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REVIEW 3 major objections 5 minor 34 references

Comparing the Effects of Persistence Barcodes Aggregation and Feature Concatenation on Medical Imaging

T0 review · 3 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read When a medical image yields multiple persistence barcodes, featurizing each barcode individually and concatenating the vectors outperforms aggregating the barcodes first.

desk verdict Useful systematic benchmark, but the headline preference for concatenation over aggregation is not supported by the paper's own supplementary tables. read the letter →

arxiv 2505.23637 v2 pith:LS7OE4G4 submitted 2025-05-29 cs.CV cs.AI

Dashti A. Ali , Richard K. G. Do , William R. Jarnagin , Aras T. Asaad , Amber L. Simpson This is my paper
classification cs.CVcs.AI
keywords TopologicaldataanalysisPersistenthomologyPersistencebarcodescodeaggregationFeatureconcatenationMedicalimageclassificationvectorization
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper asks how to combine multiple persistence barcodes computed from one medical image before classification: merge all barcodes into one summary and featurize that, or featurize each barcode and concatenate the resulting vectors. Across four datasets — liver CT, kidney CT, breast ultrasound, and mammograms — and two barcode-construction methods, the paper reports that concatenation consistently gave higher accuracy, AUC, and F1 scores than aggregation. The finding matters because many TDA pipelines that analyze 3D scans slice by slice, or use multiple landmark patterns, aggregate barcodes as a default and may be discarding per-slice information. The paper offers concatenation as a practical guideline for TDA-enabled medical image classification.

What carries the argument

The comparison turns on two ways of combining multiple persistence barcodes into one feature vector. Barcode aggregation takes the multiset union of all intervals from the per-slice or per-landmark barcodes, keeping duplicates and original order, and applies a vectorization method once; feature concatenation applies the same vectorization to each barcode independently and joins the resulting vectors. Aggregation erases which slice or landmark produced each bar before featurization, whereas concatenation keeps each barcode's contribution as a separate block of the feature vector, which the paper credits with preserving detailed topological information.

What would settle it

Run the same pipelines on the same datasets with repeated stratified cross-validation, for example 10 repeats of 5-fold CV, and count how often aggregation beats concatenation; if the win rate approaches 50 percent across folds, the claimed advantage is a selection artifact rather than a property of the combination strategy.

Watch

Extended reading notes

Core claim

The paper argues that when a single medical image gives rise to several persistence barcodes, the final topological feature vector should be built by vectorizing each barcode separately and concatenating the vectors, rather than by aggregating the barcodes into one multiset of intervals and then vectorizing the aggregate. Aggregation collapses the individual barcodes into a single summary and loses the detailed topological and geometric information that per-barcode featurization preserves. This claim is supported by experiments on liver tumour CT, kidney tumour CT, breast ultrasound, and mammography datasets, using cubical-complex and landmark-based Vietoris–Rips filtrations together with five vectorization methods: Betti curve, persistent statistics, entropy summary, persistent landscapes, and persistent tropical coordinates. Across the reported configurations, feature concatenation matched or beat aggregation on the main metrics in almost every case, with the only tie occurring on the kidney dataset with landmark-based filtration.

Load-bearing premise

The paper assumes that choosing the best classifier and vectorization for each strategy on the same validation procedure, and comparing them on a single 80/20 train-test split, is a fair measure of aggregation versus concatenation rather than an artifact of model selection or one lucky split.

Editorial extensions

If this is right

  • TDA pipelines that produce multiple barcodes per image should vectorize each barcode and concatenate the vectors when the goal is classification accuracy.
  • The benefit of concatenation appears across 2D and 3D modalities, cubical and landmark-based filtrations, and five different vectorizations, so it is not tied to one feature type.
  • Aggregation may still be preferred when feature dimension or memory is a hard constraint, since concatenation lengthens the feature vector in proportion to the number of barcodes.
  • Because the comparison uses a single held-out 80/20 split, the direction of the advantage is clearer than its exact magnitude in other settings.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A natural extension is to test learned combinations of per-barcode vectors, such as attention pooling, since plain concatenation keeps all information but grows feature dimension linearly with barcode count.
  • The proposed mechanism predicts that concatenation's advantage should increase as the number of barcodes per image grows; this could be checked by varying the number of slices on the liver CT dataset.
  • If the finding transfers, it may also guide non-medical TDA pipelines where multiple persistence diagrams are computed from one object, such as multi-view or time-varying data.
  • Replicating the comparison with repeated cross-validation would show whether the preference for concatenation holds in expectation rather than on a single split.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. The paper reports an empirical comparison of two ways to turn multiple persistence barcodes from a medical image into a single input for classifiers: (i) aggregate all barcodes and vectorize once, or (ii) vectorize each barcode and concatenate the resulting feature vectors. It applies this comparison to four medical imaging datasets, two filtration constructions, five barcode vectorizations, and 19 classifiers, and reports test-set accuracy, AUC, recall, precision, and F1 for the best configuration of each strategy. The authors conclude that feature concatenation is preferable and recommend it for similar experiments. The paper includes per-vectorization supplementary tables and a link to the experiment code.

