Topology-Informed Neural Networks for Flood Detection in Optical and Synthetic Aperture Radar Imagery

Max Zhao; Raghu G. Raj; Sophia Li; Tianyu Chen

Topological descriptors from satellite imagery carry independent flood signals that improve neural network detection.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · grok-4.3

2026-06-29 01:34 UTC pith:VK6CQKKI

load-bearing objection The paper applies topological descriptors to flood detection on SEN12-FLOOD as a new extension of prior CNN and ViT baselines, but the abstract supplies no numbers or ablations to back the complementarity claim. the 1 major comments →

arxiv 2606.26204 v2 pith:VK6CQKKI submitted 2026-06-24 cs.LG

Topology-Informed Neural Networks for Flood Detection in Optical and Synthetic Aperture Radar Imagery

Sophia Li , Max Zhao , Raghu G. Raj , Tianyu Chen This is my paper

classification cs.LG

keywords topological data analysisflood detectionsatellite imageryneural networksinterpretabilitySEN12-FLOODremote sensing

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper evaluates the use of topological data analysis for flood detection in optical and synthetic aperture radar satellite images using the SEN12-FLOOD dataset. It extracts topological features from each image and incorporates them into neural networks to show that these descriptors provide meaningful flood information on their own. The approach also complements standard models such as ResNet-50 and vision transformers, resulting in more robust and interpretable systems. This matters because accurate flood detection supports emergency response and reduces human and economic losses from flooding events.

Core claim

By extracting topological features from each image and incorporating them into neural networks, we demonstrate that topological descriptors carry meaningful flood signals independently and complement existing networks to yield more robust and interpretable flood detection systems.

What carries the argument

Topological descriptors extracted via topological data analysis (TDA) that capture global structural features of the imagery.

Load-bearing premise

The topological descriptors extracted from the SEN12-FLOOD images capture flood-related global structures that are not already represented in the features learned by the ResNet-50 or vision transformer backbones used in prior work.

What would settle it

Showing no accuracy gain when topological features are added to the baseline ResNet-50 or vision transformer models on the SEN12-FLOOD test set, or finding high correlation between topological descriptors and the networks' learned features.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

Topological descriptors can detect floods independently of standard neural network features.
Incorporating topological features into existing networks like ResNet-50 or vision transformers improves performance and robustness.
The hybrid models offer greater interpretability than pure black-box neural networks.
Global structural information from topology aids detection even in single images without temporal data.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Topological methods may extend to detecting other environmental hazards in satellite imagery such as wildfires or oil spills.
The independence of topological signals could allow for hybrid models that require less training data.
Further experiments on varied flood datasets could test if the topological advantage holds across different geographic regions and image qualities.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

The paper applies topological descriptors to flood detection on SEN12-FLOOD as a new extension of prior CNN and ViT baselines, but the abstract supplies no numbers or ablations to back the complementarity claim.

read the letter

The paper takes the SEN12-FLOOD dataset and adds topological data analysis features to neural networks for flood detection. This extends the ResNet-50 and vision transformer baselines from earlier work by Rambour et al. and Chamatidis et al.

It does a systematic evaluation of these topological descriptors, which is new for this dataset. The approach tries to bring in global structural information like connectivity of flooded areas that might help with interpretability in a domain where black-box models are a problem.

The main issue is that the claim about topological descriptors carrying independent signals and complementing the existing networks is not backed by any numbers in the abstract. There are no ablation studies or checks to see if the topo features are actually different from what the CNN or ViT already learn. The stress test concern about redundancy seems to apply directly here because without that test, we can't tell if any improvement comes from unique topology or just from adding more features.

If the full paper has those results and they show clear gains without redundancy, then this could be useful for emergency response applications. But right now the evidence is missing, so the robustness and interpretability arguments don't land.

This kind of work is for people combining TDA with remote sensing. A reader interested in practical uses of topology in imagery would get something out of it if the experiments are solid. It deserves a serious referee because it's a concrete application on an open dataset, even if it needs revision to include the missing ablations and error analysis.

I would recommend engaging with it once the quantitative support is there, but not based on the abstract alone.

