Round 1

Reviewer 1 Report

This paper presents a cold start user-item model (CSUIM) of bipartite graphs for recommendation in social networks. Based on this framework, the authors develop a set of parameters to enable the model to efficiently and effectively recommend nodes in social networks under sparse settings. Several simulations generating networks of the proposed method have been conducted to verify the theoretical properties. And the experimental results on real-life networks also validate the effectiveness of the method. In summary, the studied problem is interesting and practical, and authors provide theoretical and experimental estimations for the most important parameters. However, there are several important problems: 1) authors have not compared the proposed methods with recently proposed related methods. It would be more convicing if a comparative experiments with previous bipartite graph based methods or recommendation methods for cold-start problems (see the suggested related work) 2) Another concern is that the execution time plays an important role of this method. Therefore, it is better to provide some analysis for the time complexity. 3) Many important recent related work about recommendation have not been discussed and mentioned in related work. Just to list a few: a) MMALFM: Explainable Recommendation by Leveraging Reviews and Images. TOIS, 37(2), 2019; b)Attention-based Adaptive Model to Unify Warm and Cold Starts Recommendation, CIKM 2018; c) BiRank: Towards Ranking on Bipartite Graphs, TKDE 2018.

Author Response

Author's Response to Reviewer 1 Comments

Point 1: authors have not compared the proposed methods with recently proposed related methods. It would be more convicing if a comparative experiments with previous bipartite graph based methods or recommendation methods for cold-start problems (see the suggested related work) 

Response 1: Thank you for this suggestion and the attached list of references. Regrettably, these various research directions are a bit hard to compare because they make use of different types of information (though partially overlapping). CSUIM does not incorporate contents, so the content-based filtering  is hard to compare. Also, such issues as reviews (that represent to some extent the content) cannot be incorporated. Furthermore, the other systems are not that interested in the future history (or the statistics of that history), while this research concentrates on this aspect.  

Nonetheless, it is worth dealing with in future research. The starting point should be, however, establishing a common ground for a fair comparison. While a growth model like ours may evolve without further input, how should one handle the “moment” models: by adding the really ingoing new links or the ones predicted by the recommender system? And to whom the new link should be added: randomly or to a most likely future agent? Each decision would impact the comparison of the models, and probably a full-fledged comparative study is a good stuff for further research. The next question would be how to incorporate in our model additional information like item contents, reviews, user preferences, etc.    

Point 2: Another concern is that the execution time plays an important role of this method. Therefore, it is better to provide some analysis for the time complexity. 

Response 2: Thank you for this suggestion. I studied the time complexity issues in my PhD Theses. In this paper, I did not want to detract the user from the primary concern that is building a model of a growing network. 

Point 3: Many important recent related work about recommendation have not been discussed and mentioned in related work. Just to list a few: a) MMALFM: Explainable Recommendation by Leveraging Reviews and Images. TOIS, 37(2), 2019; b)Attention-based Adaptive Model to Unify Warm and Cold Starts Recommendation, CIKM 2018; c) BiRank: Towards Ranking on Bipartite Graphs, TKDE 2018.

Response 3: Thank you for these suggestions. I now mention the papers you indicate.

Reviewer 2 Report

The topic of this paper is paramether estimation growth model for bipartite graphs, considering the Cold Start User-Item problem and real-world data for CSUIM.
The paper is well written and explains a topic dense of mathematical notations in an understandable way.

There are some issues to clarify:

- the use of 'we' in the text even if it is a single author
- lines 137-142: bipartite graph: an introduction to this object should be mentioned (also in the introduction section) while in this paragraph can be inserted some schemes to introduce the problem with specific references
- related work: this section can be reorganized to include sections 3 and 4, highlighting with a table the different approaches used in literature
- given the hints in the text, it appears necessary a section where references to the reccomander systems can be clarified and schematized, so that can be made explicit the links with the techniques illustrated in this work.

Author Response

Author's Response to Reviewer 2 Comments

Point 1: the use of 'we' in the text even if it is a single author

Response 1: Wherever appropriate, "we" was changed to some other form. Please note that in spite of the fact that the paper has only one author, it is a result of the work of a broader research group. In Particular, the Chojnacki generator was created by himself, and my work with respect to that generator was restricted to opening for the research performed in this paper. 

Point 2: lines 137-142: bipartite graph: an introduction to this object should be mentioned (also in the introduction section) while in this paragraph can be inserted some schemes to introduce the problem with specific references

Response 2: A more detailed explanation of the term "bipartite graph" was added before these lines and in the introduction. 

Point 3: related work: this section can be reorganized to include sections 3 and 4, highlighting with a table the different approaches used in literature

Response 3: Sections 3 and 4 were turned to subsections of section 2. 

Point 4: given the hints in the text, it appears necessary a section where references to the recommender systems can be clarified and schematized, so that can be made explicit the links with the techniques illustrated in this work.

Response 4: A next subsection was added to section 2 with some additional references to recommender systems. However, not all references were pulled together because the current places where they occur better explains their purpose from the perspective of this research.

Round 2

Reviewer 1 Report

In this revision, authors put efforts on revising the writing. About the raised concerns, I think the response provided by the reviewers make senses. I appreciate that authors colored the place where they make revision. Also, lots of details about experiments are given. I accepted the current version without futher concerns.

Author Response

Point 1: I accepted the current version without futher concerns.(...) English language and style are fine/minor spell check required

Response 1: Thank you for the review and such a quick response. I double-checked the spelling and made some corrections.