A black-winged kite improved fuzzy clustering handling imbalanced uncertain data

Hung Tran-Nam; Ha Che-Ngoc

doi:10.1371/journal.pone.0349753

Peer Review History

Original SubmissionOctober 22, 2025
12 Nov 2025 Decision Letter - Zeashan Khan, Editor -->PONE-D-25-57245-->-->A Black-winged Kite Improved Fuzzy Clustering handling Imbalanced Uncertain Data-->-->PLOS ONE Dear Dr. Che Ngoc, Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process.-->--> -->-->Please submit your revised manuscript by Dec 27 2025 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file. 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There is no requirement to cite these works unless the editor has indicated otherwise. Additional Editor Comments: This paper describes an improved fuzzy clustering algorithm to handle imbalanced uncertain data. Despite an interesting approach, the authors must highlight the novelty of the work by comparing with other clustering algorithms. It is recommended to work on the reviewer's comments for quality improvement. [Note: HTML markup is below. Please do not edit.] Reviewers' comments: Reviewer's Responses to Questions -->Comments to the Author 1. Is the manuscript technically sound, and do the data support the conclusions? The manuscript must describe a technically sound piece of scientific research with data that supports the conclusions. Experiments must have been conducted rigorously, with appropriate controls, replication, and sample sizes. The conclusions must be drawn appropriately based on the data presented. --> Reviewer #1: Yes Reviewer #2: Partly ******** -->2. Has the statistical analysis been performed appropriately and rigorously? --> Reviewer #1: Yes Reviewer #2: Yes ****** -->3. Have the authors made all data underlying the findings in their manuscript fully available? The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.--> Reviewer #1: Yes Reviewer #2: Yes ****** -->4. Is the manuscript presented in an intelligible fashion and written in standard English? PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.--> Reviewer #1: Yes Reviewer #2: Yes ****** -->5. Review Comments to the Author Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)--> Reviewer #1: The manuscript presents a novel two-stage clustering algorithm designed to handle imbalanced and uncertain data. The method combines an optimization with an improved enhanced clustering framework. These The following the main concerns with regarding proposed approach. 1. There is no comparison with deep clustering or modern ensemble methods that also handle imbalance and uncertainty. address 2. The convergence proof is provided; however, the exposition is dense and may be challenging for readers without a strong background in optimization. Including a more intuitive explanation or a summary of the convergence properties would enhance accessibility. 3. Parameter sensitivity analysis is essential for validating the robustness of the results. 4. Some sentences contain minor grammatical errors. 5. In some places, the acronym BKIFF is written inconsistently. 6. Some figures (e.g., Fig. 2, Fig. 10) are not referenced in the article. Reviewer #2: 1. First of all, the paper is not well organized. Introduction, experimental work conclusion are not Labeled with proper sections which makes ambiguous to read. 2. Problem statement and motivation of the method are not clear. 3. “Given the aforementioned gaps, this study introduces a novel approach call “ – is written in two time at introduction section 4. Related works section is absence in this paper. 5. In Methodology, subsections are confusing due to Labels are not mentioned. Also, motivation of each equation is not well defined. 6. Flow of the Fig. 3 is not clear. Moreover, the framework of the proposed method is normally expected at the Methodology section. 7. In experimental section, compared methods are quite older. There should be some new existing methods to compare performance. 8. Conclusion should be rewritten. ****** -->6. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files. If you choose “no”, your identity will remain anonymous but your review may still be made public. Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.--> Reviewer #1: Yes: Mohammad Hossein Moattar Reviewer #2: No ******** [NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.] To ensure your figures meet our technical requirements, please review our figure guidelines: https://journals.plos.org/plosone/s/figures You may also use PLOS’s free figure tool, NAAS, to help you prepare publication quality figures: https://journals.plos.org/plosone/s/figures#loc-tools-for-figure-preparation. NAAS will assess whether your figures meet our technical requirements by comparing each figure against our figure specifications. https://doi.org/10.1371/journal.pone.0349753.r001
Revision 1