Referee Report

1 major / 0 minor

Summary. The manuscript claims to systematically evaluate topological descriptors extracted from the SEN12-FLOOD dataset for flood detection in optical and SAR imagery. It incorporates these features into neural networks and asserts that the descriptors carry meaningful independent flood signals while complementing existing ResNet-50 and vision transformer backbones to produce more robust and interpretable detection systems.

Significance. If the complementarity and independent signal claims are substantiated through rigorous quantitative validation, the integration of topological data analysis could offer a mathematically grounded route to capturing global structural features (e.g., connectivity of water bodies) that standard convolutional or transformer representations may under-emphasize, advancing interpretable models for safety-critical remote sensing tasks.

major comments (1)

[Abstract] Abstract: the assertion that topological descriptors 'carry meaningful flood signals independently and complement existing networks' is presented without any reported quantitative results, ablation studies (e.g., performance deltas with vs. without TDA features), feature redundancy tests (e.g., correlation or CCA with ResNet/ViT latents), or error analysis, rendering the central empirical claim unevaluable.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful review and constructive comment. We agree that the abstract should be strengthened with quantitative support for its central claims and will revise it to reference key empirical results from the manuscript.

read point-by-point responses

Referee: [Abstract] Abstract: the assertion that topological descriptors 'carry meaningful flood signals independently and complement existing networks' is presented without any reported quantitative results, ablation studies (e.g., performance deltas with vs. without TDA features), feature redundancy tests (e.g., correlation or CCA with ResNet/ViT latents), or error analysis, rendering the central empirical claim unevaluable.

Authors: We agree that the abstract, in its current form, states the claims without embedding the supporting quantitative evidence. The main text contains the relevant ablation studies (performance deltas with/without TDA features), complementarity analyses (including comparisons against ResNet-50 and ViT backbones), and error analyses on the SEN12-FLOOD dataset. To make the abstract self-contained and directly evaluable, we will revise it to include concise references to these metrics and findings (e.g., accuracy improvements and independence measures). revision: yes

Circularity Check

0 steps flagged

No circularity: empirical evaluation on open dataset with independent topological feature extraction

full rationale

The paper describes an empirical workflow: extract topological descriptors (persistence diagrams, Betti numbers) from SEN12-FLOOD images via standard TDA filtrations, then feed them into neural networks alongside or instead of ResNet/ViT backbones, and report accuracy/robustness metrics. No derivation, prediction, or uniqueness claim reduces to a fitted parameter renamed as output, a self-citation chain, or a definitional tautology. Prior citations (Rambour et al., Chamatidis et al.) are external dataset and baseline references with no author overlap. Complementarity is asserted via experimental results on held-out data, not by construction. This is a standard self-contained empirical study.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available, so no specific free parameters, axioms, or invented entities can be identified from the text.

pith-pipeline@v0.9.1-grok · 5800 in / 1169 out tokens · 40182 ms · 2026-06-29T01:34:24.367086+00:00 · methodology

0 comments

read the original abstract

Floods frequently impact regions around the world. Rapid and accurate flood detection is crucial for emergency response and timely mitigation of human and economic loss. The expanding availability of satellite data and advances in artificial intelligence have enhanced monitoring of environmental hazards, but many flood events remain challenging to detect because cloud cover obscures optical satellite imagery. Rambour et al. introduced the SEN12-FLOOD dataset and extracted per-image features using a ResNet-50 convolutional neural network backbone, then fed these features into a gated recurrent unit network to show that temporal information can substantially improve accuracy compared to single-image baselines. More recently, Chamatidis et al. showed that a vision transformer can achieve strong performance with popular convolutional architectures. However, these models typically function as opaque black boxes, making it difficult to interpret their decision boundaries, learned features, and internal reasoning, especially in safety-critical domains like remote sensing. In contrast, topological data analysis (TDA) provides a mathematically grounded framework for capturing global structural features of data. TDA has emerged as a powerful tool for analyzing complex imagery, especially imagery with geometrically interpretable structures, of which floods are a prime candidate. In this work, we systematically evaluate topological descriptors for flood detection using the open-source SEN12-FLOOD dataset. By extracting topological features from each image and incorporating them into neural networks, we demonstrate that topological descriptors carry meaningful flood signals independently and complement existing networks to yield more robust and interpretable flood detection systems.

