mlsanityData to 7 Oct 2026

Ripser: efficient computation of Vietoris-Rips persistence barcodes

arXiv 1908.02518 ↗First posted 7 Aug 2019math.AT cs.CG cs.MScited by 115

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Abstract (arXiv)

We present an algorithm for the computation of Vietoris-Rips persistence barcodes and describe its implementation in the software Ripser. The method relies on implicit representations of the coboundary operator and the filtration order of the simplices, avoiding the explicit construction and storage of the filtration coboundary matrix. Moreover, it makes use of apparent pairs, a simple but powerful method for constructing a discrete gradient field from a total order on the simplices of a simplicial complex, which is also of independent interest. Our implementation shows substantial improvements over previous software both in time and memory usage.

Key facts. Cited by 115 papers in the map (data through 7 Oct 2026). First posted on arXiv 7 Aug 2019.

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Citing papers per year: 2021: 13; 2022: 16; 2023: 18; 2024: 19; 2025: 23; 2026: 26.

115 papers.

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  1. 2023Intrinsic Dimension Estimation for Robust Detection of AI-Generated Textscited by 111
  2. 2023Dynamic Snake Convolution based on Topological Geometric Constraints for Tubular Structure Segmentationcited by 83
  3. 2021Intrinsic Dimension, Persistent Homology and Generalization in Neural Networkscited by 70
  4. 2021Z-GCNETs: Time Zigzags at Graph Convolutional Networks for Time Series Forecastingcited by 67
  5. 2024Position: Topological Deep Learning is the New Frontier for Relational Learningcited by 65
  6. 2021Artificial Text Detection via Examining the Topology of Attention Mapscited by 49
  7. 2022Topologically faithful image segmentation via induced matching of persistence barcodescited by 48
  8. 2021Topological Detection of Trojaned Neural Networkscited by 34
  9. 2021Manifold Topology Divergence: a Framework for Comparing Data Manifoldscited by 31
  10. 2022On the effectiveness of persistent homologycited by 20
  11. 2022Acceptability Judgements via Examining the Topology of Attention Mapscited by 19
  12. 2023On the Expressivity of Persistent Homology in Graph Learningcited by 18
38 more
  1. 2021Activation Landscapes as a Topological Summary of Neural Network Performancecited by 17
  2. 2023Generalization Bounds with Data-dependent Fractal Dimensionscited by 15
  3. 2021Topological Attention for Time Series Forecastingcited by 14
  4. 2022Topology and geometry of data manifold in deep learningcited by 12
  5. 2022Discrete Morse Sandwich: Fast Computation of Persistence Diagrams for Scalar Data -- An Algorithm and A Benchmarkcited by 11
  6. 2022Topological Singularity Detection at Multiple Scalescited by 11
  7. 2021Characterizing and Measuring the Similarity of Neural Networks with Persistent Homologycited by 8
  8. 2021Attribute-based Explanations of Non-Linear Embeddings of High-Dimensional Datacited by 7
  9. 2022FibeRed: Fiberwise Dimensionality Reduction of Topologically Complex Data with Vector Bundlescited by 7
  10. 2024Efficient Betti Matching Enables Topology-Aware 3D Segmentation via Persistent Homologycited by 7
  11. 2024On Logical Extrapolation for Mazes with Recurrent and Implicit Networkscited by 7
  12. 2022A novel approach for wafer defect pattern classification based on topological data analysiscited by 6
  13. 2022Dialogue Term Extraction using Transfer Learning and Topological Data Analysiscited by 5
  14. 2023Stability and Machine Learning Applications of Persistent Homology Using the Delaunay-Rips Complexcited by 5
  15. 2023Deep neural networks architectures from the perspective of manifold learningcited by 5
  16. 2023Topological Node2vec: Enhanced Graph Embedding via Persistent Homologycited by 5
  17. 2023On Characterizing the Evolution of Embedding Space of Neural Networks using Algebraic Topologycited by 5
  18. 2024On the Limitations of Fractal Dimension as a Measure of Generalizationcited by 5
  19. 2026Think Shallow, Solve Deep: Controlling Recurrent Dynamics for Reliable Test-Time Depthcited by 5
  20. 2024The Shape of Word Embeddings: Quantifying Non-Isometry With Topological Data Analysiscited by 4
  21. 2024Deep Regression Representation Learning with Topologycited by 4
  22. 2024Point-Level Topological Representation Learning on Point Cloudscited by 4
  23. 2025The Shape of Adversarial Influence: Characterizing LLM Latent Spaces with Persistent Homologycited by 4
  24. 2025From Topology to Retrieval: Decoding Embedding Spaces with Unified Signaturescited by 4
  25. 2022Classification of Stochastic Processes with Topological Data Analysiscited by 3
  26. 2023Singular value decomposition based matrix surgerycited by 3
  27. 2023Non-isotropic Persistent Homology: Leveraging the Metric Dependency of PHcited by 3
  28. 2023Persistent Homology for High-dimensional Data Based on Spectral Methodscited by 3
  29. 2024Persistent de Rham-Hodge Laplacians in Eulerian representation for manifold topological learningcited by 3
  30. 2025Topological Autoencoders++: Fast and Accurate Cycle-Aware Dimensionality Reductioncited by 3
  31. 2025Time-Series Forecasting via Topological Information Supervised Framework with Efficient Topological Feature Learningcited by 3
  32. 2025On the geometry and topology of representations: the manifolds of modular additioncited by 3
  33. 2021Topological Information Retrieval with Dilation-Invariant Bottleneck Comparative Measurescited by 2
  34. 2021A Topological Data Analysis Based Classifiercited by 2
  35. 2022Topological Data Analysis in Time Series: Temporal Filtration and Application to Single-Cell Genomicscited by 2
  36. 2022Fast Topological Signal Identification and Persistent Cohomological Cycle Matchingcited by 2
  37. 2022Do Neural Networks Trained with Topological Features Learn Different Internal Representations?cited by 2
  38. 2023Detecting out-of-distribution text using topological features of transformer-based language modelscited by 2

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