Publications

Books

  • F. Chazal, V. de Silva, M. Glisse, S. Oudot (2016), The Structure and Stability of Persistence Modules. To appear as a Monograph in SpringerBriefs, 2016.
  • F. Chazal (2016), High-Dimensional Topological Data Analysis. Book chapter to appear in the 3rd edition of the Handbook of Discrete and Computational Geometry
  • Steve Oudot (2015), Persistence Theory: From Quiver Representations to Data Analysis. AMS Mathematical Surveys and Monographs, volume 209. Bookstore.

Articles

  • F. Chazal, P. Massart, B. Michel (2016), Rates of Convergence for Robust Geometric Inference. To appear in Electronic Journal of Statistics, 2016.
    • J.D. Boissonnat, D. Mazauric (2016), On the complexity of the representation of simplicial complexes by trees. Theoretical Computer Science.
      • E. Aamari, C. Levrard (2016), Stability and Minimax Optimality of Tangential Delaunay Complexes for Manifold Reconstruction. ArXiv
        • C. Levrard (2016), Sparse Oracle Inequalities for Variable Selection via Regularized Quantization. To appear in Bernoulli.
          • J. Cochoy and S. Oudot (2016), Decomposition of exact pfd persistence bimodules. ArXiv
          • M. Carriere et S. Oudot (2016), Structure and Stability of the 1-Dimensional Mapper. To appear in Computer Graphics Forum 28(5), 2016 (Proceedings of SGP 2016).
          • V. Ganapathi-Subramanian, B. Thibert, M. Ovsjanikov, L. Guibas (2016), Stable Region Correspondences Between Non-Isometric Shapes. To appear in Computer Graphics Forum 28(5), 2016 (Proceedings of SGP 2016).
          • J. Kitagawa, Q. Mérigot, B. Thibert (2016), Convergence of a Newton algorithm for semi-discrete optimal transport. ArXiv
          • T. Bonis, M. Ovsjanikov, S. Oudot, F. Chazal (2016), 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 (2016), The observable structure of persistence modules, to appear in Homology, Homotopy and Applications, 2016.
          • M. Buchet, F. Chazal, S. Y. Oudot and D. R. Sheehy (2016), Efficient and Robust Persistent Homology for Measures. To appear in Computational Geometry: Theory and Applications, 2016.
          • F. Chazal, P. Massart, B. Michel (2015), Rates of Convergence for Robust Geometric Inference. ArXiv
          • Boissonnat, Jean-Daniel and C. S. , Karthik and Tavenas, Sébastien (2015), Building Efficient and Compact Data Structures for Simplicial Complexes. International Symposium on Computational Geometry 2015.
            • C. Levrard (2015), Non-asymptotic bounds for vector quantization. The Annals of Statistics.
              • T. Bonis (2015), Stable measures and Stein's method: rates in the Central Limit Theorem and diffusion approximation. ArXiv
              • M. Carriere and S. Y. Oudot (2015), Structure and Stability of the 1-Dimensional Mapper. ArXiv
              • M. Carriere and S. Y. Oudot and M. Ovsjanikov (2015), Stable Topological Signatures for Points on 3D Shapes. Proc. Sympos. on Geometry Processing, 2015. HAL
              • J-O Lachaud, B. Thibert (2015), Properties of Gauss digitized shapes and digital surface integration. Journal of Mathematical Imaging and Vision, accepted. HAL
              • L. Cuel, J-O Lachaud, Q. Merigot, B. Thibert (2015), Robust Geometry Estimation using the Generalized Voronoi Covariance Measure. SIAM Journal on Imaging Sciences (SIIMS), Vol. 8, No. 2. pp. 1293-1314, 2015. HAL
              • P. Machado Manhães de Castro, Q. Mérigot, B. Thibert (2015), Far-field reflector problem and intersection of paraboloids,Numerische Mathematik, accepted. HAL
              • Boissonnat, J. D., & Maria, C. (2014), The simplex tree: An efficient data structure for general simplicial complexes. Algorithmica, 70(3), 406-427. HAL
              • Boissonnat, J. D., & Maria, C. (2014), Computing persistent homology with various coefficient fields in a single pass. In Algorithms-ESA 2014 (pp. 185-196). Springer Berlin Heidelberg. HAL
              • Maria, C., Boissonnat, J. D., Glisse, M., & Yvinec, M. (2014), The Gudhi library: Simplicial complexes and persistent homology. In Mathematical Software–ICMS 2014 (pp. 167-174). Springer Berlin Heidelberg. HAL
              • Boissonnat, J. D., Dey, T. K., & Maria, C. (2013), The Compressed Annotation Matrix : an Efficient Data Structure for Computing Persistent Cohomology. In Algorithms–ESA 2013 (pp. 695-706). Springer Berlin Heidelberg. HAL
