Cross-Validation for Lower Rank Matrices Containing Outliers

Round 1

Reviewer 1 Report

Good interesting work.

Author Response

Reviewer 1 suggests a minor revision in the article edition.

Answer from the authors: Thank you for your feedback. The edition was revised and updated by our third author, a native English speaker from the University of Exeter- UK.

Reviewer 2 Report

It would be better if the authors can talk more about the use cases of cross-validation and possible parameters for those use cases so that their simulations can be better evaluated.

Tables do not fit inside the margins.

"et al." written wrongly many times, sometimes without full-stop.

Author Response

2.1 Reviewer 2 suggests: “It would be better if the authors can talk more about the use cases of cross-validation and possible parameters for those use cases so that their simulations can be better evaluated.”

Answer from the authors: The introduction mentions the cases and applied areas where the “optimal” rank of a reduced-rank approximation is required, and the description of the EK method explains to the reader the multiplicative parameters used to determine that rank. Taking this into account, the simulations generate lower rank matrices with various levels of outliers to determine the robustness of the proposed methodology on contaminated matrices. We believe that talking more about it may be a repetition of what has already been described. Please note also the extra paragraphs and table provided from lines 375 onwards, giving further details in response to a request from reviewer 4.

2.2 Reviewer 2 suggests: Tables do not fit inside the margins.

Answer from the authors: This can be adjusted by ASI-MDPI in the final editing process if the article is accepted.

2.3 Reviewer 2 suggests: "et al." written wrongly many times, sometimes without full-stop.

Answer from the authors: All “et al.” of the manuscript were corrected as requested by the reviewer.

2.4 The reviewer requests more references related to cross-validation.

Answer from the authors: The objective of our article is not to carry out a systematic review on cross-validation, however, in the introduction 15 references are presented that we consider adequate both in number and in content on the subject and to which the reader can refer if require more information than what is presented in the article.  

Reviewer 3 Report

This paper has a lot of mistakes which must be corrected before consideration for publication. Abstract, conclusion and all other findings must be improved and presented in the correct way. Authors must omit the basic information from the paper which reader already know and focus of your own findings. 

Author Response

Reviewer three states “This paper has a lot of mistakes which must be corrected before consideration for publication. Abstract, conclusion and all other findings must be improved and presented in the correct way. Authors must omit the basic information from the paper which reader already know and focus of your own findings.”

Answer from the authors: Reviewer 3 is not satisfied with the presentation of the manuscript in several sections but does not specify what the mistakes are that need to be corrected, or what the correct way is for findings to be presented. This reviewer assumes that the reader already knows the “basic” information about the cross-validation method that we describe, but that information is provided for a broader audience (possibly from different areas of knowledge) and that it can be useful in applications in a variety of different areas where real data is obtained in matrix form. Taking into account that reviewers 1,2 and 4 considered our presentation to be adequate, we decided to keep the manuscript as it currently is.

Reviewer 4 Report

The article describes an interesting method for statistical evaluation of data without the need to eliminate outliers. The method is beneficial for disciplines that process empirically obtained data.

I have 2 comments/questions about the article:

- Is the proposed method dependent on the type of distribution of values in the input data?

- What is the time and memory requirement of the algorithm of the proposed method?

Author Response

Reviewer 4 states:

I have 2 comments/questions about the article:

- Is the proposed method dependent on the type of distribution of values ​​in the input data?

- What is the time and memory requirement of the algorithm of the proposed method?

Answer from the authors: From line 375, the two comments made by the reviewer are answered with two paragraphs and a table in red.