Multi-Scale Quantitative Direction-Relation Matrix for Cardinal Directions

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

In this paper, two novel quantitative matrix models at different scales for characterizing primary directional relationships, enabling soft classification of qualitative directional relations at both order and coordinate levels were introduced. The introduction of these two quantitative models significantly improves the fidelity of qualitative direction-relations descriptions and establishes a robust conversion mechanism from quantitative vector to qualitative direction-relations, thereby addressing the computational challenges inherent in qualitative directional matrix analysis. However, it requires further improvement to meet the requirements for publication. Specific revisions are suggested as follows:

1. A large number of Figures appear in the paper. Although they are useful for understanding the article, it is suggested that they be appropriately deleted to highlight the main contributions. For example, Figures 1 - 2 can be deleted.
2. Section 3: Please explain in detail what the relationship is between the order matrix and the coordinate matrix? How to convert to each other?
3. Figure 4: What is the purpose of Figure 4? Please elaborate in detail in words.
4. Table 1-2: Please elaborate in appropriate places of basic matrix and segmentation matrix.
5. Line 614: "As illustrated in Figure 16" should be "As illustrated in Figure 19".
6. Section 7: Please also elaborate on the shortcomings of the model proposed in this article, such as whether the computational complexity has increased?

Author Response

Thank you very much for taking the time to review this manuscript. Please find the detailed responses below and the corresponding revisions/corrections highlighted/in track changes in the re-submitted files

Comments 1: A large number of Figures appear in the paper. Although they are useful for understanding the article, it is suggested that they be appropriately deleted to highlight the main contributions. For example, Figures 1 - 2 can be deleted.

Response 1: Thank you for pointing this out. We agree with this comment.

Therefore, we have removed Figures 1-3 and revised the remaining figures.

 

Comments 2: Section 3: Please explain in detail what the relationship is between the order matrix and the coordinate matrix? How to convert to each other?

Response 2: Thank you for pointing this out. We agree with this comment.

In Section 3.4, we have added the computational process from the coordinate matrix to the sequential matrix, using the four targets in Figure 11 as examples (Page 15, Paragraph 1-4, Line 517-540).

 

Comments 3: Figure 4: What is the purpose of Figure 4? Please elaborate in detail in words.

Response 3: Thank you for pointing this out. We agree with this comment.

In the third paragraph of Section 3.4, we have added an explanation for Figure 4 (current Figure 11). It illustrates an example where the sequential matrix cannot distinguish between different targets on the same ray direction. (Page 15, Paragraph 1-4, Line 517-540).

 

Comments 4: Table 1-2: Please elaborate in appropriate places of basic matrix and segmentation matrix.

Response 4: Thank you for pointing this out. We agree with this comment.

We have adjusted the style and position of Table 1-2. (Page 16-17, Tabel 1, Line 556; Page 18-20, Tabel 2, Line 591).

 

Comments 5: Line 614: "As illustrated in Figure 16" should be "As illustrated in Figure 19".

Response 5: Thank you for pointing this out. We agree with this comment.

We have checked and updated all the figure numbers references in the corrigendum.

 

Comments 6: Section 7: Please also elaborate on the shortcomings of the model proposed in this article, such as whether the computational complexity has increased?

Response 6: Thank you for pointing this out. We agree with this comment.

We have added a section at the end of Section 5 summarizing the main drawback of the two quantitative models and future directions for improvement. (Page 23, Line 685-688 ).

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

1. In Formula 5, there is an error in the calculation formula of Ose. Please correct it.
2. In Formula 6, the central object of the matrix uses Oc. What does it mean? What is the connection with Oo in Formula 7 and OoR in Formula 8? Please explain. If the meanings are similar, it is recommended to unify the symbols.
3. From the results in Table 2, whether it is the sequential or positioning matrix, it is impossible to distinguish whether the target is inside or outside the central object. How can this problem be solved?
4. In Line 455，it is proposed to adopt the discretization strategy of lines and polygons into coordinate points for direction calculation. Then, how to discretize specifically, how to control the tile size, and how to obtain the direction information of the discrete points for direct calculation or statistical processing are mentioned in Line 469.

         Secondly, what is the efficiency of using this discretization strategy?