              • F. Chazal, B.T. Fasy, F. Lecci, A. Rinaldo and L. Wasserman, Stochastic Convergence of Persistence Landscapes and Silhouettes. To appear in Journal of Computational Geometry 2015 (conference version in SoCG 2014). Preprint
              • F. Chazal, R. Huang and 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. HAL
              • A. Fischer, On two extensions of the vector quantization scheme, Accepted for publication in Journal de la Société Française de Statistique, 2015. Preprint
              • J. Dedecker, A. Fischer and B. Michel (2014), Improved rates for Wasserstein deconvolution with ordinary smooth error in dimension one, Accepted for publication in EJS. HAL
              • L. Cuel, J-O Lachaud and B. Thibert, Voronoi-based geometry estimator for 3D digital surfaces, Proc. Symp. on Discrete Geometry for Computer Imagery, 2014. HAL
              • J. André, D. Attali, Q. Mérigot and B. Thibert, Far-field reflector problem under design constraints. International Journal of Computational Geometry & Applications (IJCGA), 25(2), June 2015. Download
              • Clément Maria and Steve Y. Oudot, Zigzag Persistence via Reflections and Transpositions. To appear in Proc. ACM-SIAM Symposium on Discrete Algorithms (SODA), January 2015. HAL
              • Steve Y. Oudot and Donald R. Sheehy, Zigzag Zoology: Rips Zigzags for Homology Inference Proc. 29th Annual Symposium on Computational Geometry, June 2013. Full version in J. Foundations of Computational Mathematics, September 2014 HAL
              • F. Chazal, W. Crawley-Boevey and V. de Silva, The observable structure of persistence modules Preprint
              • C. Li, M. Ovsjanikov and F. Chazal, Persistence-based Structural Recognition. In Proc. IEEE Conference on Computer Vision and Pattern Recognition (CVPR 2014) Preprint
              • F. Chazal, B.T. Fasy, F. Lecci, B. Michel, A. Rinaldo, and L. Wasserman (2015), Subsampling Methods for Persistent Homology. In proc. International Conference on Machine Learning (ICML 2015) Preprint
              • M. Buchet, F. Chazal, S. Y. Oudot and D. R. Sheehy, Efficient and Robust Persistent Homology for Measures. To appear in ACM-SIAM Symposium on Discrete Algorithms 2015 (SODA 2015) Preprint
              • M. Buchet and F. Chazal and T. Dey and F. Fan and S. Oudot and Y. Wang, Topological Analysis of Scalar Fields with Outliers. To appear in 31st International Symposium on Computational Geometry (SOCG 2015) Preprint
              • F. Chazal, B.T. Fasy, F. Lecci, B. Michel and A. Rinaldo, L. Wasserman, Robust Topological Inference: Distance To a Measure and Kernel Distance. Preprint
              • J. Dedecker and X. Fan, McDiarmid's martingale for a class of iterated random function. Preprint
              • D. Attali, U. Bauer, O. Devillers, M. Glisse, and A. Lieutier. Homological reconstruction and simplification in R3. In Computational Geometry: Theory and Applications (CGTA), 2014.
              • D. Attali and A. Lieutier. Geometry driven collapses for converting a Cech complex into a triangulation of a shape. Discrete and Computational Geometry, 54(4):798–825, 2015.Download
              • A. Fischer, Deux méthodes d’apprentissage non supervisé : synthèse sur la méthode des centres mobiles et présentation des courbes principales, accepté pour publication dans le Journal de la SFdS, rubrique "Etats de l'art", 2014.
              • L. Cuel, J-O Lachaud, Q. Mérigot, B. Thibert, Robust Normal Estimation using Order-k Voronoi Covariance, an extended abstract has been presented at European Workshop on Computational Geometry (EuroCG), 2014.
              • F. Chazal, J. Sun, Gromov-Hausdorff Approximation of Metric Spaces with Linear Structure, to appear in ACM Symposium on Computational Geometry 2014 (arxiv versionhttp://fr.arxiv.org/abs/1305.1172 ).
              • F. Chazal, M. Glisse, C. Labruère and B. Michel (2013), Optimal rates of convergence for persistence diagrams in Topological Data Analysis. ICML 2014. Preprint Journal version in Journal of Machine Learning Research (JMLR) 2016.
              • J. Dedecker and B. Michel (2013), Minimax rates of convergence for Wasserstein deconvolution with supersmooth errors in any dimension. Accepted for publication in JMVA. Preprint

               

Acknowledgement:

ANR project TopData ANR-13-BS01-0008