mlsanityData to 7 Oct 2026

Persistence paths and signature features in topological data analysis

arXiv 1806.00381 ↗First posted 1 Jun 2018stat.ML cs.LG math.PRcited by 17

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Abstract (arXiv)

We introduce a new feature map for barcodes that arise in persistent homology computation. The main idea is to first realize each barcode as a path in a convenient vector space, and to then compute its path signature which takes values in the tensor algebra of that vector space. The composition of these two operations - barcode to path, path to tensor series - results in a feature map that has several desirable properties for statistical learning, such as universality and characteristicness, and achieves state-of-the-art results on common classification benchmarks.

Key facts. Cited by 17 papers in the map (data through 7 Oct 2026). First posted on arXiv 1 Jun 2018.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 4; 2022: 3; 2023: 4; 2024: 1; 2025: 3; 2026: 2.

17 papers.

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  1. 2021Evaluation Metrics for Graph Generative Models: Problems, Pitfalls, and Practical Solutionscited by 38
  2. 2023Topological Deep Learning: A Review of an Emerging Paradigmcited by 34
  3. 2023PCF-GAN: generating sequential data via the characteristic function of measures on the path spacecited by 13
  4. 2021Cycle Registration in Persistent Homology with Applications in Topological Bootstrapcited by 8
  5. 2022Approximating Persistent Homology for Large Datasetscited by 8
  6. 2022Euler Characteristic Curves and Profiles: a stable shape invariant for big data problemscited by 8
  7. 2023The Signature Kernelcited by 8
  8. 2021Feature Engineering with Regularity Structurescited by 7
  9. 20222-d signature of images and texture classificationcited by 2
  10. 2023FRUITS: Feature Extraction Using Iterated Sums for Time Series Classificationcited by 1
  11. 2025Comparing the Effects of Persistence Barcodes Aggregation and Feature Concatenation on Medical Imagingcited by 1
  12. 2025Global universal approximation with Brownian signaturescited by 1
5 more
  1. 2021From augmented microscopy to the topological transformer: a new approach in cell image analysis for Alzheimer's researchcited by 0
  2. 2024A Vectorization Method Induced By Maximal Margin Classification For Persistent Diagramscited by 0
  3. 2025A Novel Patch-Based TDA Approach for Computed Tomography Imagingcited by 0
  4. 2026Global universality via discrete-time signaturescited by 0
  5. 2026Voronoi Histograms for Adaptive Vectorization of Expected Persistence Diagramscited by 0