5. From the perspective of the matrix definition, the central value is always 0. Is there any redundancy in the definition?
6. Can the order and location matrices defined in this paper be inferred and converted? For instance, given the order and location matrix of target object B relative to the central object A, can the order and location matrix of A relative to B be inferred? Does the discretization strategy mentioned in the text have a negative effect on reasoning?
7. The application cases in this paper are weak, and all the cases presented are relatively simple. Can it be applied to complex cases? This needs to be strengthened and compared. For example, can the spatial relationship that Wuhan Sports University is located between Wuhan University and China University of Geosciences be inferred using the order and location matrices defined in this paper?

         Secondly, the phrase "multi-resolution spatial reasoning" in the abstract does not effectively convey the meaning in the Application experiments.

Author Response

Thank you very much for taking the time to review this manuscript. Please find the detailed responses below and the corresponding revisions/corrections highlighted/in track changes in the re-submitted files.

Comments 1: In Formula 5, there is an error in the calculation formula of Ose. Please correct it.

Response 1: Thank you for pointing this out. We agree with this comment.

We have corrected the error in Formula 5. (Page 6, Formula 5, Line 289)

Comments 2: In Formula 6, the central object of the matrix uses Oc. What does it mean? What is the connection with Oo in Formula 7 and OoR in Formula 8? Please explain. If the meanings are similar, it is recommended to unify the symbols.

Response 2: Thank you for pointing this out. We agree with this comment.

The central element ranges are defined differently for each matrix: The central element of the MBR external matrix  is the MBR itself; The central element of the MBR overall matrix  is the center of the MBR ; The central element of the external matrix within the local matrix  is the reference object R; The central element of the boundary matrix within the local matrix is the interior of the reference object ; The central element of the internal matrix within the local matrix  is the interior center.

We have revised the central elements in all relevant matrices, ensuring consistency between the corresponding central elements in the sequence matrix and the coordinate matrix (Formula 1-16). (Page 6-14, Formula 1-16, Line 242-513).

Comments 3: From the results in Table 2, whether it is the sequential or positioning matrix, it is impossible to distinguish whether the target is inside or outside the central object. How can this problem be solved?

Response 3: Thank you for pointing this out. We agree with this comment.

Determining whether a target falls within the reference object is decided by the central element of the matrix (). If the central element is 1, the target is within the reference object, and the next-level matrix is activated. The relationship between matrices is as follows: if the central element of the matrix  is 1, the matrix  is computed; if the central element of the matrix  is 1, the boundary matrix  is computed; if the central element of the boundary matrix is 1, the inner matrix is computed. If the central element is 0 during the above process, computation stops. To save space, Table 2 originally presented only the results from the lowest-level matrix. We have supplemented Table 2 with results from the preceding matrix levels to illustrate the interrelationships between different levels of matrices. (Page 18-20, Table 2, Line 591).

Comments 4: In Line 455，it is proposed to adopt the discretization strategy of lines and polygons into coordinate points for direction calculation. Then, how to discretize specifically, how to control the tile size, and how to obtain the direction information of the discrete points for direct calculation or statistical processing are mentioned in Line 469.  Secondly, what is the efficiency of using this discretization strategy?

Response 4: Thank you for pointing this out. We agree with this comment.

Given the extensibility and continuity characteristics of line and surface targets, we first calculate the node parameters of a line or polygon, then merge them to obtain the overall interval result. We have already explained this discrete strategy in the Section 3.2.1. (Page 7, Paragraph 1, Line 252-259).

Comments 5: From the perspective of the matrix definition, the central value is always 0. Is there any redundancy in the definition?

Response 5: Thank you for pointing this out. We agree with this comment.

The explanation regarding the meaning and value assignment of the central element has been fully provided in response to Comments 3. There is no redundancy issue in the definition of the central element; the original experimental results did not list the values of the upper-level matrices, which led to this misconception. (Page 18-20, Table 2, Line 591).

Comments 6: Can the order and location matrices defined in this paper be inferred and converted? For instance, given the order and location matrix of target object B relative to the central object A, can the order and location matrix of A relative to B be inferred? Does the discretization strategy mentioned in the text have a negative effect on reasoning?

Response 6: Thank you for pointing this out. We agree with this comment.

