Distributed Semi-Supervised Multi-Dimensional Uncertain Data Classification over Networks
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThis manuscript addresses the problem of classifying multi-dimensional data in distributed networks where data is both uncertain and partially labeled. It is generally well-written, the experimental design is comprehensive, and the results demonstrate superiority over several methods. I believe this paper is a candidate for publication after considering the following minor points for improvement.
1- The statement on page 1, lines 39-40, "...a large number of DL approaches have been devised and applied across a range of fields [1–9]" is somewhat vague.To strengthen this section and provide a more solid foundation for readers, I recommend citing some recent, cutting-edge surveys and application-focused works like "Applications of Distributed Machine Learning for the Internet-of-Things: A Comprehensive Survey" or "Unified Distributed Machine Learning for 6G Intelligent Transportation Systems: A Hierarchical Approach for Terrestrial and Non-Terrestrial Networks.". Moreover, including references takles real-world performance and implementation of DL frameworks, such as "Large scale performance analysis of distributed deep learning frameworks for convolutional neural networks" or "Real-world implementation and performance analysis of distributed learning frameworks for 6G IoT applications".
2- While the one-vs-one strategy (section 3.2) is a standard approach, the transformation formula presented in Equation (9) and the definitions of the sets Qj,n,q,r and Rj,n,q,r are quite complex and difficult to follow. The general formula could be explained more clearly, perhaps with a more intuitive description of the mapping process before presenting the formal mathematics.
3- The results in Tables 3-5 should be explained separately and clearly.
4- Figures 4 and 5 have not been mentioned and explained in the text. Furthermore, Figures 3 and 5 do not clearly show the values and trends; they should be zoomed or the scale should be changed in a way that presents the variations. Figures 7-9 should be explained separately and clearly to show the added benefits and comparison.
5- The limitation of the work should be clearly stated, as in this form it seems just based on many theoretical assumptions.
Author Response
Comment 1: The statement on page 1, lines 39-40, ``...a large number of DL approaches have been devised and applied across a range of fields [1–9]" is somewhat vague.To strengthen this section and provide a more solid foundation for readers, I recommend citing some recent, cutting-edge surveys and application-focused works like ``Applications of Distributed Machine Learning for the Internet-of-Things: A Comprehensive Survey" or ``Unified Distributed Machine Learning for 6G Intelligent Transportation Systems: A Hierarchical Approach for Terrestrial and Non-Terrestrial Networks.". Moreover, including references takles real-world performance and implementation of DL frameworks, such as ``Large scale performance analysis of distributed deep learning frameworks for convolutional neural networks" or ``Real-world implementation and performance analysis of distributed learning frameworks for 6G IoT applications".
Response 1: Thank you for your valuable suggestion. In the revised manuscript, we have refined the vague statement by expanding on the applications of DL across diverse fields. We have also cited the four recommended application-focused works and integrated brief analyses to strengthen the section’s foundation. Please refer to lines 37–49 on pages 1–2 for details.
Comment 2: While the one-vs-one strategy (section 3.2) is a standard approach, the transformation formula presented in Equation (9) and the definitions of the sets $\mathcal{Q}_{j,n,q}$ and $\mathcal{R}_{j,n,q}$ are quite complex and difficult to follow. The general formula could be explained more clearly, perhaps with a more intuitive description of the mapping process before presenting the formal mathematics.
Response 2: Thank you for your constructive comment. In the revised manuscript, we have re-explained the definitions of sets $\mathcal{Q}_{j,n,q}$ and $\mathcal{R}_{j,n,q}$, and added an illustrative figure to clarify the transformation process of the one-vs-one decomposition. We believe the description of Equation (9) and the one-vs-one decomposition is now clear. Please refer to Figure 2 on page 6 for details.
Comment 3: The results in Tables 3-5 should be explained separately and clearly.
Response 3: Thank you for your helpful comment. In the revised manuscript, we have discussed the experimental results in Tables 3–5 separately, and we believe the current analysis of the results is clear and detailed. Please refer to pages 18-19.
Comment 4: Figures 4 and 5 have not been mentioned and explained in the text. Furthermore, Figures 3 and 5 do not clearly show the values and trends; they should be zoomed or the scale should be changed in a way that presents the variations. Figures 7-9 should be explained separately and clearly to show the added benefits and comparison.
