mlsanityData to 7 Oct 2026

An Introduction to Multiparameter Persistence

arXiv 2203.14289 ↗First posted 27 Mar 2022math.AT cs.CG math.RTcited by 15

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Abstract (arXiv)

In topological data analysis (TDA), one often studies the shape of data by constructing a filtered topological space, whose structure is then examined using persistent homology. However, a single filtered space often does not adequately capture the structure of interest in the data, and one is led to consider multiparameter persistence, which associates to the data a space equipped with a multiparameter filtration. Multiparameter persistence has become one of the most active areas of research within TDA, with exciting progress on several fronts. In this article, we introduce multiparameter persistence and survey some of this recent progress, with a focus on ideas likely to lead to practical applications in the near future.

Key facts. Cited by 15 papers in the map (data through 7 Oct 2026). First posted on arXiv 27 Mar 2022.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 3; 2023: 5; 2024: 2; 2025: 3; 2026: 2.

15 papers.

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  1. 2023Stable Vectorization of Multiparameter Persistent Homology using Signed Barcodes as Measurescited by 15
  2. 2023Euler Characteristic Tools For Topological Data Analysiscited by 13
  3. 2023Topological Data Analysis for Neural Network Analysis: A Comprehensive Surveycited by 9
  4. 2022Euler Characteristic Curves and Profiles: a stable shape invariant for big data problemscited by 8
  5. 2023A Framework for Fast and Stable Representations of Multiparameter Persistent Homology Decompositionscited by 6
  6. 2024EMP: Effective Multidimensional Persistence for Graph Representation Learningcited by 4
  7. 2025The Shape of Adversarial Influence: Characterizing LLM Latent Spaces with Persistent Homologycited by 4
  8. 2022Topological Data Analysis in Time Series: Temporal Filtration and Application to Single-Cell Genomicscited by 2
  9. 2023Topological Parallax: A Geometric Specification for Deep Perception Modelscited by 1
  10. 2024Mix-GENEO: A Flexible Filtration for Multiparameter Persistent Homology Detects Digital Imagescited by 1
  11. 2025CuMPerLay: Learning Cubical Multiparameter Persistence Vectorizationscited by 1
  12. 2025MCbiF: Measuring Topological Autocorrelation in Multiscale Clusterings via 2-Parameter Persistent Homologycited by 1
3 more
  1. 2026TopoPrune: Robust Data Pruning via Unified Latent Space Topologycited by 1
  2. 2022Convolutional Persistence Transformscited by 0
  3. 2026Heat Field Signatures: From Point Clouds to Smooth Geometrycited by 0