This paper focuses on constructing expression models and their precision characteristics, without yet considering their reasoning properties. However, theoretically speaking, for point-to-point scenarios, the new model can achieve reverse reasoning between two objectives. For extensible objectives, the model's reasonability will be one of our next research directions. As insufficient research has been conducted, the paper has omitted descriptions of reasoning properties. (Page 1, Paragraph 1, Line 16-32).

Comments 7: The application cases in this paper are weak, and all the cases presented are relatively simple. Can it be applied to complex cases? This needs to be strengthened and compared. For example, can the spatial relationship that Wuhan Sports University is located between Wuhan University and China University of Geosciences be inferred using the order and location matrices defined in this paper? Secondly, the phrase "multi-resolution spatial reasoning" in the abstract does not effectively convey the meaning in the Application experiments.

Response 7: Thank you for pointing this out. We agree with this comment.

We are most grateful for your suggestions regarding the applied experiments. We have incorporated your feedback to refine and supplement the experimental design.

The explanation concerning multi-scale reasoning has already been addressed in the preceding point. (Page 20-21, Figure 15 and Table 3, Line 623-624; paragraph 3-4, Line 605-622)

Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

The paper is supposed to be a review article about cardinal direction relations. I am not entirely sure what the actual contribution of the paper is, or what it is intended to be. The authors have previously published the Multiscale Quantitative Direction-Relation Matrix in a paper. The paper at hand seems to extend this approach, but the actual extension does not become clear. Is it a review or a research article?

Generally, the paper is very difficult to follow. This is because of grammatical errors, imprecise wording, very long sentences, repetitions in the text and the long and confusing names of mathematical models. I don’t have the feeling that the authors did a proofread before the submission.

All parts of the paper should be carefully rewritten.

Please be precise when describing the intended goals of the paper and clearly separate it from previous work. And follow a clear storyline without repetitions.

Some more detailed comments, but this by far not a complete list:

• Line 49: literature references[8] [10-27]; I have never seen such a reference. 19(!!!) papers which is half of the cited literature papers are referenced from one sentence. Could you please be a bit more precise with your references!
• Lines 236-251 are doubled by lines 252-265
• Formula 2 looks incomplete
• Figure 7b seems to be wrong, that’s not a matrix

Comments on the Quality of English Language

All parts of the paper should be carefully rewritten.

Author Response

Thank you very much for taking the time to review this manuscript. Please find the detailed responses below and the corresponding revisions highlighted track changes in the resubmitted files.

Comments 1: The paper is supposed to be a review article about cardinal direction relations. I am not entirely sure what the actual contribution of the paper is, or what it is intended to be. The authors have previously published the Multiscale Quantitative Direction-Relation Matrix in a paper. The paper at hand seems to extend this approach, but the actual extension does not become clear. Is it a review or a research article?

Response 1: Thank you for pointing this out.

This paper is not a review article but a research paper. The primary innovation lies in proposing two novel quantitative directional relationship matrix models. These models differ from any existing pyramidal model, employing quantitative indicators rather than qualitative binary values as matrix elements. The new models utilize ordinal parameters and coordinate parameters respectively, achieving two levels of quantitative description for cardinal directions. This not only enhances the accuracy of existing principal direction models but also serves as a computational framework for the original qualitative matrices. The primary reason for this misunderstanding likely stems from the original paper's extensive focus on describing the pyramid model. We have revised the content of abstract, Chapter 2 and Section 1 of Chapter 3 to emphasize the distinctions between the new models and existing models.

(Page 1, Paragraph 1, Line 16-32; Page 4, Paragraph 1-2, Line 122-141; Page 5-6, Line 173-232;)

 

Comments 2: Generally, the paper is very difficult to follow. This is because of grammatical errors, imprecise wording, very long sentences, repetitions in the text and the long and confusing names of mathematical models. I don’t have the feeling that the authors did a proofread before the submission. All parts of the paper should be carefully rewritten. Please be precise when describing the intended goals of the paper and clearly separate it from previous work. And follow a clear storyline without repetitions.

Response 2: Thank you for pointing this out.

We have carefully reviewed the overall structure and content of the paper to make it clearer and more accessible.

Regarding the English language issues in the paper, we submitted it to the journal's recommended English editor for re-examination and revision of the English text, ensuring the article is free from grammatical errors and stylistic concerns.

 

Comments 3: Line 49: literature references [8] [10-27]; I have never seen such a reference. 19(!!!) papers which is half of the cited literature papers are referenced from one sentence. Could you please be a bit more precise with your references!.