Significance. If the headline conclusion were statistically supported, the paper would offer a practical rule for TDA practitioners. The study has real strengths: multiple datasets spanning CT, ultrasound, and mammography; two distinct topological constructions; five vectorizations; and public code. However, the central claim is currently overreaching: the comparison is built on a single train/test split with post-hoc selection of the best vectorization and classifier, no uncertainty quantification is provided, and the supplementary tables contain a clear counterexample to the "almost all metrics" statement. With the test sets for the 3D datasets containing roughly 40 patients each, the reported effect sizes are often within the range of a few patients. This is a useful benchmarking study that needs a more careful statistical analysis and a more conditional conclusion.

major comments (3)
  1. [Section 2.6.2, Tables 3–4] The headline comparison selects the best vectorization and classifier for each strategy on the same 80% training split and evaluates once on the reserved 20%. No confidence intervals, bootstrap, repeated splits, or multiplicity control are reported. Since the 3D test sets contain roughly 40 patients, a 2.5–7.5 percentage point difference corresponds to one to three patients, so the magnitudes in Tables 3 and 4 cannot be distinguished from noise without a paired test (e.g., McNemar for accuracy or DeLong for AUC). The conclusion that concatenation is "preferred" is not statistically established by the present design.
  2. [Section 3 vs. Table 8] The text states that feature concatenation outperformed aggregation on almost all metrics "except in one instance," but Table 8 contradicts this. For KiTS19 with landmark-based VR filtration, barcode aggregation achieves higher accuracy than concatenation for four of the five vectorizations: Betti curve 0.775 vs 0.750, entropy summary 0.825 vs 0.750, persistent statistics 0.825 vs 0.800, and persistent landscapes 0.800 vs 0.725. The per-vectorization comparison therefore does not support a blanket preference, and the conclusion should be conditional on dataset, filtration, and vectorization.
  3. [Section 3] The phrase "metrics show no statistically significant differences" appears without any statistical test. No p-value, confidence interval, or test name is given. Either supply appropriate paired tests (McNemar for accuracy, DeLong for AUC) or remove the significance language; otherwise the sentence is an unsupported claim.
minor comments (5)
  1. [Section 2.5 and Table 1] The BUSI dataset is described as a balanced subset of 376 patients in the text, but Table 1 reports 362 images; please reconcile the numbers.
  2. [Section 2.4] The Persistent Tropical Coordinates method uses a parameter r, but the manuscript does not state the value used for r in the experiments; please specify it, as the Betti grid size gamma is given but the tropical r is not.
  3. [Tables 5–10] These tables report only the best classifier for each vectorization; including the number of test samples and the class balance per dataset would help readers assess the precision of the reported percentages.
  4. [Throughout] Several typographical errors should be corrected: the title has "THEEFFECTS", the table headers contain "Barcod Agg.", and "V ectorization" appears in the Section 2.4 heading.
  5. [Section 2.6.2] The paper reports that the top three classifiers were selected by 5-fold CV and then fine-tuned with Optuna, but the hyperparameter search spaces and the exact criterion used to pick the final model are not specified; this limits reproducibility despite the code link.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper's central claim is an empirical comparison on held-out test data, with no parameter fitted to force the result and no load-bearing self-citation.

full rationale

The paper's central comparison—barcode aggregation versus feature concatenation—is an empirical benchmark evaluated on a single held-out 20% test split after model selection on the training 80% (Section 2.6.2). The result is a direct measurement of test-set accuracy, AUC, recall, precision, and F1, not a quantity derived from the inputs by construction. Neither aggregation nor concatenation is defined in terms of the other's outcome, and the reported 'preferred approach' conclusion is an interpretation of measured performance rather than a tautology. The only self-citation is reference [28], a survey of vectorization methods by overlapping authors; it is used to direct readers to mathematical details of the five vectorization methods and does not carry the load of the empirical claim. There is no fitted parameter renamed as a prediction, no imported uniqueness theorem, and no ansatz smuggled in via citation. The skeptical observation that Table 8 contains aggregation wins for KiTS19 with VR filtration, and that the best-of comparisons rest on a single split without confidence intervals, is a legitimate concern about statistical robustness and internal consistency of the conclusions, but it is not circularity: the empirical outcome was not preordained by the experimental setup. The paper's derivation chain is therefore self-contained, and no specific reduction of the conclusion to its inputs can be exhibited.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new entities. The central claim rests on several hand-chosen experimental parameters (slice counts, Betti grid size, ULBP subset, classifier selection rule) and on the domain assumption that TDA features capture classification-relevant structure in these medical images.

