List of Papers By topics Author List
| Paper Info | Reviews | Meta-review | Author Feedback | Post-Rebuttal Meta-reviews |
Authors
Tananun Songdechakraiwut, Bryan M. Krause, Matthew I. Banks, Kirill V. Nourski, Barry D. Van Veen
Abstract
Analysis of large and dense networks based on topology is very difficult due to the computational challenges of extracting meaningful topological features from networks. In this paper, we present a computationally tractable approach to topological data analysis of large and dense networks. The approach utilizes principled theory from persistent homology and optimal transport to define a novel vector space representation for topological features. The feature vectors are based on persistence diagrams of connected components and cycles and are computed very efficiently. The associated vector space preserves the Wasserstein distance between persistence diagrams and fully leverages the Wasserstein stability properties. This vector space representation enables the application of a rich collection of vector-based models from statistics and machine learning to topological analyses. The effectiveness of the proposed representation is demonstrated using support vector machines to classify measured functional brain networks.
Link to paper
DOI: https://doi.org/10.1007/978-3-031-43993-3_27
SharedIt: https://rdcu.be/dnwNs
Link to the code repository
Link to the dataset(s)
N/A
Reviews
Review #2
- Please describe the contribution of the paper
This work proposes a novel method for topological classification by embedding the persistent homology bar codes of networks to a vector space, such that the embedding preserves the Wasserstein distances. The experiments on classifying functional brain networks using support vector machines demonstrate the effectiveness of the method.
- Please list the main strengths of the paper; you should write about a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.
The novel formulation: The functional brain networks have complicated topological features, the persistent homology provides a power tool for classification. By changing the threshould, some links in the graph will be broken, hence the connected components and the loops will be changed accordingly. The birth and death of the components (or loops) are represented as barcodes, then represented as empirical distribution functions, their pseudoinverses give the embedding to the vector space. So that the Euclidean distance among the vectors give the Wasserstein distances among the empirical distributions on the barcodes. This formulation is rigorous and novel.
Furthermore, this formulation is very efficient for computation. The birth, death, the empircal distributions, the pseudoinverses and the Wasserstein distances are very easy to compute. The classification of the networks can be obtained by simple SVM, so the whole algorithm is simple and efficient.
- Please list the main weaknesses of the paper. Please provide details, for instance, if you think a method is not novel, explain why and provide a reference to prior work.
The authors address the limitation of TopVS at the end of the manuscript, which only captures the connected components and cycles information. It will be helpful to give some examples or theoretical results of unisomorphic graphs sharing the same barcode distributions.
- Please rate the clarity and organization of this paper
Very Good
- Please comment on the reproducibility of the paper. Note, that authors have filled out a reproducibility checklist upon submission. Please be aware that authors are not required to meet all criteria on the checklist - for instance, providing code and data is a plus, but not a requirement for acceptance
All the theoretic formulations and algorithmic details are thoroughly explained, the data sets are publically available, there are open source libraries for persistent homology, so the work is easy to be reproduced by a graduate student who is familiar with the basic concept of persistent homology.
- Please provide detailed and constructive comments for the authors. Please also refer to our Reviewer’s guide on what makes a good review: https://conferences.miccai.org/2023/en/REVIEWER-GUIDELINES.html
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More algrithmetic details for persistent homology will be helpful, how to efficiently compute the birth/death of components and cycles, their relations with the maximum spanning tree, and how to recover the original graph from the barcode in general.
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more introduction to the background of functional brain network classification, what are the meanings of each class.
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It will be more convincing to discuss whether SVM is sufficient for the purpose. Although the vectorization of the barcode preserving the Wasserstein distances, the boundary of the clusters of the networks may not be linear separatable, so maybe some non-linear classifier will further improve the performance.
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- Rate the paper on a scale of 1-8, 8 being the strongest (8-5: accept; 4-1: reject). Spreading the score helps create a distribution for decision-making
6
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
The proposed method is rigorous and elegant in theoretical aspects, it combines persistent homology and optimal transportation naturally, and embeds the barcode distribution onto a vector space preserving the Wasserstein distance. The method is also efficient and easy to implement. The experiments are thorough and convincing. I belive this is a good work showing both theoretical value and practical value.
- Reviewer confidence
Confident but not absolutely certain
- [Post rebuttal] After reading the author’s rebuttal, state your overall opinion of the paper if it has been changed
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- [Post rebuttal] Please justify your decision
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Review #3
- Please describe the contribution of the paper
In this paper, the authors introduced a computationally tractable method for topological classification of large and dense networks. The approach utilizes principled theory from persistent homology and optimal transport to establish a novel vector space representation for topological features. To evaluate its effectiveness, the authors applied the method to classify functional brain network data from an anesthesia study.
- Please list the main strengths of the paper; you should write about a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.
The approach proposed to define a novel vector space representation for topological features is novel.
- Please list the main weaknesses of the paper. Please provide details, for instance, if you think a method is not novel, explain why and provide a reference to prior work.