Response 3: Thank you for pointing this out. We agree with this comment.

We have examined and revised the citations of the literature within the paper.

(Page 2, Paragraph 4, Line 79-95)

 

Comments 4: Lines 236-251 are doubled by lines 252-265.

Response 4: Thank you for pointing this out. We agree with this comment.

We have reorganized this section and removed redundant content.

(Page 6, Paragraph 3, Line 223-232)

 

Comments 5: Formula 2 looks incomplete.

Response 5: Thank you for pointing this out. We agree with this comment.

We have revised the formula.

(Page 7, Formula 2, Line 249)

 

Comments 6: Figure 7b seems to be wrong, that’s not a matrix.

Response 6: Thank you for pointing this out. We agree with this comment.

We have corrected the figure caption (Figure 5).

(Page 9, Figure 5, Line 301)

Author Response File: Author Response.docx

Reviewer 4 Report

Comments and Suggestions for Authors

This study presents order and coordinate matrices to differentiate directional relationships between multiple targets within the same directional title. The experimental assessment confirms the new models improve directional relationship presion. However, the following areas could be improved. Please see the attached document.

Comments for author File: Comments.pdf

Author Response

Thank you very much for taking the time to review this manuscript. Please find the detailed responses in the attachment and the corresponding revisions/corrections highlighted/in track changes in the re-submitted files.

Author Response File: Author Response.pdf

Reviewer 5 Report

Comments and Suggestions for Authors

Modeling directional spatial relationship among spatial objects is an essential research topic in spatial database and spatial analysis. It is also important in various GIS applications. Researchers have made tremendous efforts in this area from using various means. Limited success has been achieved on building precise quantitative directional relationship models.

This work introduces order matrix and coordinate matrix in the four level multi scale pyramids to address the limitations of traditional rigid qualitative classifications. The concepts and definitions proposed demonstrate technical completeness in mathematical formalization. And the integration of quantitative and qualitative models within a pyramid structure is conceptually coherent although computationally heavy and following available methodologies. To validate the performance of the proposed model for representing directional relationships, the authors designed three simulation datasets and introduced rotation and translation. Comparisons of accuracy and completeness were conducted.

The manuscript is structurally sound and well written with a nice summary of available works.

 

However, the basic idea of this work represents a limited advancement, especially in the context of latest progress of spatial artificial intelligence. The two matrices can add quantitative parameters but remain matrix model’s inherent rigidity, which does not overcome the discretization of space into tiles. More details are expected concerning some parameter definitions, for example designation of reference origins and projection distances.

More experiments are expected by engaging modern spatial data types, such as 3D point clouds, dynamic spatial trajectories. And realistic operations other than synthetic rotations or translations in real-world scenarios are necessary to validate the performance of the newly proposed model.

Notably, latest ideas from contemporary advancements in spatial AI, multimodal reasoning, spatial representation learning, and vision-language models can be introduced into modeling directional relationships. Comparisons are limited to traditional qualitative models rather than building benchmarks based on deep learning for example.

 

Author Response

Thank you very much for taking the time to review this manuscript. Please find the detailed responses below and the corresponding revisions highlighted track changes in the re-submitted files.

Comments 1: The basic idea of this work represents a limited advancement, especially in the context of latest progress of spatial artificial intelligence.

Response 1: Thank you for pointing this out.

We have added an analysis of the current applications and future trends of spatial relationships in the field of spatial artificial intelligence in Section 1 (Line 58-69).

 

Comments 2: The two matrices can add quantitative parameters but remain matrix model’s inherent rigidity, which does not overcome the discretization of space into tiles.

Response 2: Thank you for pointing this out.

In order to unify two quantitative matrices with a qualitative matrix of principal directions and achieve the conversion of directional relationships across different scales, we have retained the directional matrix's directional segmentation within the quantitative matrices. The two new matrices serve the qualitative descriptive model of cardinal directions. Therefore, both of them must first be based on the cardinal direction reference frame and the concept of directional tiles partitioning from qualitative directional descriptions. The quantitative descriptions of the two different directional tiles yield distinct results, enabling the new model to perform soft classification of directional relationships.

 

Comments 3: More details are expected concerning some parameter definitions, for example designation of reference origins and projection distances.

Response 3: Thank you for pointing this out.