2 Jan 2026 Author Response I. Additional Editor Comments This paper describes an improved fuzzy clustering algorithm to handle imbalanced uncertain data. Despite an interesting approach, the authors must highlight the novelty of the work by comparing it with other clustering algorithms. It is recommended to work on the Reviewer's comments for quality improvement. Author Response: Thank you very much for the Reviewer comments. We appreciate your suggestion regarding the need to better highlight the novelty of our work. In the revised version, we will provide a more precise comparison with existing clustering algorithms and emphasise the contributions of the proposed method more explicitly. We will carefully address all reviewer comments to improve the overall quality of the manuscript. II. Reviewer 1 The manuscript presents a novel two-stage clustering algorithm designed to handle imbalanced and uncertain data. The method combines optimisation with an enhanced clustering framework; the following are the main concerns regarding the proposed approach. 1. There is no comparison with deep clustering or modern ensemble methods that also handle imbalance and uncertainty. address Authors' Response: Thank you for the Reviewer's comments. Because our research focuses on clustering methods for imbalanced and uncertain data represented by continuous distribution data, this type of data is characterised by rich distributional information; however, it requires substantial storage and is quite complicated to build deep clustering models. On the other hand, deep clustering methods rely on representation learning. They use deep neural networks to convert high-dimensional or unstructured data into a latent space where clustering becomes more discrete. These methods integrate feature learning and clustering, making them highly effective for images, signals, and other complex data types. Therefore, due to differences in data characteristics and incompatibility in feature representation, BKIFF and deep clustering operate in different feature spaces and follow different learning paradigms; a direct comparison between them would be technically inappropriate for our problem context. However, we found one paper, with DOI: http://doi.org/10.1007/s10618-025-01136-0, that employs the relevant Methodology of the proposed method for extracting image features into modern convolutional architectures via Inception-ResNet-V2. Without this paper, we have not yet found a suitable algorithm for unbalanced data with respect to the probability density function. This is a new deep learning-based method that combines global average max pooling with the network to extract features for density function estimation and beam analysis evaluation. We also consider this a potential baseline and add it to the results of a cluster analysis comparison in the disequilibrium environment we are examining. The results show that although this method is considered promising and novel in terms of extraction, the cluster analysis algorithm proposed by Dinh Pham-Toan (2025) has not been improved, rendering it unable to handle imbalanced data effectively. Furthermore, Dinh's algorithm faces several significant challenges as it repeatedly calculates the pairwise distance matrix in phase one to find the optimal number of clusters and uses that label result to perform further fuzzy clustering with the proposed Kullback-Leibler distance. Here, the phases do not include awareness of imbalance handling, leading to biased and uneven results. Moreover, image extraction via the pooling layer carries the risk of random bias as it does not contain any potentially optimised targets. Authors' Action: We incorporated the clustering extraction and analysis method proposed by Dinh Pham-Toan (2025) as an additional baseline. We have added the configuration of this algorithm to Table 4 (page 17/44), similar to other baseline algorithms. Because this is an automatic clustering algorithm, we do not need to set up a c-cluster. This method is included in Tables 11, 12, and 13 (pages 23--24/44) to facilitate a direct and transparent comparison with existing algorithms and the proposed BKIFF framework. In addition, we have added two dedicated paragraphs that discuss and critically evaluate the comparative performance of all methods, including Dinh Pham-Toan (2025), at lines 539--576, pages 22--23/44. 2. The convergence proof is provided; however, the exposition is dense and may be challenging for readers without a strong background in optimisation. Including a more intuitive explanation or a summary of the convergence properties would enhance accessibility. Authors' Response: We thank the Reviewer for this observation. We acknowledge that including the complete derivations in the main text may disrupt the conceptual flow for readers unfamiliar with nonlinear optimisation. To address this, we have relocated the complete analytic proofs to the Supporting Information and provided a more intuitive summary in the revised manuscript. Authors' Action: We have reorganised the convergence section. Specifically: - All detailed proofs of the lemmas and theorems have been moved to the Supporting Information lines 730--828, pages 30--34/44. This includes two lemmas and four theorems. - The main text now includes a concise and accessible explanation of the convergence mechanism. Specifically, the revised paragraph describes the monotonic decrease of the objective function and clarifies the contribution of each lemma and theorem to the overall convergence guarantee (lines 270--283, pages 10--11/44). - A new schematic diagram (Figure~4, page 11/44) has been added to summarise the logical structure of the convergence argument visually. 3. Parameter sensitivity analysis is essential for validating the robustness of the results. Authors' Response: We sincerely thank the Reviewer for this important comment. Accordingly, a comprehensive sensitivity evaluation has now been incorporated into the revised manuscript. Authors' Action: To address this comment thoroughly, the following additions and analyses have been made: - Performed Wilcoxon signed-rank tests, and Friedman tests for all algorithms in the three Examples, including Tables of results. - Added a new subsubsection "Sensitivity Analysis Setup" describing the experimental design, including the tested parameter groups including configurations $IR=\{20\,,50\,,80\,,100\}$, fuzziness coefficient $m=\{1.1\,,1.5\,,2.0\,,2.5\,,3.0\,,5.0\,,10.0\}$, the number of clusters $c=\{2\,,3\,,4\,,5\}$, and the type of distance metric $\{\mathcal{H}^2\,,\mathcal{L}_1\,,\mathcal{L}_2\,,CWD\}$. Each configuration has been repeated 10 times, and evaluation metrics including $ARI$, $NMI$, $Silhouette$, $Dunn$ index, computation time, and iterations (lines 436--455, page 17/44). - Added a new subsection "Sensitivity Analysis of BKIFF", presenting the interpretation of Morris and ANOVA results (line 622--647, pages 28--29/44), identifying dominant and weak factors, and discussing stability across Examples, and summarised the results in a new Table~14 (page 29/44). - Provided heatmaps and pairwise configuration comparisons for all metrics, including $ARI$, $NMI$, $Dunn$, and $ Silhouette$ value across parameter settings in the Supplementary Information named ``Pair configuations'' \textbf{(lines 839--846, page 36/44)}. - Ensured reproducibility by releasing all Octave code and sensitivity-testing scripts via a publicly accessible repository by link https://doi.org/10.6084/m9.figshare.30600539.v4 4. Some sentences contain minor grammatical errors. Authors' Response: We thank the Reviewer for pointing out the grammatical issues in several sentences. We carefully reviewed the entire manuscript and corrected all minor grammatical and stylistic errors to improve clarity and readability. Authors' Action: We revised the manuscript to fix grammatical inconsistencies, polished sentence structures, and improved overall language quality. 5. In some places, the acronym BKIFF is written inconsistently. Authors' Response: We thank the Reviewer for pointing out the inconsistency in the use of the acronym. All occurrences have been carefully checked throughout the manuscript. Authors' Action: We standardised the notation by replacing BKA with BKO where appropriate and corrected the full algorithm name in Algorithm 2 to ``Black-winged Kite Improved Fuzzy Clustering for Probability Density Functions". 6. Some figures (e.g., Fig. 2, Fig. 10) are not referenced in the article. Authors' Response: We thank the Reviewer for pointing out the missing references. Authors' Action: We have carefully reviewed the manuscript and added the appropriate in-text references for Figure 2 and Figure 10 at their relevant locations. All figures are now properly referenced and integrated into the narrative to ensure consistency and readability throughout the paper. III. Reviewer 2 1. First of all, the paper is not well organised. Introduction and experimental work conclusions are not labelled with proper sections, which makes it ambiguous to read. Authors' Response: Thank you for bringing this to my attention. To improve the clarity and organisation of the manuscript, we have revised the structure and ensured that all major sections are clearly labelled and consistently referenced. Authors' Action: We have reorganised the remaining parts of the paper and added section labels with correct \verb\|\nameref\| references (lines 121--126, page 4/44). All cross-references throughout the manuscript have been checked and updated to ensure accuracy and consistency. 2. The problem statement and motivation of the method are not clear. Authors' Response: We thank the Reviewer for their comment. We strengthened the articulation of why clustering probability density functions becomes highly unstable under imbalanced conditions and why a dedicated methodological solution is needed. Authors' Action: Sseveral changes have been made: - Clarified the problem statement by explicitly explaining how uncertainty combined with severe imbalance destabilises existing clustering methods and leads to prototype drift and minority-cluster loss (lines 22--26, page 4/44). - Expanded the motivation through a focused related-work synthesis, highlighting recent optimisation-based or self-updating clustering approaches and explaining why none of them resolve the joint challenge of uncertainty and imbalance (lines 45--52, page 3/44). - Made the research gap explicit by stating that, despite previous advances, no existing method provides a technical clustering framework tailored for imbalanced uncertain data, followed by a clear motivation for the necessity of such a method (lines 80--82, page 4/44). 3. "Given the aforementioned gaps, this study introduces a novel approach call" – is written in two times at the introduction section Authors' Response: We appreciate the Reviewer for pointing out the repetition of the phrase. Authors' Action: We have removed the redundant occurrence of the sentence and revised the surrounding text. 4. The related works section is absent in this paper. Authors' Response: Thank you for the Reviewer's observation. A related works section is indeed included in the manuscript (lines 45--52, page 3/44). However, we acknowledge that its structure and presentation may not have clearly conveyed its role as a dedicated section. Therefore, we have revised and reorganised the content to ensure that the related works are more clearly articulated and properly positioned. Authors' Action: The content of existing related works has been refined and reformatted to function as a distinct Related Works section. The revised version highlights prior studies more systematically and clarifies the positioning of our proposed method within the existing literature. 5. In Methodology, subsections are confusing because the Labels are not mentioned. Also, the motivation of each equation is not well defined. Authors' Response: Yes. We have revised the Methodology section by adding clear subsection labels and explicitly explaining the motivation of each equations. Authors' Action: - A paragraph was added to articulate the motivation for the formulation of the IFF objective function (Lines 165--168, page 6/44). This paragraph explains the dual purpose of minimising the Hellinger distance to cluster prototypes and mitigating the dominance of large clusters through cardinality-based weight factors. - Included an explanation of the rationale behind the weight definition (Lines 176--177 page 7/44), clarifying how the weighting mechanism ensures balanced influence across clusters of different sizes. - Added a sentence motivating the necessity of an explicit initialisation step (Lines 196--199, page 7/44), highlighting the idea explanation behind it. - Inserted a clarification sentence explaining that the convergence analysis is organised as a sequence of lemmas and theorems following Zangwill's global convergence framework (Lines 266--268, page 10/44). 6. The flow of Fig. 3 is not clear. Moreover, the framework of the proposed method is normally expected in the Methodology section. Authors' Response: Thank you for the Reviewer's comment. We agree that the original flow of Figure 3 (page 10/44) is more appropriately placed in the Methodology section. We have revised the figure to provide a more transparent and more coherent flow, added explicit references to the corresponding subsections, and clarified the mathematical components to improve readability. Authors' Action: The entire framework in Figure 3 (page 10/44) has been redesigned with a more transparent structure, labelled components, and more detailed formula descriptions. The updated figure has been moved to the Methodology section as suggested. 7. In the experimental section, the compared methods are quite old. There should be some new existing methods to compare performance. Authors' Response: We thank the Reviewer for the valid comment. We have incorporated an additional contemporary baseline to ensure a more comprehensive and up-to-date evaluation. Authors' Action: We have added the feature-extraction and clustering method proposed by Dinh Pham-Toan (2025) as a new baseline in Tables 11, 12, and 13 (pages 23--24/44). This inclusion enables a direct and fair performance comparison between the proposed BKIFF method and other existing algorithms, including this recent approach. 8. The conclusion should be rewritten. Authors' Response: We thank the Reviewer for their comment regarding the conclusion. Authors' Action: We have completely rewritten the conclusion to provide a clearer, more coherent summary of the methodological contributions, experimental results, and practical implications of the proposed BKIFF algorithm (lines 707--719, page 30/44). IV. Journal Requirements 1. Please ensure that your manuscript meets PLOS ONE's style requirements, including those for file naming. The PLOS ONE style templates can be found at https://journals.plos.org/plosone/s/file?id=wjVg/PLOSOne_formatting_sample_main_body.pdf and https://journals.plos.org/plosone/s/file?id=ba62/PLOSOne_formatting_sample_title_authors_affiliations.pdf Authors' Response: We thank the Editor for this reminder. Authors' Action: We have revised the manuscript to fully comply with PLOS ONE's style and formatting requirements, including file naming conventions. The manuscript has been prepared using the official PLOS ONE templates for the main body and for the title, authors, and affiliations, as provided at the referenced links. 