This paper reads overall more like a machine learning paper without providing sufficient insights into the brain network modeling/analysis and how the results can inform anesthesia study or the relevant medical application.
- Please rate the clarity and organization of this paper
Satisfactory
- Please comment on the reproducibility of the paper. Note, that authors have filled out a reproducibility checklist upon submission. Please be aware that authors are not required to meet all criteria on the checklist - for instance, providing code and data is a plus, but not a requirement for acceptance
The authors did not provide a link to their code but will share it after acceptance as indicated by their answers to the reproducibility checklist.
- Please provide detailed and constructive comments for the authors. Please also refer to our Reviewer’s guide on what makes a good review: https://conferences.miccai.org/2023/en/REVIEWER-GUIDELINES.html
- This paper reads overall more like a machine learning paper without providing sufficient insights into the brain network modeling/analysis and how the results can inform anesthesia study.
- The interpretation of the proposed method in quantifying brain biomarkers is quite limited. It is unclear why the proposed method is better than others in distinguishing the three arousal states.
- It is unclear what information were extracted from brain networks as node features and adjacent matrices for training the compared approaches.
- Rate the paper on a scale of 1-8, 8 being the strongest (8-5: accept; 4-1: reject). Spreading the score helps create a distribution for decision-making
3
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
See my comments above.
- Reviewer confidence
Very confident
- [Post rebuttal] After reading the author’s rebuttal, state your overall opinion of the paper if it has been changed
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- [Post rebuttal] Please justify your decision
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Review #4
- Please describe the contribution of the paper
This work introduces a novel topological vector space (TopVS) that can represent and analyze networks of different sizes using 1-dimensional barcodes. By embedding these barcodes, TopVS enables topological machine learning.
- Please list the main strengths of the paper; you should write about a novel formulation, an original way to use data, demonstration of clinical feasibility, a novel application, a particularly strong evaluation, or anything else that is a strong aspect of this work. Please provide details, for instance, if a method is novel, explain what aspect is novel and why this is interesting.
(1) The TopVS preserve the Wasserstein distance in the original space of barcodes (2) They compared the common methods in Persistent Homology representation, like Persistence Image, Persistence weighted Gaussian kernel. (3) a novel topological representation method.
- Please list the main weaknesses of the paper. Please provide details, for instance, if you think a method is not novel, explain why and provide a reference to prior work.
Besides the functional brain networks dataset, whether TopVS can be better in some other datasets (e.g., point clouds) as well than the persistent image (PI) vectorization, sliced Wasserstein kernel (SWK), and persistent weighted Gaussian kernel (PWGK). The sliced Wasserstein kernel (SWK) and persistent weighted Gaussian kernel (PWGK).
- Please rate the clarity and organization of this paper
Good
- Please comment on the reproducibility of the paper. Note, that authors have filled out a reproducibility checklist upon submission. Please be aware that authors are not required to meet all criteria on the checklist - for instance, providing code and data is a plus, but not a requirement for acceptance
This depends on whether the author will release the code or not.
- Please provide detailed and constructive comments for the authors. Please also refer to our Reviewer’s guide on what makes a good review: https://conferences.miccai.org/2023/en/REVIEWER-GUIDELINES.html
The authors present a novel method for barcode representation. If they can demonstrate its superiority over existing methods on other datasets as well, it would undoubtedly be an exceptional achievement.
- Rate the paper on a scale of 1-8, 8 being the strongest (8-5: accept; 4-1: reject). Spreading the score helps create a distribution for decision-making
6
- Please justify your recommendation. What were the major factors that led you to your overall score for this paper?
I really appreciate this paper and eagerly anticipate its publication.
It would be a highly significant article if they could demonstrate the effectiveness of this method on multiple datasets.
- Reviewer confidence
Very confident
- [Post rebuttal] After reading the author’s rebuttal, state your overall opinion of the paper if it has been changed
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- [Post rebuttal] Please justify your decision
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Primary Meta-Review
- Please provide your assessment of this work, taking into account all reviews. Summarize the key strengths and weaknesses of the paper and justify your recommendation. In case you deviate from the reviewers’ recommendations, explain in detail the reasons why. In case of an invitation for rebuttal, clarify which points are important to address in the rebuttal.
This work proposed a novel method for topological classification by embedding the persistent homology bar codes of networks to a vector space, such that the embedding preserves the Wasserstein distances. The experiments demonstrated the effectiveness of the method. It attracts lots of interest from the reviewers. The reviewers also asked some questions, e.g. the biological interpretation of the proposed model, the generalibility of the proposed method, etc. The authors are encouraged to address these concerns in the rebuttal period.
Author Feedback
We thank the meta reviewer and reviewers (R2-R4) for their valuable feedback. We appreciate the positive comments from all reviewers, describing our work as “novel”, “rigorous and elegant in theoretical aspects,” “very efficient computation,” and in two cases expressing strong support for its publication. In the following, we synthesize the reviewers’ comments and provide our response.
First, we kindly note a possible typo regarding the swapping of answers to questions 9 and 10 from R4, as a ranking of “4 out of 1 in the stack” seems transposed.