We have added explanations and clarifications of these parameters in the article (Line 372-378).

 

Comments 4: More experiments are expected by engaging modern spatial data types, such as 3D point clouds, dynamic spatial trajectories. And realistic operations other than synthetic rotations or translations in real-world scenarios are necessary to validate the performance of the newly proposed model.

Response 4: Thank you for pointing this out.

Since existing directional relationship models primarily target two-dimensional spaces, the models presented in this paper is also constructed based on two-dimensional space and cannot address the calculation of orientation features for 3D point clouds.

We conducted an experiment with dynamic spatial trajectories in Section 4.1.1 (Figure 13), using real-world data to validate the expressive accuracy of the new models and compare them with other models.

Comments 5: Notably, latest ideas from contemporary advancements in spatial AI, multimodal reasoning, spatial representation learning, and vision-language models can be introduced into modeling directional relationships. Comparisons are limited to traditional qualitative models rather than building benchmarks based on deep learning for example.

Response 5: Thank you for bringing this to our attention. We acknowledge the importance of integrating contemporary advancements in spatial multimodal reasoning, spatial representation learning, and vision-language models into the modeling of directional relationships. While our paper primarily focuses on traditional formal models and their expressive precision, we recognize the relevance of LLMs and AI in this area.

In response to your comment, we have included a discussion in the introduction regarding the relationship between directional relational models and LLMs/AI (Section 1, Line 58-69). Additionally, we emphasize in the conclusion that exploring the integration of these models will be a key focus of our future research efforts (Section 5, Line 750-754). We appreciate your suggestion and are committed to advancing this line of inquiry.

Reviewer 6 Report

Comments and Suggestions for Authors

1. In Formula 4, there are three O_N, but O_S and O_W are missing.
2. The rectangular coordinate system of the plane is applied in the text, but the conventions on its coordinate axes and their directions are lacking.
3. For example, lines 290 to 296, etc. It is illogical to discuss the limitations of the model in "3". If it is an existing model, it should be described in "2", and if it is a model proposed or improved in this paper, it should be discussed in "5". In a similar situation, the content of the first paragraph in Section 4.2 is also illogical.
4. Both b and c in Figure 15 are the West Campus of China University of Geosciences. One of them should be the North West Campus of China University of Geosciences.
5. The discussion was not based on genuine evidence and merely presented the conclusion the author believed in directly, lacking a reasoning process from the calculation results, others' research to the conclusion.

Author Response

Thank you very much for taking the time to review this manuscript. Please find the detailed responses below and the corresponding revisions/corrections highlighted/in track changes in the re-submitted files.

Comments 1: In Formula 4, there are three , but   and   are missing.

Response 1: Thank you for pointing this out.

We have revised the errors of Formula 4.

 

Comments 2: The rectangular coordinate system of the plane is applied in the text, but the conventions on its coordinate axes and their directions are lacking.

Response 2: Thank you for pointing this out.

In Section 3.4, we have added the computational process from the coordinate matrix to the sequential matrix, using the four targets in Figure 11 as examples (Page 15, Paragraph 1-4, Line 517-540).

 

Comments 3: For example, lines 290 to 296, etc. It is illogical to discuss the limitations of the model in "3". If it is an existing model, it should be described in "2", and if it is a model proposed or improved in this paper, it should be discussed in "5". In a similar situation, the content of the first paragraph in Section 4.2 is also illogical.

Response 3: Thank you for pointing this out.

The content from lines 290 to 296 is moved to the end of the second paragraph in Section 2.1 (Line 148-156).

The content of the first paragraph in Section 4.2 has been moved to the end of Section 3.1 (Line 253-261).

 

Comments 4: Both b and c in Figure 15 are the West Campus of China University of Geosciences. One of them should be the North West Campus of China University of Geosciences.

Response 4: Thank you for pointing this out.

We have replaced the original image in Figure 15 c.

 

Comments 5: The discussion was not based on genuine evidence and merely presented the conclusion the author believed in directly, lacking a reasoning process from the calculation results, others' research to the conclusion.

Response 5: Thank you for pointing this out.

In Section 4.1.1, we have provided the application experiment examples for a group of dynamic trajectory points and included comparative data with other models in the Table 1, analyzing and comparing the accuracy of the new models against existing models.