free parameters (5)
  • Number of selected CT slices per 3D scan = 15 for liver, 5 for KiTS19
    Chosen manually based on ROI size; the number of barcodes aggregated or concatenated changes feature vector length and may affect the comparison.
  • Betti curve grid size gamma = 100
    Set in Section 2.4 for all Betti curve vectorizations; affects feature vector resolution for both methods.
  • ULBP geometry subset for landmark point selection = G4 and G5 for 2D; G4R1 for 3D VR
    Chosen manually; different landmark sets would change barcodes and could shift the aggregation versus concatenation comparison.
  • Top-k classifiers selected after 5-fold CV = 3
    Only top 3 of 19 classifiers are fine-tuned and ensembled, biasing comparison toward configurations that perform well in CV.
  • Random 80/20 data split seed = not reported
    A single split without reported seed or repeats; performance estimates have unknown variance.
assumptions (4)
  • domain assumption Persistent homology captures clinically relevant topology in medical images that is usable for classification.
    The whole pipeline assumes TDA features carry signal; no baseline against radiomics or deep learning is given.
  • domain assumption Uniform local binary patterns (ULBPs) represent 90% of natural image patterns, so restricting to G4 and G5 is representative.
    Invoked from Ojala et al. via Section 2.1; the chosen subset is not validated on these medical images.
  • domain assumption Resampling CT images to average spacing and selecting slices with largest ROI preserves the topological information relevant to each class.
    Section 2.6.1; preprocessing choices could destroy or distort small topological features.
  • ad hoc to paper The 19 classifiers and 5 vectorizations span a fair enough model class to compare aggregation and concatenation.
    No argument that the chosen set is unbiased; best-of selection is post hoc.

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Cite this review

Pith. "Pith review of Comparing the Effects of Persistence Barcodes Aggregation and Feature Concatenation on Medical Imaging." pith.science (2026). https://pith.science/paper/LS7OE4G4

@misc{pith2026250523637,
  author       = {Pith},
  title        = {Pith review of: Comparing the Effects of Persistence Barcodes Aggregation and Feature Concatenation on Medical Imaging},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/LS7OE4G4}},
  note         = {Machine review of arXiv:2505.23637}
}
read the original abstract

In medical image analysis, feature engineering plays an important role in the design and performance of machine learning models. Persistent homology (PH), from the field of topological data analysis (TDA), demonstrates robustness and stability to data perturbations and addresses the limitation from traditional feature extraction approaches where a small change in input results in a large change in feature representation. Using PH, we store persistent topological and geometrical features in the form of the persistence barcode whereby large bars represent global topological features and small bars encapsulate geometrical information of the data. When multiple barcodes are computed from 2D or 3D medical images, two approaches can be used to construct the final topological feature vector in each dimension: aggregating persistence barcodes followed by featurization or concatenating topological feature vectors derived from each barcode. In this study, we conduct a comprehensive analysis across diverse medical imaging datasets to compare the effects of the two aforementioned approaches on the performance of classification models. The results of this analysis indicate that feature concatenation preserves detailed topological information from individual barcodes, yields better classification performance and is therefore a preferred approach when conducting similar experiments.

Figures

Figures reproduced from arXiv: 2505.23637 by the authors.

Figure 1
Figure 1. The LBP process takes patches of 3x3 pixels from the image, compares the central pixel with its neighbours, [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Geometric visualization of the ULBP method. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Cubical complex filtration and persistence barcodes representations in dimension zero and one for a 4x4 [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Left: persistence barcodes per slice, Right: aggregated persistence barcodes of all slices. 2.5 Datasets In this work we have experimented with various datasets of 2D and 3D medical images. For the 3D images we mainly focused on computed tomography (CT) imaging modalit…
Figure 5
Figure 5. Figure 5: TDA pipeline, which includes A) PH construction using cubical complex filtration, B) PH construction using [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: Top: sample slices of CT images from 3D datasets of liver tumours and KiTS19 with ROI highlighted in red [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]
Figure 7
Figure 7. Figure 7: An overview of different experiment pipelines for datasets of 3D images. [PITH_FULL_IMAGE:figures/full_fig_p009_7.png]
Figure 8
Figure 8. Figure 8: An overview of different experiment pipelines for datasets of 2D images. [PITH_FULL_IMAGE:figures/full_fig_p009_8.png]

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