mlsanityData to 7 Oct 2026

Euler Characteristic Tools For Topological Data Analysis

arXiv 2303.14040 ↗First posted 24 Mar 2023cs.LG cs.CG math.ATcited by 13

Not on the map. Why?

Abstract (arXiv)

In this article, we study Euler characteristic techniques in topological data analysis. Pointwise computing the Euler characteristic of a family of simplicial complexes built from data gives rise to the so-called Euler characteristic profile. We show that this simple descriptor achieve state-of-the-art performance in supervised tasks at a very low computational cost. Inspired by signal analysis, we compute hybrid transforms of Euler characteristic profiles. These integral transforms mix Euler characteristic techniques with Lebesgue integration to provide highly efficient compressors of topological signals. As a consequence, they show remarkable performances in unsupervised settings. On the qualitative side, we provide numerous heuristics on the topological and geometric information captured by Euler profiles and their hybrid transforms. Finally, we prove stability results for these descriptors as well as asymptotic guarantees in random settings.

Key facts. Cited by 13 papers in the map (data through 7 Oct 2026). Builds on 27 of its 90 references that are in the map. First posted on arXiv 24 Mar 2023.

Builds on

27 of 90 references.

References · 27

  1. 2016XGBoost: A Scalable Tree Boosting Systemcited by 5,120
  2. 2018How Powerful are Graph Neural Networks?cited by 4,355
  3. 2015Persistence Images: A Stable Vector Representation of Persistent Homologycited by 235
  4. 2017An introduction to Topological Data Analysis: fundamental and practical aspects for data scientistscited by 171
  5. 2019PersLay: A Neural Network Layer for Persistence Diagrams and New Graph Topological Signaturescited by 125
  6. 2017Sliced Wasserstein Kernel for Persistence Diagramscited by 77
  7. 2018Persistence Fisher Kernel: A Riemannian Manifold Kernel for Persistence Diagramscited by 33
  8. 2018RetGK: Graph Kernels based on Return Probabilities of Random Walkscited by 32
  9. 2020Uncovering the Topology of Time-Varying fMRI Data using Cubical Persistencecited by 26
  10. 2019Persistent homology detects curvaturecited by 25
  11. 2021Persformer: A Transformer Architecture for Topological Machine Learningcited by 19
  12. 2015Interactive Visualization of 2-D Persistence Modulescited by 18
15 more
  1. 2018DTM-based Filtrationscited by 16
  2. 2022An Introduction to Multiparameter Persistencecited by 15
  3. 2019Embeddings of Persistence Diagrams into Hilbert Spacescited by 11
  4. 2020The Weighted Euler Curve Transform for Shape and Image Analysiscited by 10
  5. 2018On the Metric Distortion of Embedding Persistence Diagrams into separable Hilbert spacescited by 9
  6. 2021Euler Characteristic Surfacescited by 8
  7. 2022Euler Characteristic Curves and Profiles: a stable shape invariant for big data problemscited by 8
  8. 2017Persistence Diagrams with Linear Machine Learning Modelscited by 7
  9. 2020Capturing Dynamics of Time-Varying Data via Topologycited by 7
  10. 2021On the stability of multigraded Betti numbers and Hilbert functionscited by 5
  11. 2013The Morse theory of vCech and Delaunay complexescited by 4
  12. 2017Streaming Algorithm for Euler Characteristic Curves of Multidimensional Imagescited by 4
  13. 2021Hybrid transforms of constructible functionscited by 2
  14. 2022Randomness of Shapes and Statistical Inference on Shapes via the Smooth Euler Characteristic Transformcited by 2
  15. 2020Optimal transport between determinantal point processes and application to fast simulationcited by 1

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 3; 2024: 1; 2025: 3; 2026: 6.

13 papers.

Sort:

  1. 2023Stable Vectorization of Multiparameter Persistent Homology using Signed Barcodes as Measurescited by 15
  2. 2025Follow the Energy, Find the Path: Riemannian Metrics from Energy-Based Modelscited by 7
  3. 2023A Framework for Fast and Stable Representations of Multiparameter Persistent Homology Decompositionscited by 6
  4. 2026A Closed-Form Persistence-Landmark Pipeline for Certified Point-Cloud and Graph Classificationcited by 3
  5. 2026A Closed-Form Adaptive-Landmark Kernel for Certified Point-Cloud and Graph Classificationcited by 2
  6. 2023Discrete transforms of quantized persistence diagramscited by 1
  7. 2024Hypergraph clustering using Ricci curvature: an edge transport perspectivecited by 1
  8. 2025Quasi Zigzag Persistence: A Topological Framework for Analyzing Time-Varying Datacited by 1
  9. 2025EuLearn: A 3D database for learning Euler characteristicscited by 1
  10. 2026Certified Topological Interaction in Neural Representations: Exact Tests and the Statistic They Requirecited by 1
  11. 2026Topological Characterization of Churn Flow and Unsupervised Correction to the Wu Flow-Regime Map in Small-Diameter Vertical Pipescited by 0
  12. 2026Global and Local Topology-Aware Attention with Persistent Homology and Euler Biases for Time-Series Forecastingcited by 0
1 more
  1. 2026COMPLEX: A Closed-Form Certified Embedding of Multiparameter Persistence Modulescited by 0