Blind Source Separation Using Time-Delayed Dynamic Mode Decomposition

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

This paper addresses the limitations of traditional Blind Source Separation (BSS) methods by proposing a novel approach based on time-delayed dynamic mode decomposition (TD-DMD). The study demonstrates improved separation of mixed signals, validated through numerical examples across audio, image, and overdetermined scenarios. While the paper presents a compelling case for TD-DMD, several technical and contextual issues should be addressed to enhance its scientific rigor.

 

1：Although the manuscript compares TD-DMD with PCA and FastICA, it lacks detailed comparison with other advanced BSS techniques, such as convolutional ICA or non-negative tensor factorization. This omission weakens the generalizability and significance of the presented method.

2：The paper predominantly uses synthetic and controlled examples (e.g., predefined mixing matrices, artificial signals). The method's robustness in real-world noisy or high-dimensional data, such as EEG signals or environmental audio, is not evaluated.

3：The choice of the delay embedding parameter and rank reduction parameter lacks a systematic exploration or justification. The optimality of these parameters significantly affects the results.

4：While the manuscript mentions TD-DMD's applicability in overdetermined cases, the results and discussions appear less rigorous than those for standard cases. The specific challenges or adjustments required for overdetermined scenarios are not fully addressed.

5：The introduction lacks references to closely related works in the context of blind source separation of SOBI. Including these two articles can bridge the methodological development:

An advanced scheme for range ambiguity suppression of spaceborne SAR based on blind source separation

Patterns identification using blind source separation with application to neural activities associated with anticipated falls

 

Author Response

Dear Reviewer,

Sincerely appreciate your thorough evaluation of our work and your guidance for its improvement. I hope these changes address your concerns adequately. I am grateful for your input, as it has undoubtedly improved the quality of our paper.

Please find my response in the attached file.

 

Author Response File: Author Response.docx

Reviewer 2 Report

Comments and Suggestions for Authors

（1）In example 1, why is the mixing matrix A set as like?It maybe random to generate.

（2）The Figure 12 is completely black. Is it correct? ICA is worsen than PCA?The separation results are also worsen than the mixed signals. 

（3）In Table 6, which ICA is chosen for comparaison?

（4）The label "Signal-to-Noise Ratio(SNR)"of table 6 is not completed. It should be clearly illustrated.

（5）In the experiements, the BSS with the dynamical systems is not shown.

Author Response

Dear Reviewer,

Sincerely appreciate your thorough evaluation of our work and your guidance for its improvement. I hope these changes address your concerns adequately. I am grateful for your input, as it has undoubtedly improved the quality of our paper.

Please find my response in the attached file.

Author Response File: Author Response.docx

Reviewer 3 Report

Comments and Suggestions for Authors

The paper ``Blind Source Separation Using Time-Delayed Dynamic Mode Decomposition'' by Gyurhan Nedzhibov is extending a numerical method (BSS) handling complex, non-stationary signals aiming to identify the original source of the signal under analysis from mixed observations. The paper is well written and of interest for scientist working in many areas, where signals of complex nature are analysed. In my opinion, the paper can be reconsidered for publication in Computation (Section: Computational Engineering; Special Issue: Mathematical Modeling and Study of Nonlinear Dynamic Processes) where it is submitted, after addressing the following issues.

 

The Introduction is too short and, hence, not informative. I would suggest introducing the reader to the area in a broader way. For instance, I would suggest mentioning more methods of the similar nature. I would also suggest mentioning the areas, where a similar analysis can be applied, e.g.  for predictions of magnetic field reversals, see doi:10.3390/math12030490 

 

Unfortunately, the authors do not discuss wall times of the simulations and if the simulations were performed on a parallel high performance computer (with multiple computational cores). If the simulations were parallel, I wander what was parallel efficiency and scalability.  I recommend the authors to comment on this.

 

It is not clear what was the method (and its implementation) used in numerical examples to compute the SVD decomposition. I would suggest commenting on this in the paper.

 

Future plans to advance that line of research are not presented at all.

Author Response

Dear Reviewer,

Sincerely appreciate your thorough evaluation of our work and your guidance for its improvement. I hope these changes address your concerns adequately. I am grateful for your input, as it has undoubtedly improved the quality of our paper.

Please find my response in the attached file.

Author Response File: Author Response.docx

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

accept

 

Reviewer 2 Report

Comments and Suggestions for Authors

The authors have completed the paper revisions according to the reviewers' comments. 

Reviewer 3 Report

Comments and Suggestions for Authors

The author addressed all  the issues raised in my review. The paper can be published in the present form.