2. PLOS requires an ORCID iD for the corresponding author in Editorial Manager on papers submitted after December 6th, 2016. Please ensure that you have an ORCID iD and that it is validated in Editorial Manager. Authors' Response: We acknowledge the Editor's request regarding the ORCID iD requirement. 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18 Mar 2026 Decision Letter - Zeashan Khan, Editor -->PONE-D-25-57245R1-->-->A Black-winged Kite Improved Fuzzy Clustering handling Imbalanced Uncertain Data-->-->PLOS One Dear Dr. Che Ngoc, Thank you for submitting your manuscript to PLOS ONE. After careful consideration, we feel that it has merit but does not fully meet PLOS ONE’s publication criteria as it currently stands. Therefore, we invite you to submit a revised version of the manuscript that addresses the points raised during the review process. Please submit your revised manuscript by May 02 2026 11:59PM. If you will need more time than this to complete your revisions, please reply to this message or contact the journal office at plosone@plos.org. When you're ready to submit your revision, log on to https://www.editorialmanager.com/pone/ and select the 'Submissions Needing Revision' folder to locate your manuscript file. 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Please review your reference list to ensure that it is complete and correct. If you have cited papers that have been retracted, please include the rationale for doing so in the manuscript text, or remove these references and replace them with relevant current references. Any changes to the reference list should be mentioned in the rebuttal letter that accompanies your revised manuscript. If you need to cite a retracted article, indicate the article’s retracted status in the References list and also include a citation and full reference for the retraction notice. Additional Editor Comments (if provided): The revised version has been evaluated for the accuracy of results and novelty. However, there are few areas which still require improvements. Moreover, particularly in the methodology and discussion sections, key innovations could be elaborated briefly for better comprehension. [Note: HTML markup is below. 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Has the statistical analysis been performed appropriately and rigorously? --> Reviewer #1: Yes Reviewer #3: Yes ****** -->4. Have the authors made all data underlying the findings in their manuscript fully available? The PLOS Data policy requires authors to make all data underlying the findings described in their manuscript fully available without restriction, with rare exception (please refer to the Data Availability Statement in the manuscript PDF file). The data should be provided as part of the manuscript or its supporting information, or deposited to a public repository. For example, in addition to summary statistics, the data points behind means, medians and variance measures should be available. If there are restrictions on publicly sharing data—e.g. participant privacy or use of data from a third party—those must be specified.--> Reviewer #1: No Reviewer #3: No ****** -->5. Is the manuscript presented in an intelligible fashion and written in standard English? PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.--> Reviewer #1: Yes Reviewer #3: Yes ****** -->6. Review Comments to the Author Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)--> Reviewer #1: Thanks the authors. All comments are answered properly and the article can be published in the present form Reviewer #3: 1. The abstract reports very strong performance, including an ARI of 1.00 and lower execution times, but it does not provide enough quantitative comparison against specific baseline methods. Naming the main competing algorithms and indicating the magnitude of improvement would make the claims more convincing. 2. Although the paper mentions theoretical convergence via Zangwill’s theorem, the abstract does not clearly explain what is improved in the fuzzy clustering framework beyond the BKO-based initialization. A more explicit statement of the methodological novelty would help distinguish the proposed contribution from existing optimized fuzzy clustering methods. 3. The introduction should clearly conclude with a distinct section highlighting the novel contributions of your work. 4. At the ending of the intro, it is advised to add a para that mentions briefly what each next section contains. 5. The literature review should benefit from more explorations of previous studies. 6. The discussion section needs to be expanded to more thoroughly analyze the results. 7. The first paragraph of the conclusion should succinctly summarize the contributions of the study in past tense. 