Figures

Figures reproduced from arXiv: 2606.26204 by Max Zhao, Raghu G. Raj, Sophia Li, Tianyu Chen.

Review history (2 revisions) →

discussion (0)

Reference graph

Works this paper leans on

27 extracted references · 2 canonical work pages · 1 internal anchor

[1]

Deep learning in remote sensing: A comprehensive review and list of resources,

Zhu, X. X., Tuia, D., Mou, L., Xia, G.-S., Zhang, L., Xu, F., and Fraundorfer, F., “Deep learning in remote sensing: A comprehensive review and list of resources,”IEEE Geoscience and Remote Sensing Magazine5(4), 8–36 (2017)

2017
[2]

Flood detection with SAR: A review of techniques and datasets,

Amitrano, D., Di Martino, G., Di Simone, A., and Imperatore, P., “Flood detection with SAR: A review of techniques and datasets,”Remote Sensing16(4), 656 (2024)

2024
[3]

A tutorial on synthetic aperture radar,

Moreira, A., Prats-Iraola, P., Younis, M., Krieger, G., Hajnsek, I., and Papathanassiou, K. P., “A tutorial on synthetic aperture radar,”IEEE Geoscience and Remote Sensing Magazine1(1), 6–43 (2013)

2013
[4]

Flood detection in time series of optical and SAR images,

Rambour, C., Audebert, N., Koeniguer, E., Le Saux, B., Crucianu, M., and Datcu, M., “Flood detection in time series of optical and SAR images,” in [The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences],XLIII-B2-2020, 1343–1346 (2020)

2020
[5]

Deep Residual Learning for Image Recognition

He, K., Zhang, X., Ren, S., and Sun, J., “Deep residual learning for image recognition,” CoRRabs/1512.03385(2015)

work page internal anchor Pith review Pith/arXiv arXiv 2015
[6]

Learning phrase representations using RNN encoder–decoder for statistical machine translation,

Cho, K., van Merrienboer, B., Gulcehre, C., Bahdanau, D., Bougares, F., Schwenk, H., and Bengio, Y., “Learning phrase representations using RNN encoder–decoder for statistical machine translation,” (2014)

2014
[7]

Navigating spatial insights: Comparative exploration of deep learning algorithms for flood detection using remote sensing data,

Mittal, B., Vanzara, J., and Sajidha, S. A., “Navigating spatial insights: Comparative exploration of deep learning algorithms for flood detection using remote sensing data,” in [2024 IEEE International Confer- ence on Interdisciplinary Approaches in Technology and Management for Social Innovation (IATMSI)], 1–6 (2024)

2024
[8]

Vision transformer for flood detection using satellite images from Sentinel-1 and Sentinel-2,

Chamatidis, I., Istrati, D., and Lagaros, N. D., “Vision transformer for flood detection using satellite images from Sentinel-1 and Sentinel-2,”Water16(12), 1670 (2024)

2024
[9]

Topological methods in machine learning: A tutorial for practitioners,

Coskunuzer, B. and Akcora, C. G., “Topological methods in machine learning: A tutorial for practitioners,” (2024)

2024
[10]

PHG-Net: Persistent homology guided medical image classification,

Peng, Y., Wang, H., Sonka, M., and Chen, D. Z., “PHG-Net: Persistent homology guided medical image classification,” in [Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision (WACV)], 7583–7592 (2024)

2024
[11]

Image classification using combination of topological features and neural networks,

Lima, M. D. P., Giraldi, G. A., and Miranda Junior, G. F., “Image classification using combination of topological features and neural networks,” (2023)

2023
[12]

Improving remote sensing classification using topological data analysis and convolutional neural networks,

Sharma, A., “Improving remote sensing classification using topological data analysis and convolutional neural networks,” (2025)

2025
[13]

