DTM-based Filtrations, Topological Data Analysis, pp.33-66, 2020. ,
URL : https://hal.archives-ouvertes.fr/hal-02093445
Persistence images: A stable vector representation of persistent homology, The Journal of Machine Learning Research, vol.18, issue.1, pp.218-252, 2017. ,
Persistence-sensitive simplification of functions on surfaces in linear time, TOPOINVIS, vol.9, pp.23-24, 2009. ,
Geometric and topological inference, vol.57, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01615863
Topology-aware surface reconstruction for point clouds, Computer Graphics Forum, vol.39, pp.197-207, 2020. ,
Statistical topological data analysis using persistence landscapes, The Journal of Machine Learning Research, vol.16, issue.1, pp.77-102, 2015. ,
A topological loss function for deep-learning based image segmentation using persistent homology, IEEE Transactions on Pattern Analysis and Machine Intelligence, 2020. ,
Perslay: A neural network layer for persistence diagrams and new graph topological signatures, International Conference on Artificial Intelligence and Statistics, pp.2786-2796, 2020. ,
The density of expected persistence diagrams and its kernel based estimation, 34th International Symposium on Computational Geometry, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-01716181
, Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik, 2018.
The structure and stability of persistence modules, SpringerBriefs in Mathematics, 2016. ,
URL : https://hal.archives-ouvertes.fr/hal-01107617
Subsampling methods for persistent homology, International Conference on Machine Learning, pp.2143-2151, 2015. ,
URL : https://hal.archives-ouvertes.fr/hal-01073073
Topological approaches to deep learning, Topological Data Analysis, pp.119-146, 2020. ,
A topological regularizer for classifiers via persistent homology, The 22nd International Conference on Artificial Intelligence and Statistics, pp.2573-2582, 2019. ,
An introduction to o-minimal geometry, 2000. ,
Extending persistence using Poincaré and Lefschetz duality, Foundations of Computational Mathematics, vol.9, issue.1, pp.79-103, 2009. ,
Lipschitz functions have L p -stable persistence, Foundations of computational mathematics, vol.10, issue.2, pp.127-139, 2010. ,
Vines and vineyards by updating persistence in linear time, 22nd Annual Symposium on Computational Geometry, pp.119-126, 2006. ,
Stochastic subgradient method converges on tame functions, Found. Comput. Math, vol.20, issue.1, pp.119-154, 2020. ,
Understanding the topology and the geometry of the persistence diagram space via optimal partial transport, 2019. ,
Topological data analysis for arrhythmia detection through modular neural networks, Canadian Conference on Artificial Intelligence, pp.177-188, 2020. ,
URL : https://hal.archives-ouvertes.fr/hal-02155849
Computational topology: an introduction, 2010. ,
Exposition and interpretation of the topology of neural networks, 18th IEEE International Conference On Machine Learning And Applications (ICMLA), pp.1069-1076, 2019. ,
Continuation of point clouds via persistence diagrams, Physica D: Nonlinear Phenomena, vol.334, pp.118-132, 2016. ,
A topology layer for machine learning, International Conference on Artificial Intelligence and Statistics, pp.1553-1563, 2020. ,
Connectivity-optimized representation learning via persistent homology, International Conference on Machine Learning, pp.2751-2760, 2019. ,
Deep learning with topological signatures, Advances in Neural Information Processing Systems, pp.1634-1644, 2017. ,
Efficient topological layer based on persistent landscapes, NeurIPS 2020, p.2020 ,
A framework for differential calculus on persistence barcodes, 2019. ,
URL : https://hal.archives-ouvertes.fr/hal-02304300
The gudhi library: Simplicial complexes and persistent homology, International Congress on Mathematical Software, pp.167-174, 2014. ,
URL : https://hal.archives-ouvertes.fr/hal-01108461
, , 2019.
Topological function optimization for continuous shape matching, Computer Graphics Forum, vol.37, pp.13-25, 2018. ,
URL : https://hal.archives-ouvertes.fr/hal-02953321
, Neural persistence: A complexity measure for deep neural networks using algebraic topology, 2018.
A fast and robust method for global topological functional optimization, 2020. ,
Time series classification via topological data analysis, Information and Media Technologies, vol.12, pp.228-239, 2017. ,
Model completeness results for expansions of the ordered field of real numbers by restricted pfaffian functions and the exponential function, Journal of the American Mathematical Society, vol.9, issue.4, pp.1051-1094, 1996. ,
Topogan: A topology-aware generative adversarial network, European Conference on Computer Vision(ECCV), p.2020 ,
Computing persistent homology, Discrete & Computational Geometry, vol.33, issue.2, pp.249-274, 2005. ,