8. The second paragraph of the conclusion should provide clear and actionable future recommendations. 9. Equations are not properly cited, please add original references. 10. Why are the sections not numbered? this gives a hard time for the reviewers to do their job, please number each section and each subsection of the article in the second round of review. ****** -->7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). If published, this will include your full peer review and any attached files. If you choose “no”, your identity will remain anonymous but your review may still be made public. Do you want your identity to be public for this peer review? For information about this choice, including consent withdrawal, please see our Privacy Policy.--> Reviewer #1: No Reviewer #3: Yes: Luttfi A. Al-Haddad ******** [NOTE: If reviewer comments were submitted as an attachment file, they will be attached to this email and accessible via the submission site. Please log into your account, locate the manuscript record, and check for the action link "View Attachments". If this link does not appear, there are no attachment files.] To ensure your figures meet our technical requirements, please review our figure guidelines: https://journals.plos.org/plosone/s/figures You may also use PLOS’s free figure tool, NAAS, to help you prepare publication quality figures: https://journals.plos.org/plosone/s/figures#loc-tools-for-figure-preparation. NAAS will assess whether your figures meet our technical requirements by comparing each figure against our figure specifications. --> https://doi.org/10.1371/journal.pone.0349753.r003
Revision 2
30 Mar 2026 Author Response - Additional Editor Comments The revised version has been evaluated for the accuracy of results and novelty. However, there are few areas which still require improvements. Moreover, particularly in the methodology and discussion sections, key innovations could be elaborated briefly for better comprehension. - Author’s Response: We would like to express our sincere gratitude to the Editor and the Reviewer for this insightful observation. Additionally, we are pleased that our subsequent revisions have successfully addressed the previous concerns raised by the Reviewer. - Authors’ Action: We have extensively revised the Methodology (Section 3, pp. 16/44) and Discussion (Section 6, pp. 24/44) to explicitly elaborate on the core innovations of the BKIFF framework. Specifically: • In the Discussion section, we expanded our analysis to examine the interplay between these initialisation strategies and imbalance ratios, providing deeper insights into the algorithm’s imbalanced-immunity threshold where baseline methods typically fail. This provides a clearer understanding of the algorithm’s robustness (Section 6, lines 653-666, pp. 24/44). • In the Methodology section, we added a new illustration (Figure 9, pp. 16/44) to clearly depict the proposed patch-based transformation pipeline. The figure visualises the process of generating local patches, applying a sliding window mechanism, unfolding each patch into column vectors, and subsequently performing kernel density estimation on these transformed representations. This addition improves the interpretability of the data transformation procedure and clarifies how the probabilistic structure is constructed for clustering. - Reviewer #1 Thanks the authors. All comments are answered properly and the article can be published in the present form. - Authors’ Response: We are deeply grateful to the Reviewer for their thorough evaluation and for the favorable recommendation regarding the publication of our manuscript. We sincerely appreciate the time and expertise the Reviewer has dedicated to the review process. - Reviewer #3 1. The abstract reports very strong performance, including an ARI of 1.00 and lower execution times, but it does not provide enough quantitative comparison against specific baseline methods. Naming the main competing algorithms and indicating the magnitude of improvement would make the claims more convincing. - Authors’ Response: We sincerely appreciate the Reviewer’s constructive observation. We concur that the initial version of the abstract lacked sufficient detail to fully support the claims of superiority. Therefore, we have revised the abstract to clearly specify the main competing algorithms (FCF, FCF-L1, KMEANS, and Self-Updating) and to include the magnitude of improvements in terms of ARI, NMI, and computational time across different experimental settings. - Authors’ Action: We have revised the abstract to explicitly describe the methodological novelty of the proposed framework. Specifically, we have updated the abstract to explicitly list the baseline methods used for comparison and report quantitative improvements. Specifically, the revised version now highlights that BKIFF achieves near-perfect ARI (up to 1.00), improves ARI by approximately 30–35% in moderately imbalanced cases and from near-zero in highly imbalanced scenarios, increases NM I by about 25–95%, and reduces computational time by approximately 95–99% compared to the baseline methods. These additions provide clearer and more convincing evidence of the superiority of the proposed approach. 