. Please refer to the revised manuscript for specific changes. Wishing you a pleasant day!

Author Response File: Author Response.docx

Reviewer 2 Report

I appreciate that the reported contribution is sufficiently interesting and it has a good potential. Nevertheless, there are drawbacks concerning the paper, which should be addressed.

1. The mathematical apparatus should be better and clearer linked to the real-world applications of reported contribution, especially the mathematical elements that are presented in section 3. Thus, the authors should describe the algorithmic and functional relevance of mathematical expressions and related mathematical components.

2. The features of practical performance assessment are not clear. Did the authors implement a prototype? If yes, its software architecture should be fully described, and the specifications of the involved hardware should be presented. 

3. Was the performance assessment conducted in some other way, apart from an implemented prototype? If yes, the methodology should be presented and justified.

4. The considered networked structures seem to be rather thin, particularly regarding the number of time-determined network links, even Email-EU-core does not provide an impressive number of links considering the rather extended data collection period, 803 days. Therefore, the authors should discuss on the approach's suitability for real-time or near real-time scenarios. Is the model capable to process/analyze large networked structures in a timely fashion? This should offer a clearer insight on whether the presented model is a proper research construct, or even more, a relevant real-world solution.

5. The potential real-world use cases for reported model should be clearer suggested, and two-three examples would help readers to better understand the importance of reported work.

6. The list of references should be extended with more relevant contributions, especially considering related use cases, which may benefit from such an algorithmic model. As an example, near real-time networks of IoT-based autonomous vehicles could provide a relevant example in this respect, and such an article would be https://www.mdpi.com/2079-9292/10/23/2903 . 

7. The English language should be enhanced through at least one full round of proofreading.

Please see my comments, point 7. In general, the language is acceptable, but it can be improved.

Author Response

Thank you very much for your comments and suggestions on our paper. We would like to provide the following responses to your feedback:

1. We have provided further descriptions of the formulas in Section 3, including the algorithmic functionality and their relevance to real-world applications. Please refer to lines 301-303, 320-321, 331-333, 347-351, and 357-359.

2. We have provided a description of the software architecture used in our study, along with the relevant hardware specifications. Please refer to lines 480-486.

3. We have evaluated the proposed method from two dimensions as mentioned in the manuscript. Please refer to line 452.

4. We have provided a detailed description of the network scale to which our method is applicable and the reasons behind it. Additionally, we have discussed the feasibility of handling real-time data based on the predictive characteristics of our method. Please refer to lines 587-591 for more details.

5. We have included some practical use cases in the manuscript to ensure that readers have a better understanding of our work. Please refer to lines 266-271 for more details.

6. We have added more relevant literature and case studies in the manuscript, including the articles you mentioned. Please refer to line 667 for more details.

7. We have conducted a thorough proofreading of the manuscript and improved the level of English in the article.

Thank you for your valuable feedback and suggestions on our paper. We have made revisions based on the questions and suggestions you provided. Please refer to the revised manuscript for specific changes. Wishing you a pleasant day!

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

1) Use consistent format in subtitles 2.6 and 4.6:

2.6 The eigenvector centrality of nodes -> 2.6 The Eigenvector Centrality of Nodes

4.6 discussion -> 4.6 Discussion

2) In the Conclusions section (lines 599-600), you state: "The experimental results verify that the OESMNIE method outperforms its competitors."

In lines 482-485, you state:  "These selected indictors are all based on local information to construct the similarity between nodes and have been widely applied in link prediction. Therefore, they are similar to OESMNIE method in terms of the topological structure and are representative in the field."

I recommend that you check these and clarify or specify "outperforms its competitors". In what category does the OESMNIE method outperform? Just saying "competitors" is too general in the Conclusions section.

Are there other link prediction methods than "local"? Please clarify this and explain and cite briefly methods that work also for non-local topologies.

Use of "the" in " the OESMNIE method" should be consistent. Lines 360, 484.

Minor/moderate editing of English language required.

Author Response

Thank you very much for your comments and suggestions on our manuscript. They have been extremely helpful to us. Here is our feedback on the questions you raised:

1. We have revised the headings of subtitles 2.6 and 4.6 to ensure their format consistency with the rest of the paper (see lines 285 and 704 for details).

2. We have taken note of your suggestion regarding the term "competitors" used in the conclusion and have made the appropriate modification. We now explicitly state in which category our method performs exceptionally well (see lines 728-729). Furthermore, in addition to the time series-based link prediction methods based on local node similarity, temporal prediction can be classified into five major categories. We have provided a brief explanation of each category in our paper to offer a more comprehensive background and understanding (see lines 49-69)。
3. We have completed the final editing of the manuscript, ensuring the accuracy of the terminology and sentence structure. (Please refer to the marked changes in the manuscript for details.)

Thank you for your valuable feedback and suggestions on our paper. We have made revisions based on the questions and suggestions you provided. Please refer to the revised manuscript for specific changes. Wishing you a pleasant day!

Author Response File: Author Response.docx

Reviewer 2 Report

I acknowledge the receipt and analysis of this revision. I appreciate that the applied improvements warrant for this paper consideration for possible publication. Nevertheless, another round of English proofreading would be advised.

Another round of proofreading would be advised.

Author Response

Thank you very much for your comments and suggestions on our manuscript. They have been extremely helpful to us. Here is our feedback on the questions you raised:

We have completed the final editing of the manuscript, ensuring the accuracy of the terminology and sentence structure. (Please refer to the marked changes in the manuscript for details.)

Thank you for your valuable feedback and suggestions on our paper. We have made revisions based on the questions and suggestions you provided. Please refer to the revised manuscript for specific changes. Wishing you a pleasant day!

Author Response File: Author Response.docx