Frédéric Chazal

Directeur de Recherche, INRIA Saclay -- Île-de-France

Directeur de Recherche, INRIA Saclay -- Île-de-France
Head of the DataShape group
Scientific director of the DATAIA Institute
Holder of an ANR Chair in Artificial Intelligence TopAI: Topological Data Analysis for Machine Learning and AI
Address:


 Institut de Mathématique d’Orsay
Building 307, rue Michel Magat, Office 3J1
Faculté des Sciences d’Orsay, Université Paris-Saclay
F-91405 Orsay Cedex
France
email:frederic.chazal[at]inria.fr

Research interests

  • Topological and Geometric Data Analysis: statistical methods, inference and learning, AI, theory and applications
  • Topological persistence
  • Geometric inference and geometric learning
  • Computational Geometry, Geometry processing, and Solid Modeling
  • Geometry and Topology

PhD students (current and former)

Course notes

On-going industrial projects (TDA, and geometric approaches to Machine Learning and AI)
Fujitsu : Collaborative Research Project between Fujitsu and DataShape on Topological Data Analysis, Machine Learning and Artificial Intelligence.
Sysnav : Pedestrian activity recognition and movement analysis for medical studies.
Sysnav : ANR/DGA Challenge MALIN (MAitrise de la LOcalisation Indoor).
IFPEN : Collaborative Research Project between IFPEN and DataShape on Topological Data Analysis.