2. Although the paper mentions theoretical convergence via Zangwill’s theorem, the abstract does not clearly explain what is improved in the fuzzy clustering framework beyond the BKO-based initialization. A more explicit statement of the methodological novelty would help distinguish the proposed contribution from existing optimized fuzzy clustering methods. - Authors’ Response: We thank the reviewer for this important comment. We have consequently revised the manuscript to explicitly delineate the methodological novelties of the BKIFF framework, thereby clearly distinguishing our contribution from conventional optimised improved fuzzy clustering approaches. - Authors’ Action: We clarify that BKIFF incorporates the Hellinger distance into the clustering objective to better model similarities between probability density functions, and introduces improved membership updating and prototype estimation mechanisms through the proposed Improved Fuzzy clustering for probability density Functions (IFF), which is designed to effectively handle uncertainty and data imbalance. 3. The introduction should clearly conclude with a distinct section highlighting the novel contributions of your work. - Authors’ Response: We sincerely appreciate the Reviewer’s constructive suggestion. We concur that a dedicated section outlining the main contributions improves the clarity and structural flow of the Introduction. - Authors’ Action: We have revised the Introduction to include a dedicated paragraph that explicitly summarises the main contributions of this study, specifically, Contributions (SubSection 1.4, lines 115-150, pp. 5/44). 4. At the ending of the intro, it is advised to add a para that mentions briefly what each next section contains. - Authors’ Response: We sincerely thank the Reviewer for this constructive comment. Accordingly, we have revised the manuscript by adding a description of its structure. - Authors’ Action: A paragraph summarizing the structure of the paper has been added at the end of the Introduction, specifically, Organisation (SubSection 1.6, lines 151-158, pp. 5/44) 5. The literature review should benefit from more explorations of previous studies. - Authors’ Response: We sincerely appreciate the Reviewer’s constructive assessment regarding the scope of the literature review. We have revised the Related Works section to include a more thorough exploration of prior studies. - Authors’ Action: We have extensively revised and restructured the Related Works section to provide a more comprehensive literature review. Specifically: • We have provided a more detailed description of representative methods such as Uncertain k-means, Uncertain k-medoids, kernel-based approaches, and density-based methods (lines 42-57, pp. 3/44). Moreover, we have cited additional foundational articles, such as https://doi.org/10.1007/s00778-005-0159-3, and https://doi.org/10.1016/j.neunet.2017.06.004, for further analytical depth. • We have explicitly analysed the underlying mechanisms and inherent limitations of these existing methods (lines 60-74, pp. 3-4/44). • We have expanded the discussion on advances in recent algorithms based on evolutionary and adaptive strategies, such as genetic algorithms, differential evolution, and self-updating frameworks (lines 79-81, pp. 4/44). 6. The discussion section needs to be expanded to more thoroughly analyse the results. - Authors’ Response: We sincerely thank the Reviewer’s constructive recommendation. - Authors’ Action: We have expanded the Discussion section (Section 6, lines 653-666, pp. 24/44) to provide a more thorough analysis of the results and explicitly analyse the interplay between initialisation strategies, imbalance ratios, and membership regularisation mechanisms. 7. The first paragraph of the conclusion should succinctly summarize the contributions of the study in past tense. - Authors’ Response: Thank you for your constructive comment. - Authors’ Action: The first paragraph of the Conclusion section has been carefully revised to succinctly summarize the key contributions of the study, with all descriptions consistently expressed in past tense (lines 717-728, pp. 27/44). 8. The second paragraph of the conclusion should provide clear and actionable future recommendations. - Authors’ Response: Thank you for your valuable comment. In the original manuscript, these recommendations were presented in a dedicated Future Work subsection within the Discussion. - Authors’ Action: We have moved and incorporated the key future research directions into the second paragraph of Conclusion (lines 730-739, pp. 27-28/44). Specific recommendations include integrating deep clustering, expanding to contrastive learning for images/video, and applying the density framework to areas such as solar radiation analysis or species distribution modeling. Additionally, we cited two article https://doi.org/10.1371/journal.pone.0317396 which involve the clustering-based SMOTE technique to handle imbalanced data and https://doi.org/10.1371/journal.pone.0340758 on evolutionary undersampling to detect rare events in complex data environments. 