Additionally, Section 4.2 incorporates discussion of the novel model (Line 651-657).

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have revised the paper according to my opinions. I would like to see it published in IJGI.

Author Response

Thank you for your positive feedback. We appreciate your support and look forward to the publication of the paper in IJGI.

Reviewer 2 Report

Comments and Suggestions for Authors

This paper has been meticulously revised. It is recommended that this paper be published in this journal.

Author Response

Thank you for your positive feedback. We appreciate your support and look forward to the publication of the paper in IJGI.

Reviewer 4 Report

Comments and Suggestions for Authors

This study has been greatly improved. However, the following issues require further attention:

• Lines 133, 317, 350

Different notations such as “3*3” or “3x3” are used interchangeably. Please unify these expressions to maintain a consistent style throughout the manuscript.

• Figure 8

What does the “Q” mean? Plase clarify its meaning or definition, as it does not correspond to any variable in Equation (7).

(3) Line 412

where BO_R denotes the interior of the reference object R. Could the authors clarify the meaning of the letter “B”? It appears to relate to “boundary,” but this not explicitly explanined.

• Equation (9)

Equation (9) contains the expression , while Equation (8) uses . Please verify whether these expressions are intended to be consistent or if they represent distinct mathematical objects.

• Figure 12

The coordinates labeled as “XE1”, “XN1” in Figure 12 appear to show 5 and 3, respectively. However, these numbers seem to be be inversed relative to their positions in the figure. Please review and correct them accordingly.

Author Response

Thank you very much for taking the time to review this manuscript. Please find the detailed responses below and the corresponding revisions highlighted track changes in the re-submitted files.

Comments 1: Lines 133, 317, 350

Different notations such as “3*3” or “3x3” are used interchangeably. Please unify these expressions to maintain a consistent style throughout the manuscript.

Response 1: Thank you for pointing this out.

We have corrected the error in Lines 133. All definitions are uniformly represented in the “3×3” format.

 

Comments 2: Figure 8，What does the “Q” mean? Please clarify its meaning or definition, as it does not correspond to any variable in Equation (7).

Response 2: Thank you for pointing this out.

Q in Figure 8b is a target point located northeast of the exterior region within theMBR. Using the two target points P and Q as examples, we illustrate the projection distance and the method for determining the primary direction outside the MBR.

We have added a sentence before the Definition 4 to explain the meaning of this example.

 

Comments 3: Line 412, where BOR denotes the interior of the reference object R. Could the authors clarify the meaning of the letter “B”? It appears to relate to “boundary,” but this not explicitly explained.

Response 3: Thank you for pointing this out.

To distinguish directional tile definitions across different topological regions, we use distinct initial letters to represent each region. For example, B denotes boundary, and all corresponding directional tiles share the initial letter B. , for instance, represents the central element of the boundary. We have added explanatory notes before Equation 3 (Line 315-321), Equation 8 (Line 410-414) and Equation 9 (Line 432-437).

 

Comments 4: Equation (9). Equation (9) contains the expression, while Equation (8) uses . Please verify whether these expressions are intended to be consistent or if they represent distinct mathematical objects.

Response 4: Thank you for pointing this out.

We have added explanatory notes before Equation 3 (Line 315-321), Equation 8 (Line 410-414) and Equation 9 (Line 432-437).

 

Comments 5: Figure 12, The coordinates labeled as “XE1”, “XN1” in Figure 12 appear to show 5 and 3, respectively. However, these numbers seem to be inversed relative to their positions in the figure. Please review and correct them accordingly.

Response 5: Thank you for pointing this out.

The letters in Figure 12 are correct; we have corrected Equations 17–22 (Line 586-594).

Author Response File: Author Response.docx

Reviewer 5 Report

Comments and Suggestions for Authors

The authors made relevant revisions.

A remained concern in my last review was comparisons of results from this traditional matrix based approach with those from available LLMs tools, using the "application experiments".

Author Response

Thank you very much for taking the time to review this manuscript. Please find the detailed responses below and the corresponding revisions highlighted track changes in the re-submitted files.

 

Comments 1: A remained concern in my last review was comparisons of results from this traditional matrix based approach with those from available LLMs tools, using the "application experiments".

Response 1: Thank you for pointing this out.

Based on your feedback, we have added comparative experiments with big data models in the application testing section and conducted the analysis. (Line 719-740)