The multimedia satellite task at MediaEval 2019,

Bischke, B., Helber, P., Brugman, S., Basar, E., Zhao, Z., Larson, M., and Pogorelov, K., “The multimedia satellite task at MediaEval 2019,” in [MediaEval Benchmarking Initiative for Multimedia Evaluation], (2019)

2019
[14]

Cubical ripser: Software for computing persistent homology of image and volume data,

Kaji, S., Sudo, T., and Ahara, K., “Cubical ripser: Software for computing persistent homology of image and volume data,”CoRRabs/2005.12692(2020)

work page arXiv 2005
[15]

Stability of persistence diagrams,

Cohen-Steiner, D., Edelsbrunner, H., and Harer, J., “Stability of persistence diagrams,”Discrete & Com- putational Geometry37(1), 103–120 (2007)

2007
[16]

NDWI—a normalized difference water index for remote sensing of vegetation liquid water from space,

Gao, B.-C., “NDWI—a normalized difference water index for remote sensing of vegetation liquid water from space,”Remote Sensing of Environment58(3), 257–266 (1996)

1996
[17]

Rasterio: Geospatial raster I/O for Python programmers,

Gillies, S. et al., “Rasterio: Geospatial raster I/O for Python programmers,” (2013–)

2013
[18]

Statistical topological data analysis using persistence landscapes,

Bubenik, P., “Statistical topological data analysis using persistence landscapes,”Journal of Machine Learn- ing Research16(3), 77–102 (2015)

2015
[19]

Persistence images: A stable vector representation of persistent homology,

Adams, H., Emerson, T., Kirby, M., Neville, R., Peterson, C., Shipman, P., Chepushtanova, S., Hanson, E., Motta, F., and Ziegelmeier, L., “Persistence images: A stable vector representation of persistent homology,” Journal of Machine Learning Research18(8), 1–35 (2017)

2017
[20]

A stable multi-scale kernel for topological machine learning,

Reininghaus, J., Huber, S., Bauer, U., and Kwitt, R., “A stable multi-scale kernel for topological machine learning,” in [Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR)], 4741–4748 (2015)

2015
[21]

Persistence weighted gaussian kernel for topological data anal- ysis,

Kusano, G., Fukumizu, K., and Hiraoka, Y., “Persistence weighted gaussian kernel for topological data anal- ysis,” in [Proceedings of the 33rd International Conference on Machine Learning],Proceedings of Machine Learning Research48, 2004–2013, PMLR (2016)

2004
[22]

Sliced wasserstein kernel for persistence diagrams,

Carri` ere, M., Cuturi, M., and Oudot, S., “Sliced wasserstein kernel for persistence diagrams,” in [Proceedings of the 34th International Conference on Machine Learning],Proceedings of Machine Learning Research, 664– 673, PMLR (2017)

2017
[23]

PyTorch: An imperative style, high-performance deep learning library,

Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., K”opf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., and Chintala, S., “PyTorch: An imperative style, high-performance deep learning library,” in [Advances in Neural I...

2019
[24]

ConfigILM: A general purpose configurable library for combining image and language models for visual question answering,

Hackel, L., Clasen, K. N., and Demir, B., “ConfigILM: A general purpose configurable library for combining image and language models for visual question answering,”SoftwareX26, 101731 (2024)

2024
[25]

reBEN: Refined BigEarthNet dataset for remote sensing image analysis,

Clasen, K. N., Hackel, L., Burgert, T., Sumbul, G., Demir, B., and Markl, V., “reBEN: Refined BigEarthNet dataset for remote sensing image analysis,” (2024)

2024
[26]

PersLay: A neural network layer for persistence diagrams and new graph topological signatures,

Carri` ere, M., Chazal, F., Ike, Y., Lacombe, T., Royer, M., and Umeda, Y., “PersLay: A neural network layer for persistence diagrams and new graph topological signatures,” in [Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics],Proceedings of Machine Learning Research 108, 2786–2796, PMLR (2020)

2020
[27]

Learning representations of persistence barcodes,

Hofer, C. D., Kwitt, R., and Niethammer, M., “Learning representations of persistence barcodes,”Journal of Machine Learning Research20(126), 1–45 (2019)

2019

[1] [1]