Recent publications (full list available here)
F. Chazal, B. Michel, W. Reise. Topological signatures of periodic-like signals. To appear in Bernoulli, 2024.   
F. Chazal, C. Levrard, M. Royer Topological Analysis for Detecting Anomalies (TADA) in Time Series. To appear in Journal on Machine Learning Research (JMLR), 2025.   
S. Gaucher, G. Blanchard, F. Chazal. Supervised Contamination Detection, with Flow Cytometry Application. arXiv:2404.06093, 2024.   
F. Hensel, C. Arnal, M. Carrière, T. Lacombe, H. Kurihara, Y. Ike, F. Chazal. MAGDiff: Covariate Data Set Shift Detection via Activation Graphs of Deep Neural Networks. To appear in Transactions on Machine Learning Research (TMLR), 2024.   
T. Bonis, F. Chazal, B. Michel, W. Reise. Topological phase estimation method for reparameterized periodic functions. To appear in Advances in Computational Mathematics, 2024.   
F. Chazal, L. Ferraris, P. Groisman, M. Jonckheere, F. Pascal, F. Sapienza. Choosing the parameter of the Fermat distance: navigating geometry and noise. To appear in Transactions on Machine Learning Research (TMLR), 2024.   
F. Chazal, B. Michel, W. Reise. Topological signatures of periodic-like signals. arXiv:2306.13453, 2023.   
T. de Surrel, F. Hensel, M. Carrière, T. Lacombe, Y. Ike, H. Kurihara, M. Glisse, F. Chazal RipsNet: a general architecture for fast and robust estimation of the persistent homology of point clouds. Topological, Algebraic and Geometric Learning Workshops 2022, Proc. Machine Learning Research, volume 196, 2022..   
Mathieu Carrière, Frédéric Chazal, Marc Glisse, Yuichi Ike, Hariprasad Kannan. Optimizing persistent homology based functions. In Proc. ICML 2021.   
Iniesta, R., Carr, E., Carriere, M., Yerolemou, N., Michel, B. and Chazal, F. Topological Data Analysis and its usefulness for precision medicine studies. In Statistics Operations and Research Transactions (SORT), 46(1), 115-136, 2022.   
Boissonnat, JD., Chazal, F., Michel, B. Topological Data Analysis. In: Günther, M., Schilders, W. (eds) Novel Mathematics Inspired by Industrial Challenges. Mathematics in Industry, vol 38. Springer, 2022.   
E. Carr, M. Carrière, B. Michel, F. Chazal, R. Iniesta. Identifying homogeneous subgroups of patients and important features: a topological machine learning approach. BMC Bioinformatics volume 22, Article number: 449 (2021).   
T. Lacombe, M. Carrière, F. Chazal, Y. Ike, M. Glisse, Y. Umeda. Topological Uncertainty: Monitoring trained neural networks through persistence of activation graphs}. Proc. IJCAI 2021.   
F. Chazal, C. Levrard, M. Royer. Optimal quantization of the mean measure and application to clustering of measures. In Electronic Journal of Statistics, 2021.   
F. Chazal, C. Levrard, Y. Ike, M. Royer, Y. Umeda. ATOL: Measure Vectorization for Automatic Topologically-Oriented Learning. AISTATS 2021.   
Kwangho Kim, Jisu Kim, Manzil Zaheer, Joon Sik Kim, Frederic Chazal, Larry Wasserman. Efficient Topological Layer based on Persistent Landscapes. NeurIPS 2020.   
M. Dindin, Y. Umeda, F. Chazal. Topological Data Analysis for Arrhythmia Detection through Modular Neural Networks. To appear in Proc. 33rd Canadian Conference on Artificial Intelligence, 2020.   
Jisu Kim, Jaehyeok Shin, Frederic Chazal, Alessandro Rinaldo and Larry Wasserman. Homotopy Reconstruction via the Cech Complex and the Rips Complex. To appear in Proc Symposium on Comp. Geom. 2020 (SoCG 2020).   
Q. Mérigot, A. Delalande, F. Chazal. Quantitative stability of optimal transport maps and linearization of the 2-wasserstein space. To appear in AISTATS 2020.   
M. Carriere, F. Chazal, Y. Ike, T. Lacombe, M. Royer, Y. Umeda, PersLay: A Simple and Versatile Neural Network Layer for Persistence Diagrams, preprint, April (initial version) and June (updated version) 2019. To appear in AISTATS 2020.   
B. Beaufils, F. Chazal, M. Grelet, B. Michel. Stride Detector from Ankle-Mounted Inertial Sensors for Pedestrian Navigation and Activity Recognition with Machine Learning Approaches. Sensors 2019, 19, 4491.   
B. Beaufils, F. Chazal, M. Grelet, B. Michel. Robust pedestrian trajectory reconstruction from inertial sensor. IPIN 2019 - 10th International Conference on Indoor Positioning and Indoor Navigation.   
H. Anai, F. Chazal, M. Glisse, Y. Ike, H. Inakoshi, R. Tinarrage, Y. Umeda, DTM-based filtrations, in proc Symp. of Computational Geometry 2019 (SoCG 2019). Extended version to appear in Abel Symposium, 2019.   
E. Aamari, J. Kim, F. Chazal, B. Michel, A. Rinaldo, L. Wasserman. Estimating the Reach of a Manifold, Electronic Journal of Statistics 2019, Vol. 13, No. 1, 1359-1399.   
B. Beaufils, F. Chazal, M. Grelet, B. Michel. Activity recognition from stride detection: a machine learning approach based on geometric patterns and trajectory reconstruction. IPIN 2018 - 9th International Conference on Indoor Positioning and Indoor Navigation.   
V. Divol, F. Chazal. The density of expected persistence diagrams and its kernel based estimation. To appear in Proc. 34th int. Symposium on Computational Geometry (SoCG 2018). Extended version to appear in Journal of Computational Geometry.   
J.-D. Boissonnat, F. Chazal, M. Yvinec. Geometric and Topological Inference. Cambridge Texts in Applied Mathematics, vol. 57, Cambridge University Press, 2018.   
F. Chazal, B. Michel. An introduction to Topological Data Analysis: fundamental and practical aspects for data scientists. Frontiers in AI, 2021.   
