Reviewer has chosen to be Anonymous

Summary of paper in a few sentences:

The paper tests a new set of persistent homology-based predictor variables to inform several classifiers for binary classification. The methods used to extract the necessary information to craft these predictor variables are described, with appropriate justifications on some choices made. The effectivity of the predictor variables are then tested via the standard pipeline for binary classifiers.

Reasons to accept:

The manuscript is technically sound. The general pipeline follows a standard flow, and the highlighted results reflect acceptable values for standard metrics. The necessary background materials are sufficiently presented at an appropriate level of detail. The novelty of the manuscript lies in the use of a new class of predictor variables that utilize actual cycle representatives of persistent homology classes, and the experimental design used to test this is sufficiently justified. The results, while not entirely groundbreaking, are illustrative of the effectivity and utility of the proposed set of predictor variables.

Reasons to reject:

Since the novelty of the manuscript lies in the demonstration of the effectivity and utility of a new class of predictor variables, an analysis of feature importance across the binary classifiers becomes almost a necessity to further understand the effectivity of the proposed predictor variables.

Nanopublication comments:

Further comments:

The figures can be improved for publication.
An illustration of the isoelectric line can be useful when describing the methods used to generate the persistent-homology-based variables.
The writing of some sections (Construction of Predictor Variables, results and discussion) can also be improved for better readability.
Instead of reporting simple mean or max values for the metrics, presenting the distribution across cross validations can be more informative.

By Francesca D. https://orcid.org/0000-0002-8720-1256

Review Details

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Reviewer has chosen not to be Anonymous

Summary of paper in a few sentences:

The paper present a novel application of cycle representatives of topological features in constructing predictor variables for use in machine learning models to classify ECG rhythms. They introduce an isoelectric baseline to yield non-trivial topological features corresponding to the P, Q, S, and T-waves (if they exist) and utilize the N-most persistent 1-dimensional homological features and their corresponding area-minimal cycle representatives to construct predictor variables derived from the persistent homology of the ECG signal for some choice of N.

Reasons to accept:

The paper is well structured and presents indeed an interesting application in ECG.
With some efffort the paper can be accepted.

1) The SoA of application of Topological Data Analysis in Cardiovascular Signals is missing

-Hernández-Lemus, E., Miramontes, P., & Martínez-García, M. (2024). Topological Data Analysis in Cardiovascular Signals: An Overview. Entropy, 26(1), 67.
-Liu, Y., Wang, L., & Yan, Y. (2023, October). Persistence Landscape-based Topological Data Analysis for Personalized Arrhythmia Classification. In 2023 IEEE 19th International Conference on Body Sensor Networks (BSN) (pp. 1-6). IEEE.
Ling, T., Zhu, Z., Zhang, Y., & Jiang, F. (2022). Early Ventricular Fibrillation Prediction Based on Topological Data Analysis of ECG Signal. Applied Sciences, 12(20), 10370.

and many others studies should be analysed, compared against your work .

2) Line 23 : pls use the same number of digits.
3) If your focus is on Arrythmia, you sd give the prevalence of Arrythmia
4) there is a typo : "off of"
5) The difference between homology and homotopy is not clear
6) Some data is discarded: in relation to the real tiem series what does it mean ? Large Amplitude? High/Low Frequency ?
7) One page to describe well known evaluation metrics is too much, can you condense pag 10
8) Why do you think Gradient Boosted Decision Tree results as optimal ? A nd what about the other results ? Results are just reported and not commented at all
9) The standard deviation of the metrics across the 5 folds could be reported in the tables for completeness. it would be useful to highlight best results in bold in the tables
10) Fig. 6. Receiver Operator Characteristic Curve for Classification of Arrhythmia vs. Sinus Rhythm, presents very bad results, what is the reason of presenting it ?
11) A Table to compare your results with other studies that approach ECG rhythm classification through TDA and machine learning, would be recommended.
12) page 16 line 11 , there is a typo "nonempty"

In general the application of Topological Data Analysis in Cardiovascular Signals as in all Time Series, is interesting, could you give an easier explanation of what is the meaning of this approach based on shape in ECG ? Graphs/Images could be helpfuls

Reasons to reject:

The paper is well structured and presents indeed an interesting application in ECG.
With some efffort the paper can be accepted.

1) The SoA of application of Topological Data Analysis in Cardiovascular Signals is missing

-Hernández-Lemus, E., Miramontes, P., & Martínez-García, M. (2024). Topological Data Analysis in Cardiovascular Signals: An Overview. Entropy, 26(1), 67.
-Liu, Y., Wang, L., & Yan, Y. (2023, October). Persistence Landscape-based Topological Data Analysis for Personalized Arrhythmia Classification. In 2023 IEEE 19th International Conference on Body Sensor Networks (BSN) (pp. 1-6). IEEE.
Ling, T., Zhu, Z., Zhang, Y., & Jiang, F. (2022). Early Ventricular Fibrillation Prediction Based on Topological Data Analysis of ECG Signal. Applied Sciences, 12(20), 10370.

and many others studies should be analysed, compared against your work .

2) Line 23 : pls use the same number of digits.
3) If your focus is on Arrythmia, you sd give the prevalence of Arrythmia
4) there is a typo : "off of"
5) The difference between homology and homotopy is not clear
6) Some data is discarded: in relation to the real tiem series what does it mean ? Large Amplitude? High/Low Frequency ?
7) One page to describe well known evaluation metrics is too much, can you condense pag 10
8) Why do you think Gradient Boosted Decision Tree results as optimal ? A nd what about the other results ? Results are just reported and not commented at all
9) The standard deviation of the metrics across the 5 folds could be reported in the tables for completeness. it would be useful to highlight best results in bold in the tables
10) Fig. 6. Receiver Operator Characteristic Curve for Classification of Arrhythmia vs. Sinus Rhythm, presents very bad results, what is the reason of presenting it ?
11) A Table to compare your results with other studies that approach ECG rhythm classification through TDA and machine learning, would be recommended.
12) page 16 line 11 , there is a typo "nonempty"

In general the application of Topological Data Analysis in Cardiovascular Signals as in all Time Series, is interesting, could you give an easier explanation of what is the meaning of this approach based on shape in ECG ? Graphs/Images could be helpfuls

Nanopublication comments:

Further comments: