mlsanityData to 14 Oct 2026

A Kernel for Multi-Parameter Persistent Homology

arXiv 1809.10231 ↗First posted 26 Sep 2018cs.LG cs.CG math.ATcited by 13

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Abstract (arXiv)

Topological data analysis and its main method, persistent homology, provide a toolkit for computing topological information of high-dimensional and noisy data sets. Kernels for one-parameter persistent homology have been established to connect persistent homology with machine learning techniques. We contribute a kernel construction for multi-parameter persistence by integrating a one-parameter kernel weighted along straight lines. We prove that our kernel is stable and efficiently computable, which establishes a theoretical connection between topological data analysis and machine learning for multivariate data analysis.

Key facts. Cited by 13 papers in the map (data through 14 Oct 2026). First posted on arXiv 26 Sep 2018.

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Citing papers per year: 2021: 2; 2022: 0; 2023: 5; 2024: 4; 2025: 1; 2026: 1.

13 papers.

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  1. 2023Stable Vectorization of Multiparameter Persistent Homology using Signed Barcodes as Measurescited by 15
  2. 2023GRIL: A 2-parameter Persistence Based Vectorization for Machine Learningcited by 13
  3. 2024Graphcode: Learning from multiparameter persistent homology using graph neural networkscited by 8
  4. 2023A Framework for Fast and Stable Representations of Multiparameter Persistent Homology Decompositionscited by 7
  5. 2021Augmenting Molecular Deep Generative Models with Topological Data Analysis Representationscited by 6
  6. 2024D-GRIL: End-to-End Topological Learning with 2-parameter Persistencecited by 5
  7. 2024EMP: Effective Multidimensional Persistence for Graph Representation Learningcited by 4
  8. 2021A Multi-parameter Persistence Framework for Mathematical Morphologycited by 2
  9. 2024Time-Aware Knowledge Representations of Dynamic Objects with Multidimensional Persistencecited by 2
  10. 2023Stability for Inference with Persistent Homology Rank Functionscited by 1
  11. 2023A Topological Machine Learning Pipeline for Classificationcited by 1
  12. 2025Quasi Zigzag Persistence: A Topological Framework for Analyzing Time-Varying Datacited by 1
1 more
  1. 2026The sublevel Flood bifiltration: towards scalable 2-parameter persistent homologycited by 0