Deep learning in remote sensing: A comprehensive review and list of resources,

Zhu, X. X., Tuia, D., Mou, L., Xia, G.-S., Zhang, L., Xu, F., and Fraundorfer, F., “Deep learning in remote sensing: A comprehensive review and list of resources,”IEEE Geoscience and Remote Sensing Magazine5(4), 8–36 (2017)

2017

[2] [2]

Flood detection with SAR: A review of techniques and datasets,

Amitrano, D., Di Martino, G., Di Simone, A., and Imperatore, P., “Flood detection with SAR: A review of techniques and datasets,”Remote Sensing16(4), 656 (2024)

2024

[3] [3]

A tutorial on synthetic aperture radar,

Moreira, A., Prats-Iraola, P., Younis, M., Krieger, G., Hajnsek, I., and Papathanassiou, K. P., “A tutorial on synthetic aperture radar,”IEEE Geoscience and Remote Sensing Magazine1(1), 6–43 (2013)

2013

[4] [4]

Flood detection in time series of optical and SAR images,

Rambour, C., Audebert, N., Koeniguer, E., Le Saux, B., Crucianu, M., and Datcu, M., “Flood detection in time series of optical and SAR images,” in [The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences],XLIII-B2-2020, 1343–1346 (2020)

2020

[5] [5]

Deep Residual Learning for Image Recognition

He, K., Zhang, X., Ren, S., and Sun, J., “Deep residual learning for image recognition,” CoRRabs/1512.03385(2015)

work page internal anchor Pith review Pith/arXiv arXiv 2015

[6] [6]

Learning phrase representations using RNN encoder–decoder for statistical machine translation,

Cho, K., van Merrienboer, B., Gulcehre, C., Bahdanau, D., Bougares, F., Schwenk, H., and Bengio, Y., “Learning phrase representations using RNN encoder–decoder for statistical machine translation,” (2014)

2014

[7] [7]

Navigating spatial insights: Comparative exploration of deep learning algorithms for flood detection using remote sensing data,

Mittal, B., Vanzara, J., and Sajidha, S. A., “Navigating spatial insights: Comparative exploration of deep learning algorithms for flood detection using remote sensing data,” in [2024 IEEE International Confer- ence on Interdisciplinary Approaches in Technology and Management for Social Innovation (IATMSI)], 1–6 (2024)

2024

[8] [8]

Vision transformer for flood detection using satellite images from Sentinel-1 and Sentinel-2,

Chamatidis, I., Istrati, D., and Lagaros, N. D., “Vision transformer for flood detection using satellite images from Sentinel-1 and Sentinel-2,”Water16(12), 1670 (2024)

2024

[9] [9]

Topological methods in machine learning: A tutorial for practitioners,

Coskunuzer, B. and Akcora, C. G., “Topological methods in machine learning: A tutorial for practitioners,” (2024)

2024

[10] [10]

PHG-Net: Persistent homology guided medical image classification,

Peng, Y., Wang, H., Sonka, M., and Chen, D. Z., “PHG-Net: Persistent homology guided medical image classification,” in [Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision (WACV)], 7583–7592 (2024)

2024

[11] [11]

Image classification using combination of topological features and neural networks,

Lima, M. D. P., Giraldi, G. A., and Miranda Junior, G. F., “Image classification using combination of topological features and neural networks,” (2023)

2023

[12] [12]

Improving remote sensing classification using topological data analysis and convolutional neural networks,

Sharma, A., “Improving remote sensing classification using topological data analysis and convolutional neural networks,” (2025)

2025

[13] [13]

The multimedia satellite task at MediaEval 2019,

Bischke, B., Helber, P., Brugman, S., Basar, E., Zhao, Z., Larson, M., and Pogorelov, K., “The multimedia satellite task at MediaEval 2019,” in [MediaEval Benchmarking Initiative for Multimedia Evaluation], (2019)

2019

[14] [14]

Cubical ripser: Software for computing persistent homology of image and volume data,

Kaji, S., Sudo, T., and Ahara, K., “Cubical ripser: Software for computing persistent homology of image and volume data,”CoRRabs/2005.12692(2020)

work page arXiv 2005

[15] [15]