9. Equations are not properly cited, please add original references. - Authors’ Response: We sincerely thank the reviewers for their valuable comments. We have reviewed the entire manuscript and added citations to the Hellinger Distance, Dunn Index, and Silhouette Coefficient. - Authors’ Action: We have made the following specific updates to the revised manuscript, including • We added Hellinger (1909) https://doi.org/10.1515/crll.1909.136.210 in (Definition 3, pp. 6/44) to acknowledge the theoretical origin of this measure. • We added Dunn (1973) https://doi.org/10.1080/01969727308546046 (Section 3.6.3, pp. 13/44) when defining the standard for evaluating the distance between clusters. • We added Rousseeuw (1987) https://doi.org/10.1016/0377-0427(87)90125-7 (Section 3.6.4, pp. 13/44) to confirm the origin of the method of measuring cluster separation. 10. Why are the sections not numbered? this gives a hard time for the reviewers to do their job, please number each section and each subsection of the article in the second round of review. - Authors’ Response: We sincerely appreciate the Reviewer’s constructive observation regarding the manuscript’s structural organisation. - Authors’ Action: All sections and subsections have been numbered and highlighted in the revised manuscript. Attachments Attachment Submitted filename: Response_to_Reviewers_auresp_2.pdf https://doi.org/10.1371/journal.pone.0349753.r004
5 May 2026 Decision Letter - Zeashan Khan, Editor A Black-winged Kite Improved Fuzzy Clustering handling Imbalanced Uncertain Data PONE-D-25-57245R2 Dear Dr. Che Ngoc, We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements. Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication. An invoice will be generated when your article is formally accepted. Please note, if your institution has a publishing partnership with PLOS and your article meets the relevant criteria, all or part of your publication costs will be covered. Please make sure your user information is up-to-date by logging into Editorial Manager at Editorial Manager® and clicking the ‘Update My Information' link at the top of the page. 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Is the manuscript presented in an intelligible fashion and written in standard English? PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here.--> Reviewer #3: (No Response) Reviewer #4: Yes ****** -->6. Review Comments to the Author Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters)--> Reviewer #3: (No Response) Reviewer #4: Clustering uncertain data is a fundamental problem in data mining. Imbalance among uncertain objects significantly degrades clustering performance, as minority clusters are repeatedly overshadowed by dominant ones. Consequently, existing clustering techniques often fail due to initialisation biases and inadequate similarity modelling. This paper proposes a novel algorithm, the Black-winged Kite Improved Fuzzy clustering for probability density Functions (BKIFF), which combines an optimisation-based initialisation strategy with an enhanced fuzzy clustering framework. Specifically, BKIFF incorporates the Hellinger distance into the clustering objective to more reliably capture similarities between pdfs, and introduces improved membership updating and prototype estimation mechanisms tailored for uncertain and imbalanced data formulated as Imporved Fuzzy clustering for probability density Functions (IFF) while theoretical convergence is established. In addition, the algorithm employs Black-winged Kite Optimisation (BKO) to enhance prototype selection, improving clustering stability and convergence. As a result, comprehensive experiments with synthetic Gaussian probability distributions, skewed probability density functions (pdfs), and real-world image datasets demonstrate that BKIFF consistently outperforms baseline methods such as FCF, FCF-L1, KMEANS, and Self-Updating. Across all three examples, BKIFF achieves near-perfect ARI, improving from near-zero values in highly imbalanced cases {20, 50, 80, 100} by approximately 30–35% in moderate settings, while increasing NMI by about 25–95%. Additionally, it reduces computational time by approximately 95–99% compared to baseline methods. In conclusion, BKIFF demonstrates superior performance and opens up new possibilities for applications in medical diagnostics, ecological analysis, and high-dimensional uncertain data mining, particularly in imbalanced environments. The authors have done well the revision work. ****** -->7. PLOS authors have the option to publish the peer review history of their article (what does this mean?). 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Formally Accepted
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