Response 4: Thank you for your valuable comment. In the revised manuscript, we have supplemented detailed explanations for Figures 6 and 7 (corresponding to Figures 4 and 5 in the previous version), which are available on page 17. Additionally, we have expanded the parameter value investigation range for Figures 5 and 7 (previously Figures 3 and 5 in the previous version). The updated curves now clearly illustrate the performance variation trends of the algorithm, with relevant details provided on pages 16-17.
Furthermore, we have conducted separate in-depth discussions on the results presented in Figures 9-11 (formerly Figures 7-9 in the previous version), and incorporated specific comparisons of the performance among different competing algorithms. For comprehensive details, please refer to pages 19-21 of the revised manuscript.
Comment 5: The limitation of the work should be clearly stated, as in this form it seems just based on many theoretical assumptions.
Response 5: Thank you for your insightful comment. We have elaborated on the limitations of our work in Section 5, which mainly includes two aspects. First, our algorithm is predicated on the assumption that data across all nodes adheres to an identical distribution. Such a premise that may not fully align with the heterogeneity of practical application scenarios. To address this constraint, future work will focus on developing personalized uncertain data learning algorithms tailored for distributed network environments. Second, while the algorithm assumes that uncertain information follows a Gaussian distribution (a supposition that holds in numerous real-world scenarios), non-Gaussian noise may exist in certain cases, potentially leading to performance degradation. Consequently, we also plan to explore and develop advanced algorithms capable of effectively handling non-Gaussian noise in our subsequent research endeavors.
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsOverall, I think that this article is quite good. It has been written in a competent and professional manner, having the following strong points:
(1) Although, this is rather subjective, I believe it investigates an interesting subject.
(2) The organization of the paper is very good. The overall analysis helps the reader understand and appreciate the aim of the paper.
(3) The other noteworthy observation is the good formatting and typesetting of all the math formulas, the Figures and the Tables.
Their command of the English language is also very good.
The only substantial remark I must make is that I, being a computer scientist, have found the technicalities difficult to follow. This combined with the rather lengthy exposition make the overall reading challenging. I think that the proofs and formulas are correct, but to be honest, I am 100% sure. I would like to urge the authors to doublecheck their equations just to be safe. Perhaps a valid suggestion would be to relocate the proofs to an Appendix.
I noticed that there is only one Example, namely Example 1 on page 6. Initially, I thought that more Examples would follow, something that would greatly facilitate the understanding of this paper. I feel that perhaps the authors should enhance their work with more examples, particularly in later Sections.
Finally, the only awkward expression I found was “The computational complexity and communication cost of the dSMUDC method are discussed.” (line 396), which, although correct per se, feels out of place.
Author Response
Comment 1: The only substantial remark I must make is that I, being a computer scientist, have found the technicalities difficult to follow. This combined with the rather lengthy exposition make the overall reading challenging. I think that the proofs and formulas are correct, but to be honest, I am 100$\%$ sure. I would like to urge the authors to doublecheck their equations just to be safe. Perhaps a valid suggestion would be to relocate the proofs to an Appendix.
Response 1: Thank you for your valuable feedback. Following your suggestion, we have streamlined unnecessary expressions and formulas, and relocated the relevant proofs to the Appendix. Additionally, we have carefully rechecked all equations throughout the manuscript to ensure their accuracy. We believe the technical details in the revised version are now clearly presented and more accessible to read.
Comment 2: I noticed that there is only one Example, namely Example 1 on page 6. Initially, I thought that more Examples would follow, something that would greatly facilitate the understanding of this paper. I feel that perhaps the authors should enhance their work with more examples, particularly in later Sections.
Response 2: Thank you for your helpful suggestion. In response, we have supplemented an illustrative figure based on Example 1 to clearly depict the one-vs-one spatial encoding process. Please refer to page 6 for details. Additionally, we have added another figure at the end of the algorithm to illustrate the one-vs-one decoding process, with details available on page 13. We believe the presentation in the revised manuscript is more conducive to readers’ understanding.
Comment 3: Finally, the only awkward expression I found was ``The computational complexity and communication cost of the dSMUDC method are discussed.'' (line 396), which, although correct perse, feels out of place.
Response 3: Thank you for your careful observation. We have revised the awkward expression to make it more coherent with the context of the section. The revised sentence now fits naturally into the narrative. Please refer to lines 401-408 on pages 13-15 for details.
Author Response File: Author Response.pdf
