MSGL+: Fast and Reliable Model Selection-Inspired Graph Metric Learning^†

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This study presents a novel approach to acquiring knowledge of graph structures based on data features, drawing inspiration from both model selection techniques and graph spectral signal processing methodologies. The method, called MSGL+, is based on a learnable kernel function that represents the inverse covariance matrix of the graph nodes, and uses a convex optimization objective with linear constraints to find the optimal kernel parameters. The paper claims that MSGL+ has several advantages over existing methods, such as graphical Lasso and feature-based graph learning, in terms of efficiency, accuracy, and scalability.

The paper is well-written and organized, and provides a clear motivation and background for the problem. The paper also reviews the related work and highlights the main contributions and novelties of MSGL+. The paper introduces the mathematical formulation and the optimization algorithm of MSGL+ in detail, and provides some theoretical analysis and properties of the method. The paper also evaluates the performance of MSGL+ on various applications, such as binary and multi-class classification, binary image denoising, and time-series analysis, and compares it with several baselines. The paper shows that MSGL+ achieves competitive or better accuracy results with much faster running time than the baselines.

 

The paper is original and significant, as it proposes a new and efficient way to learn graph structures from data features, which is a challenging and important problem in many domains. The paper also demonstrates the applicability and effectiveness of MSGL+ on different types of data and tasks. The paper is technically sound and rigorous, as it provides a solid mathematical foundation and a thorough experimental evaluation for MSGL+.

The paper could be improved by addressing the following comments:

- The study lacks sufficient elucidation and explanation for the selection of the polynomial function and the parameter P in the formulation of MSGL+. It would be beneficial to provide some insights or examples on how these choices affect the graph structure and the performance of the method.

- The paper does not discuss the limitations or drawbacks of MSGL+, such as the sensitivity to the choice of the kernel order, the scalability to large graphs, or the robustness to noise or outliers. It would be interesting to see some analysis or experiments on these aspects, and how they could be mitigated or overcome.

- Page 6: in the equation (6) , on the right-hand side,  it is noted that the right-hand side of the equation lacks the presence of the "-" sign..

- Page 6: in the equation (7) , in the first component of the vector, the power "1" is missing on both L and \lambda_{k}.

- Page 6: in the equation (8) , in the first component of the vector, the power "1" is missing on both L and \lambda_{k}.

Overall, the paper is a valuable contribution to the field of graph learning, and I recommend it for acceptance with minor revisions.

 

Author Response

We thank the reviewer deeply for conducting a thorough examination of our manuscript.

We are also thankful for all the valuable and insightful comments provided.

In the process of addressing them, we believe that the quality of our manuscript has been improved significantly.

Please see the attachment for the detailed responses to the comments of the reviewer.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

The authors presented well written manuscript, with proper scientific structure and coherent English. They proposed interesting model that tackles well increasing number of features in graph-based learning models. The results outperformed other models in biomedical binary datasets such as diabetes and liver disorders. These results suggest potential utility of this model in the field of medicine. However, authors did not rise this issue neither in discussion nor in conclusions section. Authors did not support their rationale for model improvements (bullet points lines 80-107). In the current form those statements look like private opinion of the authors, that was not supported by the current literature. This should be improved. Finally, in the conclusion’s sections, author cited other authors works what is inappropriate. Conclusions should have been solely drown on the authors own results. Overall, if authors address mentioned concerns, article will be suitable for publication. 

Author Response

We thank the reviewer deeply for conducting a thorough examination of our manuscript.

We are also thankful for all the valuable and insightful comments provided.

In the process of addressing them, we believe that the quality of our manuscript has been improved significantly.

Please see the attachment for the detailed responses to the comments of the reviewer.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The manuscript with the title "MSGL+: Fast and Reliable Model Selection-Inspired Graph Metric Learning" builds on the author's earlier work. Compared to the existing MSGL, the newly proposed MSGL+ changes the optimisation function, which affects both execution time and accuracy. There are no obvious grammatical or linguistic errors, but the manuscript lacks readability.

Most of the formulae proposed in this manuscript are from previous research and should be treated as such and only referenced from the original manuscript or moved to the appendix.

The proposed algorithm (Alg. 1) has not changed, but it optimises other optimisation functions. So the question is whether the contribution is a new algorithm or a new metric (optimisation function) that is then optimised. I would suggest separating these two terms.

I also question the statistical significance of the improvement compared to other algorithms (especially MSGL). An appropriate statistical comparison should be made.

Author Response

We thank the reviewer deeply for conducting a thorough examination of our manuscript.

We are also thankful for all the valuable and insightful comments provided.

In the process of addressing them, we believe that the quality of our manuscript has been improved significantly.

Please see the attachment for the detailed responses to the comments of the reviewer.

Author Response File: Author Response.pdf