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An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists

arXiv 1710.04019 ↗First posted 11 Oct 2017math.ST cs.LG math.ATcited by 171

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Abstract (arXiv)

Topological Data Analysis is a recent and fast growing field providing a set of new topological and geometric tools to infer relevant features for possibly complex data. This paper is a brief introduction, through a few selected topics, to basic fundamental and practical aspects of tda for non experts.

Key facts. Cited by 171 papers in the map (data through 7 Oct 2026). First posted on arXiv 11 Oct 2017.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 22; 2022: 15; 2023: 29; 2024: 36; 2025: 33; 2026: 36.

171 papers.

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  1. 2023Intrinsic Dimension Estimation for Robust Detection of AI-Generated Textscited by 111
  2. 2021A Survey on Bias in Visual Datasetscited by 84
  3. 2021Representation Topology Divergence: A Method for Comparing Neural Network Representationscited by 66
  4. 2021Artificial Text Detection via Examining the Topology of Attention Mapscited by 49
  5. 2021A Survey on Graph-Based Deep Learning for Computational Histopathologycited by 41
  6. 2021Category Theory in Machine Learningcited by 36
  7. 2023Financial Fraud Detection using Quantum Graph Neural Networkscited by 35
  8. 2023Topological Deep Learning: A Review of an Emerging Paradigmcited by 34
  9. 2021Manifold Topology Divergence: a Framework for Comparing Data Manifoldscited by 31
  10. 2023Learning Topology-Preserving Data Representationscited by 30
  11. 2021Topological Relational Learning on Graphscited by 27
  12. 2021Topological Uncertainty: Monitoring trained neural networks through persistence of activation graphscited by 20
38 more
  1. 2022Acceptability Judgements via Examining the Topology of Attention Mapscited by 19
  2. 2025Hallucination Detection in LLMs with Topological Divergence on Attention Graphscited by 18
  3. 2021Dist2Cycle: A Simplicial Neural Network for Homology Localizationcited by 16
  4. 2023Stable Vectorization of Multiparameter Persistent Homology using Signed Barcodes as Measurescited by 15
  5. 2026Learning Global Hypothesis Space for Enhancing Synergistic Reasoning Chaincited by 15
  6. 2022ToDD: Topological Compound Fingerprinting in Computer-Aided Drug Discoverycited by 13
  7. 2023Euler Characteristic Tools For Topological Data Analysiscited by 13
  8. 2023TopP&R: Robust Support Estimation Approach for Evaluating Fidelity and Diversity in Generative Modelscited by 13
  9. 2021Tangent Space and Dimension Estimation with the Wasserstein Distancecited by 10
  10. 2025Understanding Mode Connectivity via Parameter Space Symmetrycited by 10
  11. 2025Topological Signatures vs. Gradient Histograms: A Comparative Study for Medical Image Classificationcited by 10
  12. 2022Topological Data Analysis for Speech Processingcited by 9
  13. 2023Uncertainty Estimation of Transformers' Predictions via Topological Analysis of the Attention Matricescited by 8
  14. 2021Helmholtzian Eigenmap: Topological feature discovery & edge flow learning from point cloud datacited by 7
  15. 2022Enhancing cluster analysis via topological manifold learningcited by 6
  16. 2024Topology-Aware 3D Gaussian Splatting: Leveraging Persistent Homology for Optimized Structural Integritycited by 6
  17. 2023Persistent Homology Meets Object Unity: Object Recognition in Cluttercited by 5
  18. 2023On Characterizing the Evolution of Embedding Space of Neural Networks using Algebraic Topologycited by 5
  19. 2024Differentiable Mapper For Topological Optimization Of Data Representationcited by 5
  20. 2025Topology Optimization in Medical Image Segmentation with Fast Euler Characteristiccited by 5
  21. 2026Four-Stage Alzheimer's Disease Classification from MRI Using Topological Feature Extraction, Feature Selection, and Ensemble Learningcited by 5
  22. 2021Learning the Next Best View for 3D Point Clouds via Topological Featurescited by 4
  23. 2023Disentanglement Learning via Topologycited by 4
  24. 2023Prediction of Effective Elastic Moduli of Rocks using Graph Neural Networkscited by 4
  25. 2024EMP: Effective Multidimensional Persistence for Graph Representation Learningcited by 4
  26. 2024Deep Regression Representation Learning with Topologycited by 4
  27. 2024Point-Level Topological Representation Learning on Point Cloudscited by 4
  28. 2024MOUNTAINEER: Topology-Driven Visual Analytics for Comparing Local Explanationscited by 4
  29. 2025RTD-Lite: Scalable Topological Analysis for Comparing Weighted Graphs in Learning Taskscited by 4
  30. 2025Staying on the Manifold: Geometry-Aware Noise Injectioncited by 4
  31. 2021Persistence Homology of TEDtalk: Do Sentence Embeddings Have a Topological Shape?cited by 3
  32. 2022Classification of Stochastic Processes with Topological Data Analysiscited by 3
  33. 2022An Adversarial Robustness Perspective on the Topology of Neural Networkscited by 3
  34. 2023Singular value decomposition based matrix surgerycited by 3
  35. 2023Non-isotropic Persistent Homology: Leveraging the Metric Dependency of PHcited by 3
  36. 2023Persistent Homology for High-dimensional Data Based on Spectral Methodscited by 3
  37. 2024Cracking Factual Knowledge: A Comprehensive Analysis of Degenerate Knowledge Neurons in Large Language Modelscited by 3
  38. 2024A Survey of Features Used for Representing Black-box Single-objective Continuous Optimizationcited by 3

50 most cited of 171 All 171 (JSON)