Stability of persistence diagrams,

Cohen-Steiner, D., Edelsbrunner, H., and Harer, J., “Stability of persistence diagrams,”Discrete & Com- putational Geometry37(1), 103–120 (2007)

2007

[16] [16]

NDWI—a normalized difference water index for remote sensing of vegetation liquid water from space,

Gao, B.-C., “NDWI—a normalized difference water index for remote sensing of vegetation liquid water from space,”Remote Sensing of Environment58(3), 257–266 (1996)

1996

[17] [17]

Rasterio: Geospatial raster I/O for Python programmers,

Gillies, S. et al., “Rasterio: Geospatial raster I/O for Python programmers,” (2013–)

2013

[18] [18]

Statistical topological data analysis using persistence landscapes,

Bubenik, P., “Statistical topological data analysis using persistence landscapes,”Journal of Machine Learn- ing Research16(3), 77–102 (2015)

2015

[19] [19]

Persistence images: A stable vector representation of persistent homology,

Adams, H., Emerson, T., Kirby, M., Neville, R., Peterson, C., Shipman, P., Chepushtanova, S., Hanson, E., Motta, F., and Ziegelmeier, L., “Persistence images: A stable vector representation of persistent homology,” Journal of Machine Learning Research18(8), 1–35 (2017)

2017

[20] [20]

A stable multi-scale kernel for topological machine learning,

Reininghaus, J., Huber, S., Bauer, U., and Kwitt, R., “A stable multi-scale kernel for topological machine learning,” in [Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR)], 4741–4748 (2015)

2015

[21] [21]

Persistence weighted gaussian kernel for topological data anal- ysis,

Kusano, G., Fukumizu, K., and Hiraoka, Y., “Persistence weighted gaussian kernel for topological data anal- ysis,” in [Proceedings of the 33rd International Conference on Machine Learning],Proceedings of Machine Learning Research48, 2004–2013, PMLR (2016)

2004

[22] [22]

Sliced wasserstein kernel for persistence diagrams,

Carri` ere, M., Cuturi, M., and Oudot, S., “Sliced wasserstein kernel for persistence diagrams,” in [Proceedings of the 34th International Conference on Machine Learning],Proceedings of Machine Learning Research, 664– 673, PMLR (2017)

2017

[23] [23]

PyTorch: An imperative style, high-performance deep learning library,

Paszke, A., Gross, S., Massa, F., Lerer, A., Bradbury, J., Chanan, G., Killeen, T., Lin, Z., Gimelshein, N., Antiga, L., Desmaison, A., K”opf, A., Yang, E., DeVito, Z., Raison, M., Tejani, A., Chilamkurthy, S., Steiner, B., Fang, L., Bai, J., and Chintala, S., “PyTorch: An imperative style, high-performance deep learning library,” in [Advances in Neural I...

2019

[24] [24]

ConfigILM: A general purpose configurable library for combining image and language models for visual question answering,

Hackel, L., Clasen, K. N., and Demir, B., “ConfigILM: A general purpose configurable library for combining image and language models for visual question answering,”SoftwareX26, 101731 (2024)

2024

[25] [25]

reBEN: Refined BigEarthNet dataset for remote sensing image analysis,

Clasen, K. N., Hackel, L., Burgert, T., Sumbul, G., Demir, B., and Markl, V., “reBEN: Refined BigEarthNet dataset for remote sensing image analysis,” (2024)

2024

[26] [26]

PersLay: A neural network layer for persistence diagrams and new graph topological signatures,

Carri` ere, M., Chazal, F., Ike, Y., Lacombe, T., Royer, M., and Umeda, Y., “PersLay: A neural network layer for persistence diagrams and new graph topological signatures,” in [Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics],Proceedings of Machine Learning Research 108, 2786–2796, PMLR (2020)

2020

[27] [27]

Learning representations of persistence barcodes,

Hofer, C. D., Kwitt, R., and Niethammer, M., “Learning representations of persistence barcodes,”Journal of Machine Learning Research20(126), 1–45 (2019)

2019