(R2) More algorithmic details; (R3, R4) Link to/release of code; (R3) Unclear what info was extracted… for training the compared approaches
We will provide a GitHub link to the code used to produce all the results upon acceptance of the paper. The code completely describes all algorithmic details and will ensure reproducibility. Space limitations in the paper preclude full description of implementation details for both the proposed and compared approaches, but all of the algorithmic details, node features for training, and so on are presented in the code. In summary, PI, SWK and PWGK utilize Rips filtration on point clouds derived from networks to generate 2D barcodes [Otter 2017, EPJ DS]. Prop and GHK follow the approach described in [Borgwardt 2020, FTML], where a node attribute is the sum of edge weights incident to the node. GCN and GIN employ edge weights as well as weighted node degree if applicable.
(R2, R3) More introductory background, insights into brain network classification, quantifying brain biomarkers, informing anesthesia study
We apologize for the lack of clarity and will modify the text to address this family of concerns. An open problem in neuroscience is identifying an algorithm that reliably extracts a patient’s level of consciousness from passively recorded brain signals (i.e., biomarkers) and is robust to inter-patient variability, including where the signals are recorded in the brain. Conveniently, the anesthesia dataset is labeled according to consciousness state, and electrode placement (node location) was dictated solely by clinical considerations and thus varied across patients. Importantly, the relatively robust performance across patients suggests there are reliable topological signatures of consciousness captured by TopVS. The distinction between Wake and Sedated states involves relatively nuanced differences in connectivity, yet TopVS exploits the subtle differences in topology that differentiate these states better than the competing methods. Our results suggest that the neural correlates of consciousness can be captured in measurements of brain network topology, a longstanding problem of great significance. We are at the earliest stages developing this understanding, so there remain many open questions.
(R3) Unclear why TopVS is better than others in distinguishing arousal states
Because TopVS accurately computes exact barcodes and their true Wasserstein distance, setting it apart from other persistent homology methods that rely on approximations. Support for this point is most evident in Fig 2 that shows TopVS best differentiates Wake and Sedated states, despite their similarities in connectivity patterns and overlapping features.
(R2) Discuss whether linear SVM is sufficient
The potential improvement from nonlinear classifiers is an intriguing direction for further study. We had tested SVM with a Gaussian kernel and obtained performance comparable to that of linear SVM, but chose not to include those results as space constraints would preclude full exploration of nonlinear classification.
(R4) Demonstrate effectiveness on multiple datasets
We agree with this worthwhile suggestion, but are unable to introduce new results in accordance with MICCAI rules. However, the most convincing demonstration is when the community at large showcases effectiveness on their datasets, an outcome we hope to facilitate through the full release of our code.
Post-rebuttal Meta-Reviews
Meta-review # 1 (Primary)
- Please provide your assessment of the paper taking all information into account, including rebuttal. Highlight the key strengths and weaknesses of the paper, clarify how you reconciled contrasting review comments and scores, indicate if concerns were successfully addressed in the rebuttal, and provide a clear justification of your decision. If you disagree with some of the (meta)reviewer statements, you can indicate so in your meta-review. Please make sure that the authors, program chairs, and the public can understand the reason for your decision.
The authors provided a strong rebuttal, addressing all the questions asked by the reviewers, especially on the biological interpretation one. Although none of the reviewers provided post-rebuttal comments, the AC thinks that the rebuttal significantly improved the manuscript quality. Therefore, a acceptance recommendation is made. The authors should try to incorporate their rebuttal materials in the manuscript and GitHub link.
Meta-review #2
- Please provide your assessment of the paper taking all information into account, including rebuttal. Highlight the key strengths and weaknesses of the paper, clarify how you reconciled contrasting review comments and scores, indicate if concerns were successfully addressed in the rebuttal, and provide a clear justification of your decision. If you disagree with some of the (meta)reviewer statements, you can indicate so in your meta-review. Please make sure that the authors, program chairs, and the public can understand the reason for your decision.
This paper proposed a computationally tractable method for topological classification of large networks by embedding the persistent homology bar codes of networks to a vector space. In general, it is technically novel and clearly presented.
The authors have provided detailed rebuttal to address the reviewers and AC’s concerns. A majority of reviewers retain positive comments on this paper. And I also recommend acceptance of this paper.
Meta-review #3
- Please provide your assessment of the paper taking all information into account, including rebuttal. Highlight the key strengths and weaknesses of the paper, clarify how you reconciled contrasting review comments and scores, indicate if concerns were successfully addressed in the rebuttal, and provide a clear justification of your decision. If you disagree with some of the (meta)reviewer statements, you can indicate so in your meta-review. Please make sure that the authors, program chairs, and the public can understand the reason for your decision.
The overall sentiment from the reviewers is praise for the paper’s technical content. I do recommend an acceptance but I’d like to see some more visualization of the “medical imaging” involved in the results to give reader a bit of context. Right now, it indeed does read like a machine learning paper - which is fine, but for the miccai audience, a bit of visual aid would help.