Frac-Vector: Better Category Representation

Round 1

Reviewer 1 Report

In my opinion, the manuscript is well written and interesting one. Authors are advised to check the language using Grammerly, because it seems that there are several couples of sentences having no space in between e,g., see Section 1 (lines 32-34), Section 2 (lines 67-69) Section 4 (lines 182-188).

Section "5 Discussion" can be replaced by "5 Discussion and future directions".

Author Response

   Dear editors and reviewers,

    Many thanks for the insightful comments and suggestions. The comments are all valuable and helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have made corresponding revision according to your advice. Words in red are the changes we have made in the text. 

    The main correction are as following:

1. We have linguistically revised the entire manuscript, using Deepl, and carefully proofread the entire manuscript;

2. Section 5 has been changed to Discussion and Future Directions.

3. Major changes have been made to the INTRODUCTION and some terms have been explained or replaced.  

4. "the distance" refers to Euclidean distance. I should specify this in the revision, but I'm very sorry to ignore it in this revision.  

5. Regarding the fractional derivatives, in the revision we only briefly explained them at the beginning of the introduction, and in Section 3 we construct vectors based on the numerical solution of the fractional derivative to represent the category, with 1 at the target position, i.e. the position of x. The values at non-target positions are the other coefficients. Perhaps we should have elaborated more to make it more readable.

Author Response File: Author Response.docx

Reviewer 2 Report

The paper is quite well-written and the results are quite clearly presented.

I have just a couple of minor remarks.

1) The introduction should be written in a more readable way, the terminology must be clarified for non-experts, whenever possible. 

2) Some minor English correction is required. For example, the sentence on lines 22-23 (page 1) may be reformulated (a predicate is missed). 

3) There are some unclear sentences. For example (Page 2, Line 75), I do not uinderstrand what does the sentence "the distance between any two vector is unequal" mean.

4) It is a bit unclear for me which kinds of functions do the authors operate with. For example: are the fractional derivatives, introduced in the paper, regular functions or distributions?

Author Response

    Dear editors and reviewers,

    Many thanks for the insightful comments and suggestions. The comments are all valuable and helpful for revising and improving our paper, as well as the important guiding significance to our researches. We have made corresponding revision according to your advice. Words in red are the changes we have made in the text. 

    The main correction are as following:

1. We have linguistically revised the entire manuscript, using Deepl, and carefully proofread the entire manuscript;

2. Section 5 has been changed to Discussion and Future Directions.

3. Major changes have been made to the INTRODUCTION and some terms have been explained or replaced.  

4. "the distance" refers to Euclidean distance. I should specify this in the revision, but I'm very sorry to ignore it in this revision.  

5. Regarding the fractional derivatives, in the revision we only briefly explained them at the beginning of the introduction, and in Section 3 we construct vectors based on the numerical solution of the fractional derivative to represent the category, with 1 at the target position, i.e. the position of x. The values at non-target positions are the other coefficients. Perhaps we should have elaborated more to make it more readable.

Author Response File: Author Response.docx