B. Beaufils, F. Chazal, M. Grelet, B. Michel. Stride detection for pedestrian trajectory reconstruction: a machine learning approach based on geometric patterns. To appear in Proc. of the Eighth International Conference on Indoor Positioning and Indoor Navigation 2017 (IPIN 2017).   
M. Ovsjanikov, E. Corman, M. Bronstein, E. Rodolà, M. Ben-Chen, L. Guibas, F. Chazal, A. Bronstein. Computing and Processing Correspondences with Functional Maps, Proc. SIGGRAPH Asia Courses 2016.   
R. Huang, F. Chazal, M. Ovsjanikov. On the Stability of Functional Maps and Shape Difference Operators. Computer Graphics Forum, 37 (1), 145--158, 2018.   
F. Chazal, D. Cohen-Steiner, A. Lieutier, Q. Mérigot, B. Thibert. Inference of curvature using tubular neighborhoods. in Modern Approaches to Discrete Curvature; Lecture Notes in Mathematics 2184, Springer, 2017.   
F. Chazal, B. T. Fasy, F. Lecci, B. Michel, A. Rinaldo, L. Wasserman. Robust Topological Inference: Distance To a Measure and Kernel Distance arXiv:1412.7197. In Journal of Machine Learning Research 18 (2018) 1-40   
F. Chazal, I. Giulini, B. Michel. Data driven estimation of Laplace-Beltrami operator}. The Thirtieth Annual Conference on Neural Information Processing Systems (NIPS 2016).   
F. Chazal, P. Massart, B. Michel. Rates of Convergence for Robust Geometric Inference. Electronic Journal of Statistics Volume 10, Number 2 (2016), 2243-2286.   
F. Chazal, High-Dimensional Topological Data Analysis. To appear in the 3rd edition of the Handbook of Discrete and Computational Geometry.
T. Bonis, M. Ovsjanikov, S. Oudot, F. Chazal. Persistence-based Pooling for Shape Pose Recognition. 6th International Workshop on Computational Topology in Image Context (CTIC 2016), June 2016, Marseille, France.
F. Chazal, W. Crawley-Boevey, V. de Silva. The observable structure of persistence modules, in Homology, Homotopy and Applications,vol. 18, 2, p.247-265 2016.
F. Chazal, V. de Silva, M. Glisse, S. Oudot. The Structure and Stability of Persistence Modules. Monograph published in SpringerBriefs in Mathematics, Springer, 2016.
F. Chazal, M. Glisse, C. Labruere, B. Michel. Convergence rates for persistence diagram estimation in Topological Data Analysis. In Journal of Machine Learning Research (JMLR), Vol. 16, p. 3603-3635, Dec. 2015 (extended version of a paper presented at ICML 2014).
F. Chazal, B.T. Fasy, F. Lecci, B. Michel, A. Rinaldo, L. Wasserman. Subsampling Methods for Persistent Homology. In proc. International Conference on Machine Learning (ICML 2015).   
F. Chazal, B. T. Fasy, F. Lecci, B. Michel, A. Rinaldo, L. Wasserman. Robust Topological Inference: Distance To a Measure and Kernel Distance arXiv:1412.7197   
M. Buchet and F. Chazal and T. Dey and F. Fan and S. Oudot and Y. Wang. Topological Analysis of Scalar Fields with Outliers. arXiv:1412.1680 [cs.CG]. To appear in 31st International Symposium on Computational Geometry (SOCG 2015).   
F. Chazal, R. Huang, J. Sun. Gromov-Hausdorff Approximation of Filament Structure Using Reeb-type Graph. To appear in Discrete and Computational Geometry (Extended version of the SoCG 2014 version with topological guarantees), 2015.   
O. Azencot, M. Ovsjanikov, F. Chazal, M. Ben-Chen. Discrete Derivatives of Vector Fields on Surfaces An Operator Approach. ACM Transactions on Graphics (TOG), Volume 34 Issue 3, April 2015, Article No. 29.   
F. Chazal, B.T. Fasy, F. Lecci, A. Rinaldo, L. Wasserman. Stochastic Convergence of Persistence Landscapes and Silhouettes. In proc. ACM Symposium of Computational Geometry 2014. - Full version to appear in Journal of Computational Geometry.   
F. Chazal, B. T. Fasy, F. Lecci, B. Michel, A. Rinaldo, L. Wasserman. Robust Topological Inference: Distance To a Measure and Kernel Distance arXiv:1412.7197   
M. Buchet and F. Chazal and S. Y. Oudot and D. R. Sheehy. Efficient and Robust Persistent Homology for Measures. In ACM-SIAM Symposium on Discrete Algorithms 2015 (SODA 2015). Full version available in arXiv:1306.0039 [cs.CG] and to appear in Computational Geometry: Theory and Applications, 2016.   
C. Li, M. Ovsjanikov, F. Chazal. Persistence-based Structural Recognition. In Proc. IEEE Conference on Computer Vision and Pattern Recognition (CVPR 2014).
F. Chazal, R. Huang, J. Sun. Gromov-Hausdorff Approximation of Filament Structure Using Reeb-type Graph. Extended version of the SoCG 2014 version with topological guarantees (submitted).   
F. Chazal, J. Sun. Gromov-Hausdorff Approximation of Filament Structure Using Reeb-type Graph. In proc. ACM Symposium of Computational Geometry 2014.   
R. Rustamov, M. Ovsjanikov, O. Azencot, M. Ben-Chen, F. Chazal, L. Guibas Map-Based Exploration of Intrinsic Shape Differences and Variability. In SIGGRAPH 2013.
O. Azencot, M. Ben-Chen, F. Chazal, M. Ovsjanikov. An Operator Approach to Tangent Vector Field Processing. In Computer Graphics Forum (proc. SGP 2013).
F. Chazal, V. de Silva. S. Oudot. Persistence Stability for Geometric Complexes. To appear in Geometriae Dedicata (online First, December 2013), see arXiv:1207.3885v1 [math.AT].   
F. Chazal, L. J. Guibas, S. Y. Oudot, P. Skraba. Persistence-Based Clustering in Riemannian Manifolds. Proc. 27th Annual ACM Symposium on Computational Geometry, pages 97-106, 2011. Full version in Journal of the ACM, volume 60, issue 6, article 41.