mlsanityData to 13 Oct 2026

Graph Filtration Learning

arXiv 1905.10996 ↗First posted 27 May 2019cs.LG math.AT stat.MLcited by 68

Not on the map. Why?

Abstract (arXiv)

We propose an approach to learning with graph-structured data in the problem domain of graph classification. In particular, we present a novel type of readout operation to aggregate node features into a graph-level representation. To this end, we leverage persistent homology computed via a real-valued, learnable, filter function. We establish the theoretical foundation for differentiating through the persistent homology computation. Empirically, we show that this type of readout operation compares favorably to previous techniques, especially when the graph connectivity structure is informative for the learning problem.

Key facts. Cited by 68 papers in the map (data through 13 Oct 2026). First posted on arXiv 27 May 2019.

Builds on

No reference list yet.

Built on by

Cited by year (2026 to 13 Oct)

Citing papers per year: 2021: 15; 2022: 9; 2023: 11; 2024: 16; 2025: 10; 2026: 7.

68 papers.

Sort:

By area:

  1. 2021Topological Graph Neural Networkscited by 86
  2. 2021Graph Representation Learning in Biomedicinecited by 80
  3. 2024Position: Topological Deep Learning is the New Frontier for Relational Learningcited by 65
  4. 2021Trigger Hunting with a Topological Prior for Trojan Detectioncited by 39
  5. 2021Evaluation Metrics for Graph Generative Models: Problems, Pitfalls, and Practical Solutionscited by 38
  6. 2021Link Prediction with Persistent Homology: An Interactive Viewcited by 37
  7. 2021Topological Detection of Trojaned Neural Networkscited by 34
  8. 2023Topological Deep Learning: A Review of an Emerging Paradigmcited by 34
  9. 2021Cycle Representation Learning for Inductive Relation Predictioncited by 23
  10. 2023Going beyond persistent homology using persistent homologycited by 21
  11. 2023Curvature Filtrations for Graph Generative Model Evaluationcited by 18
  12. 2023On the Expressivity of Persistent Homology in Graph Learningcited by 18
38 more
  1. 2023Differentiable Euler Characteristic Transforms for Shape Classificationcited by 18
  2. 2022Neural Approximation of Graph Topological Featurescited by 16
  3. 2021Exploring the Geometry and Topology of Neural Network Loss Landscapescited by 14
  4. 2021Topological Attention for Time Series Forecastingcited by 14
  5. 2022Capturing Shape Information with Multi-Scale Topological Loss Terms for 3D Reconstructioncited by 14
  6. 2022ToDD: Topological Compound Fingerprinting in Computer-Aided Drug Discoverycited by 13
  7. 2023GRIL: A 2-parameter Persistence Based Vectorization for Machine Learningcited by 13
  8. 2024CLDG: Contrastive Learning on Dynamic Graphscited by 12
  9. 2023Topological Pooling on Graphscited by 9
  10. 2023PHG-Net: Persistent Homology Guided Medical Image Classificationcited by 9
  11. 2024Boosting Graph Pooling with Persistent Homologycited by 9
  12. 2023Adaptive Topological Feature via Persistent Homology: Filtration Learning for Point Cloudscited by 8
  13. 2021Learning Hyperbolic Representations of Topological Featurescited by 7
  14. 2024Diffeomorphic interpolation for efficient persistence-based topological optimizationcited by 6
  15. 2024Diss-l-ECT: Dissecting Graph Data with Local Euler Characteristic Transformscited by 6
  16. 2025Enhancing Graph Representation Learning with Localized Topological Featurescited by 6
  17. 2025The Flood Complex: Large-Scale Persistent Homology on Millions of Pointscited by 6
  18. 2021A Gradient Sampling Algorithm for Stratified Maps with Applications to Topological Data Analysiscited by 5
  19. 2021Fast Topological Clustering with Wasserstein Distancecited by 5
  20. 2024GEFL: Extended Filtration Learning for Graph Classificationcited by 5
  21. 2024D-GRIL: End-to-End Topological Learning with 2-parameter Persistencecited by 5
  22. 2022Topology-Preserving Dimensionality Reduction via Interleaving Optimizationcited by 3
  23. 2024CliquePH: Higher-Order Information for Graph Neural Networks through Persistent Homology on Clique Graphscited by 3
  24. 2021Optimisation of Spectral Wavelets for Persistence-based Graph Classificationcited by 2
  25. 2022On the Convergence of Optimizing Persistent-Homology-Based Lossescited by 2
  26. 2022Reduction Algorithms for Persistence Diagrams of Networks: CoralTDA and PrunITcited by 2
  27. 2024Time-Aware Knowledge Representations of Dynamic Objects with Multidimensional Persistencecited by 2
  28. 2024Dynamic Neural Dowker Network: Approximating Persistent Homology in Dynamic Directed Graphscited by 2
  29. 2024When Witnesses Defend: A Witness Graph Topological Layer for Adversarial Graph Learningcited by 2
  30. 2025Towards Understanding the Shape of Representations in Protein Language Modelscited by 2
  31. 2025Integrating Multi-scale and Multi-filtration Topological Features for Medical Image Classificationcited by 2
  32. 2023Filtration Surfaces for Dynamic Graph Classificationcited by 1
  33. 2023Algebraic Topological Networks via the Persistent Local Homology Sheafcited by 1
  34. 2024TopER: Topological Embeddings in Graph Representation Learningcited by 1
  35. 2025Quasi Zigzag Persistence: A Topological Framework for Analyzing Time-Varying Datacited by 1
  36. 2025Cover Learning for Large-Scale Topology Representationcited by 1
  37. 2025TopInG: Topologically Interpretable Graph Learning via Persistent Rationale Filtrationcited by 1
  38. 2026TopoFormer: Topology Meets Attention for Graph Learningcited by 1

50 most cited of 68 All 68 (JSON)