Aging Residual Factorization Machines: A Multi-Layer Residual Network Based on Aging Mechanisms

Round 1

Reviewer 1 Report

The manuscript is aimed at the development of models and algorithms of data analysis to improve the quality of recommendation systems. With the wide application of recommendation systems in many areas, including online shopping, study and work, the problem in question appears to be of practical importance and theoretical interest.

However, the accuracy and completeness of presentation are sometimes not adequate and must be improved to meet publication requirements. Specifically, the text in Section 3, which apparently describes the main approach and thus is the key part of the manuscript, looks too sketchy to follow. This seems to result in the lack or insufficient formal description of problem statement and objective, input and output data, and related notions and concepts. Such an uncomplete presentation, which one can consider uncommon in writing mathematics, makes it difficult to understand and evaluate the actual contribution of the paper.

Some other comments include:

P.1, line 18. The abbreviation ARFM is used without reference to the full term. See also VGG on line 135 and COCO on line 141 of page 3.

P.2, lines 93-94. Wrong punctuation: a superfluous period before and missing period after the formula. See also incorrect or missing punctuation marks on page 4, lines 162-163 and line 194; page 5, lines 203-204 and others.

P.4, line 194. The symbol X is undefined. Other notations that are not formally introduced or defined include f_PI, e, v_i and v_j on line 229 of page 5. Due to the lack of definitions of some elements, the formula on line 211 of page 5 is unclear.

Author Response

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Reviewer 2 Report

Review

1. The authors should carry out a major bibliographic review in addition to updating the references.
2. The authors must contrast the current methodologies and what is proposed.
3. Section 2 can be attached to section 1.
4. The paper's motivation should be better described in terms of the innovation or the contribution that the authors intend to make.
5. The figures in the manuscript are of poor quality, making it difficult to establish what they represent.
6. The authors should explain the imposed conditions in which the designed framework can obtain the results described throughout section 4.
7. There is little discussion of the results, so the authors should delve into this.

Author Response

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Round 2

Reviewer 1 Report

The revised paper does not adequately address all concerns raised. Specifically, the abbreviation ARFM in the abstract is still not spelled out. Incorrect punctuation occurs in formulas accompanied by a list of variables (see, e.g. formula (2) that ends with a period instead of comma). Formula (1) looks confusing: the symbols n, w_J, x_j are not introduced, the index expression j₂=j₁₊₁ seems to read j₂=j₁+1. It is not clear from the paragraph after this formula, where k comes from, and why the number n² of parameters reduces to kn.

The text in Section 3 is still obscure and difficult to follow with the formulas poorly introduced or explained. Specifically, the formula at (2) is not completely understandable. It is not clear what the symbol n stands for (or N should be written instead?), where the label y_i of a sample comes from and what values the variable y_i (and p_i) may take. The symbols X and F appeared in Figure 1 are undefined.

Formula (3) uses the symbol d, the meaning of which is not defined. It is not clear how the symbol X (which is referred to as the set of features) on the left-hand side is connected with the right-hand side. The rest of the formulas are also not entirely clear and raise questions.

Considering that the previous concerns have not been satisfactorily addressed and the issues still remain, the recommendation is to reject the paper.

Author Response

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Reviewer 2 Report

The authors have satisfactorily answered my questions and suggestions. Therefore, a recommendation to publish this manuscript can be extended.

Author Response

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Round 3

Reviewer 1 Report

The mathematical text in the revised version looks more consistent, but still needs further clarification and improvement.

Some related comments and suggestions are as follows:

P.3, line 125. Please add the word “vector” to be more specific here (and in other similar cases):

“Specifically, let the feature be ?, weight be ?,”-> Specifically, let the feature vector be ?, weight vector be ?,”.

P.7, lines 305-308. The symbols ⊙ and R_x are undefined.

P.10, lines 441-445. The symbol W_i (with capital W) mentioned in the text (line 445) does not appear in the formula, which seems to include w_i (with small w) instead.

P.13, lines 611-614. The symbol h_q is undefined. The symbol n is listed in the where-clause on line 614, but does not appear in the formula.

Author Response

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Author Response File: Author Response.docx